UCSD Physics 12

Work and EnergyWork and Energy

The physical description of energyThe physical description of energy

UCSD Physics 12

Spring 2013 2

Energy the capacity to do workEnergy the capacity to do work

bull This notion makes sense even in a colloquial This notion makes sense even in a colloquial contextcontextndash hard to get work done when yoursquore wiped out (low on

energy)

ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energy much But we can make this definition of energy much more precise by specifying exactly what we mean more precise by specifying exactly what we mean by by workwork

UCSD Physics 12

Spring 2013 3

Work more than just unpleasant tasksWork more than just unpleasant tasks

bull In physics the definition of work is the In physics the definition of work is the application of a application of a force through a distanceforce through a distance

W = FW = Fdd

bull WW is the is the work work donedonebull FF is the is the forceforce applied appliedbull dd is the is the distancedistance through which the force acts through which the force actsbull Only the force that acts in the direction of motion Only the force that acts in the direction of motion

counts towards workcounts towards work

UCSD Physics 12

Spring 2013 4

Okay what is Force thenOkay what is Force then

bull Force is a pushingpulling agentForce is a pushingpulling agent

bull ExamplesExamplesndash gravity exerts a downward force on you

ndash the floor exerts an upward force on a ball during its bounce

ndash a car seat exerts a forward force on your body when you accelerate forward from a stop

ndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)

ndash you exert a sideways force on a couch that you slide across the floor

ndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a string that yoursquore twirling over your head

ndash the expanding gas in your carrsquos cylinder exerts a force against the piston

UCSD Physics 12

Spring 2013 5

Forces have DirectionForces have Directionbull In all the previous examples force had a direction In all the previous examples force had a direction

associated with itassociated with itbull If multiple forces act on an object they could If multiple forces act on an object they could

potentially add or cancel depending on directionpotentially add or cancel depending on direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 2

Energy the capacity to do workEnergy the capacity to do work

bull This notion makes sense even in a colloquial This notion makes sense even in a colloquial contextcontextndash hard to get work done when yoursquore wiped out (low on

energy)

ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energy much But we can make this definition of energy much more precise by specifying exactly what we mean more precise by specifying exactly what we mean by by workwork

UCSD Physics 12

Spring 2013 3

Work more than just unpleasant tasksWork more than just unpleasant tasks

bull In physics the definition of work is the In physics the definition of work is the application of a application of a force through a distanceforce through a distance

W = FW = Fdd

bull WW is the is the work work donedonebull FF is the is the forceforce applied appliedbull dd is the is the distancedistance through which the force acts through which the force actsbull Only the force that acts in the direction of motion Only the force that acts in the direction of motion

counts towards workcounts towards work

UCSD Physics 12

Spring 2013 4

Okay what is Force thenOkay what is Force then

bull Force is a pushingpulling agentForce is a pushingpulling agent

bull ExamplesExamplesndash gravity exerts a downward force on you

ndash the floor exerts an upward force on a ball during its bounce

ndash a car seat exerts a forward force on your body when you accelerate forward from a stop

ndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)

ndash you exert a sideways force on a couch that you slide across the floor

ndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a string that yoursquore twirling over your head

ndash the expanding gas in your carrsquos cylinder exerts a force against the piston

UCSD Physics 12

Spring 2013 5

Forces have DirectionForces have Directionbull In all the previous examples force had a direction In all the previous examples force had a direction

associated with itassociated with itbull If multiple forces act on an object they could If multiple forces act on an object they could

potentially add or cancel depending on directionpotentially add or cancel depending on direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 3

Work more than just unpleasant tasksWork more than just unpleasant tasks

bull In physics the definition of work is the In physics the definition of work is the application of a application of a force through a distanceforce through a distance

W = FW = Fdd

bull WW is the is the work work donedonebull FF is the is the forceforce applied appliedbull dd is the is the distancedistance through which the force acts through which the force actsbull Only the force that acts in the direction of motion Only the force that acts in the direction of motion

counts towards workcounts towards work

UCSD Physics 12

Spring 2013 4

Okay what is Force thenOkay what is Force then

bull Force is a pushingpulling agentForce is a pushingpulling agent

bull ExamplesExamplesndash gravity exerts a downward force on you

ndash the floor exerts an upward force on a ball during its bounce

ndash a car seat exerts a forward force on your body when you accelerate forward from a stop

ndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)

ndash you exert a sideways force on a couch that you slide across the floor

ndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a string that yoursquore twirling over your head

ndash the expanding gas in your carrsquos cylinder exerts a force against the piston

