PHY205H1F Summer Physics of Everyday Life

Class 3: Energy & Rotation• Energy• Power• Potential and Kinetic• Conservation of

Energy• Efficiency• Recycled Energy• Energy for Life• Sources of Energy

• Circular Motion• Rotational Inertia• Torque• Centre of Mass and

Centre of Gravity• Centripetal Force• Centrifugal Force• Angular Momentum

Work• involves force and distance.• is force distance.• in equation form: W

Two things occur whenever work is done:

• application of • of something by

that force Unit of work:

newton-meter (N·m) or ( )

Work can be positive, zero or negative

• When the force and the distance are in the same direction, you are helping the motion with the force, so the work done on the object is .

• The force is to the object + environment.

Fd

• Maybe this force is speeding the object up.

Work can be positive, zero or negative

• When the force and the distance are at right angles, you are not helping the motion with the force, so the work is .

• This force is the energy of the object.

Fd

• This force won’t speed the object up or slow it down.

Work can be positive, zero or negative

• When the force and distance are in opposite directions, you are hindering the motion with the force, so the work done on the object is

. • This force is the energy of the

object.

F d• Maybe this

force is slowing the object down.

• Justin is doing a bench press, and he slowly pushes the bar up a distance of 0.30 m while pushing upwards on the bar with a force of 200 N. The bar moves with a constant velocity during this time.

• During the upward push, how much work does Justin do on the bar?

A. 60 JB. 120 JC. 0 JD. -60 JE. -120 J

Discussion Question

• Justin is doing a bench press, and he slowly lowers the bar down a distance of 0.30 m while pushing upwards on the bar with a force of 200 N. The bar moves with a constant velocity during this time.

• During the downward lowering, how much work does Justin do on the bar?

A. 60 JB. 120 JC. 0 JD. -60 JE. -120 J

Discussion Question

• Justin is doing a bench press, and he slowly lowers the bar down a distance of 0.30 m while pushing upwards on the bar with a force of 200 N. He then pushes it up slowly the same distance of 0.30 m back to its starting position, also pushing upwards on the bar with a force of 200 N.

• During the complete downward and upward motion, how much total work does Justin do on the bar? A. 60 J

B. 120 JC. 0 JD. -60 JE. -120 J

Discussion Question

Power• Measure of how fast work

is done• In equation form:

Power = work done

time interval

Unit of power• joule per second, called the

watt after James Watt, developer of the steam engine• 1 joule/second 1 • 1 kilowatt 1000

Power

• 1 kWh is the amount of energy used by a power of over

• 1 kWh = 1000 J/s * 60 min/hour * 60 s/min• 1 kWh = Joules[Chart downloaded from http://www.ontario-hydro.com/index.php?page=current_rates ]

• The unit of power is the watt, which is defined as 1 watt = 1 W = 1 J/s

• Energy is measured by Ontario Hydro in kWh “kiloWatt hours”.

• Example: Your clothes dryer uses 5000 Watts and you need to run it for 1 hour to dry your clothes.

• If you run it during “on peak” time, such as between 7 and 11am on a weekday, the cost is 12 cents/kWh.

• If you run it during “off peak” on the weekend the price for Ontario Hydro electricity is 6 cents/kWh.

• How much money do you save per load by doing your laundry on the weekend?

Elastic Potential Energy

Stored energy held in readiness with a potential for doing workExamples: • A stretched bow has stored energy

that can do on an arrow.• A stretched rubber band of a slingshot

has stored energy and is capable of doing .

• Demonstration: A mousetrap that is “set” has elastic potential energy that is capable of killing the mouse!

Gravitational Potential EnergyPotential energy due to elevated position

Example: • coffee mug on the top

shelf• In equation form:

Potential energy mass acceleration due to gravity height

𝑈𝑔=¿

Gravitational Potential EnergyDemonstrationA rectangular solid such as a domino has more

gravitational potential energy when it is tipped up on its edge, because its centre of mass is higher

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The energy is added to the domino by the work you do in

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𝑈𝑔= h𝑚𝑔

Kinetic Energy• Energy of motion• Depends on the mass of the object and square of

its speed:

If object speed is doubled kinetic energy is quadrupled.

History Question

• Chapter 7 opens with a story about the physicist who first advocated the correct equation for kinetic energy. Who was this physicist?

A. Du ChâteletB. EinsteinC. GalileoD. LeibnizE. Newton

𝐾=12𝑚𝑣2

Work and Kinetic Energy• If