UCSD Physics 12

Spring 2013 5

Forces have DirectionForces have Directionbull In all the previous examples force had a direction In all the previous examples force had a direction

associated with itassociated with itbull If multiple forces act on an object they could If multiple forces act on an object they could

potentially add or cancel depending on directionpotentially add or cancel depending on direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 4

Okay what is Force thenOkay what is Force then

bull Force is a pushingpulling agentForce is a pushingpulling agent

bull ExamplesExamplesndash gravity exerts a downward force on you

ndash the floor exerts an upward force on a ball during its bounce

ndash a car seat exerts a forward force on your body when you accelerate forward from a stop

ndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)

ndash you exert a sideways force on a couch that you slide across the floor

ndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a string that yoursquore twirling over your head

ndash the expanding gas in your carrsquos cylinder exerts a force against the piston

UCSD Physics 12

Spring 2013 5

Forces have DirectionForces have Directionbull In all the previous examples force had a direction In all the previous examples force had a direction

associated with itassociated with itbull If multiple forces act on an object they could If multiple forces act on an object they could

potentially add or cancel depending on directionpotentially add or cancel depending on direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 5

Forces have DirectionForces have Directionbull In all the previous examples force had a direction In all the previous examples force had a direction

associated with itassociated with itbull If multiple forces act on an object they could If multiple forces act on an object they could

potentially add or cancel depending on directionpotentially add or cancel depending on direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 6

When net force is not zeroWhen net force is not zero

bull When an object experiences a non-zero net force When an object experiences a non-zero net force it it must must accelerateaccelerate

bull Newtonrsquos second lawNewtonrsquos second law

FF = = mmaa Force = mass times Force = mass times accelerationacceleration

bull The same force makes a small object accelerate The same force makes a small object accelerate more than it would a more massive objectmore than it would a more massive objectndash hit a golf ball and a bowling ball with a golf club and

see what happens

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 7

Yeah but what is acceleration exactlyYeah but what is acceleration exactly

bull This is getting to be like the ldquohole in the bucketrdquo This is getting to be like the ldquohole in the bucketrdquo song but wersquore almost therehellipsong but wersquore almost therehellip

bull Acceleration is Acceleration is anyany change in change in velocityvelocity (speed (speed andorandor direction of motion) direction of motion)

bull Measured as rate of change of velocityMeasured as rate of change of velocityndash velocity is expressed in meters per second (ms)

ndash acceleration is meters per second per second

ndash expressed as ms2 (meters per second-squared)

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 8

Putting it back together Units of EnergyPutting it back together Units of Energy

bull Force is a mass times an accelerationForce is a mass times an accelerationndash mass has units of kilograms

ndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distanceWork is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)

ndash One Joule is one Newton of force acting through one meter

ndash Imperial units of force and distance are pounds and feet so unit of energy is foot-pound which equals 136 J

bull Energy has the same units as work JoulesEnergy has the same units as work Joules

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 9

A Zoo of UnitsA Zoo of Units

bull Our Our main unitmain unit of energy will be the metric unit of the of energy will be the metric unit of the JouleJoule but many others exist but many others exist

bull The The ccalorie is 4184 Joulesalorie is 4184 Joulesndash raise 1 gram (cc) of water one degree Celsius

bull The The CCalorie (kilocalorie) is 4184 Jalorie (kilocalorie) is 4184 Jndash raise 1 kg (1 liter) of water one degree Celsius

bull The Btu (British thermal unit) is 1055 J (roughly 1 kJ)The Btu (British thermal unit) is 1055 J (roughly 1 kJ)ndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 JThe kilowatt-hour (kWh) is 3600000 Jndash one Watt (W) is one Joule per second

ndash a kWh is 1000 W for one hour (3600 seconds)

Q

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 10

A note on arithmetic of unitsA note on arithmetic of units

bull You should carry units in your calculations and You should carry units in your calculations and multiply and divide them as if they were numbersmultiply and divide them as if they were numbers

bull Example the force of air drag is given byExample the force of air drag is given by

FFdragdrag = = frac12cfrac12cDDAvAv22

bull cD is a dimensionless drag coefficient

is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in ms

units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) = kgmm22mm22

m3ss22

kgmm44

m3ss22= = kgmsms22 = Newtons = Newtons

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 11

Kinetic EnergyKinetic Energy

bull Kinetic Energy the energy of motionKinetic Energy the energy of motionbull Moving things carry energy in the amountMoving things carry energy in the amount

KEKE = = frac12frac12mvmv22

bull Note the Note the vv22 dependence dependencemdashmdashthis is whythis is whyndash a car at 60 mph is 4 times more dangerous than a car at

30 mphndash hurricane-force winds at 100 mph are much more

destructive (4 times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as

destructive as a thrown bullet even if you can throw it a tenth as fast as you could shoot it

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 12

Numerical examples of kinetic energyNumerical examples of kinetic energy

bull A baseball (mass is 0145 kg = 145 g) moving at A baseball (mass is 0145 kg = 145 g) moving at 30 ms (67 mph) has kinetic energy30 ms (67 mph) has kinetic energy

KE = frac12(0145 kg)(30 ms)2

= 6525 kgm2s2 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped A quarter (mass = 000567 kg = 567 g) flipped about four feet into the air has a speed on reaching about four feet into the air has a speed on reaching your hand of about 5 ms The kinetic energy isyour hand of about 5 ms The kinetic energy is

KE = frac12(000567 kg)(5 ms)2

= 007 kgm2s2 = 007 J

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 13

More numerical examplesMore numerical examples

bull A 1500 kg car moves down the freeway at 30 ms A 1500 kg car moves down the freeway at 30 ms (67 mph)(67 mph)

KE = frac12(1500 kg)(30 ms)2

= 675000 kgm2s2 = 675 kJ

bull A 2 kg (~44 lb) fish jumps out of the water with a A 2 kg (~44 lb) fish jumps out of the water with a speed of 1 ms (22 mph)speed of 1 ms (22 mph)

KE = KE = frac12frac12(2 kg)(2 kg)(1 ms)(1 ms)22

= 1 kgm2s2 = 1 J

2Q

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 14

Gravitational Potential EnergyGravitational Potential Energybull It takes It takes workwork to lift a mass against the pull (force) of to lift a mass against the pull (force) of

gravitygravitybull The force of gravity is The force of gravity is mmgg where where mm is the mass and is the mass and gg is is

the gravitational accelerationthe gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earthndash g 10 ms2 works well enough for this class

bull Lifting a height Lifting a height hh against the gravitational force requires against the gravitational force requires an energy input (work) ofan energy input (work) of

E = W = F E = W = F h = mghh = mghbull Rolling a boulder up a hill and perching it on the edge of a Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational cliff gives it gravitational potentialpotential energy that can be later energy that can be later released when the roadrunner is down belowreleased when the roadrunner is down below

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 15

bull When the boulder falls off the cliff it picks up When the boulder falls off the cliff it picks up speed and therefore gains kinetic energyspeed and therefore gains kinetic energy

bull Where does this energy come fromWhere does this energy come from

from the from the gravitational potential energygravitational potential energybull The higher the cliff the more kinetic energy the The higher the cliff the more kinetic energy the

boulder will have when it reaches the groundboulder will have when it reaches the ground

First Example of Energy ExchangeFirst Example of Energy Exchange

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 16

Examples of Gravitational Potential EnergyExamples of Gravitational Potential Energy

bull How much gravitational potential energy does a How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform70 kg high-diver have on the 10 meter platform

mgh = (70 kg)(10 ms2)(10 m)

= 7000 kgm2s2 = 7 kJ

bull How massive would a book have to be to have a How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two potential energy of 40 J sitting on a shelf two meters off the floormeters off the floor

mgh = m(10 ms2)(2 m) = 40 J

so m must be 2 kg

2Q

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 17

The Energy of HeatThe Energy of Heat

bull Hot things have more energy than their cold Hot things have more energy than their cold counterpartscounterparts

bull Heat is really just kinetic energy on microscopic Heat is really just kinetic energy on microscopic scales the vibration or otherwise fast motion of scales the vibration or otherwise fast motion of individual atomsmoleculesindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are random

bull Heat is frequently quantified by calories (or Btu)Heat is frequently quantified by calories (or Btu)ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 18

Energy of Heat continuedEnergy of Heat continued

bull Food Calories are with the ldquobigrdquo C or kilocalories Food Calories are with the ldquobigrdquo C or kilocalories (kcal)(kcal)

bull Since water has a density of one gram per cubic Since water has a density of one gram per cubic centimeter 1 cal heats 1 cc of water 1centimeter 1 cal heats 1 cc of water 1ordmC and ordmC and likewise 1 kcal (Calorie) heats one liter (1 kg) of likewise 1 kcal (Calorie) heats one liter (1 kg) of water 1ordmCwater 1ordmCndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the Example to heat a 2-liter bottle of Coke from the 55ordmC refrigerator temperature to 20ordmC room ordmC refrigerator temperature to 20ordmC room temperature requires 30 Calories or 1225 kJtemperature requires 30 Calories or 1225 kJ

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 19

Heat CapacityHeat Capacitybull Different materials have different Different materials have different capacitiescapacities for for

heatheatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)

bull Example to add 10Example to add 10ordmC to a room 3 meters on a side ordmC to a room 3 meters on a side (cubic) how much energy do we need(cubic) how much energy do we need

air density is 13 kgm3 and we have 27 m3 so 35 kg of air and we need 1000 J per kg per ordmC so we end up needing 350000 J (= 836 Cal)

2Q

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 20

PowerPower

bull Power is simply energy exchanged Power is simply energy exchanged per unit time or how fast you get per unit time or how fast you get work done (Watts = Joulessec) work done (Watts = Joulessec)

bull One horsepower = 745 WOne horsepower = 745 W

bull Perform 100 J of work in 1 s and Perform 100 J of work in 1 s and call it 100 Wcall it 100 W

bull Run upstairs raising your 70 kg Run upstairs raising your 70 kg (700 N) mass 3 m (2100 J) in 3 (700 N) mass 3 m (2100 J) in 3 seconds seconds 700 W output 700 W output

bull Shuttle puts out a few GW Shuttle puts out a few GW (gigawatts or 10(gigawatts or 1099 W) of power W) of power

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 21

Power ExamplesPower Examples

bull How much power does it take to lift 10 kg up 2 How much power does it take to lift 10 kg up 2 meters in 2 secondsmeters in 2 secondsmgh = (10 kg)(10 ms2)(2 m) = 200J

200 J in 2 seconds 100 Watts

bull If you want to heat the 3 m cubic room by 10If you want to heat the 3 m cubic room by 10ordmC ordmC with a 1000 W space heater how long will it takewith a 1000 W space heater how long will it take

We know from before that the room needs to have 360000 J added to it so at 1000 W = 1000 Js this will take 360 seconds or six minutes

But the walls need to be warmed up too so it will actually take longer (and depends on quality of insulation etc)

2Q

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 22

Getting to know the WattGetting to know the Watt

bull How much energy does a 100 W light bulb useHow much energy does a 100 W light bulb usendash what does 100 W mean

bull itrsquos a rate of energy expenditure

ndash does 100 W per second per minute etc make sensebull this would be an acceleration of energy use

ndash answer depends on time the light bulb is onbull 100 W bulb uses 100 Js or 6000 J per minute 360000 Jhr

bull Think of power as something measured by a speedometerThink of power as something measured by a speedometerndash a rate of usage

bull And energy as the odometer measurementAnd energy as the odometer measurementndash the amount used

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 23

Examples of Power in WattsExamples of Power in Watts

3 W

20 W

40 W (100 W incand equiv)

100 W

1000 W

1500 W1800 W

5000 W

heating lots of power

200 W

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 24

The kilowatt-hourThe kilowatt-hour

bull We will often see the kilowatt-hour (kWh) as a We will often see the kilowatt-hour (kWh) as a unit ofhellipunit ofhellip

bull helliphellipEnergyEnergybull 1 kWh is a power times a time 1 kWh is a power times a time energy energy

ndash 1000 W (kW) for one hourbull 1 hr = 3600 sec 1 kWh = 3600000 J = 36 MJ

ndash 1 W for 1000 hoursndash 100 W for 10 hoursndash 2000 W for 30 minutesndash 36 MW for one second

bull so a 100 W bulb left on for a day is 24 kWhso a 100 W bulb left on for a day is 24 kWh

Q

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Clip from todayrsquos paperClip from todayrsquos paper

Spring 2013 25

Throughout the Andes glaciers are now melting so rapidly that scientists have grown deeplyconcerned about water supplies for the people living there Glacial meltwater is essential forhelping Andean communities get through the dry season

In the short run the melting is producing an increase of water supplies and feeding populationgrowth in major cities of the Andes the experts said But as the glaciers continue shrinkingtrouble almost certainly looms

Douglas R Hardy a University of Massachusetts researcher who works in the region saidldquoHow much time do we have before 50 percent of Limarsquos or La Pazrsquos water resources are gonerdquo

(transient) itrsquos what we do

just like our jar doubling time questions

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online

UCSD Physics 12

Spring 2013 26

AssignmentsAssignments

bull Read Chapter 1 and Appendix in textbookRead Chapter 1 and Appendix in textbookbull Homework 1 due April 12 in classHomework 1 due April 12 in class

ndash Chapter 1 QampP 1 2 8 MC 2 3 4 5 7 8 11 14

ndash plus supplemental required problems posted online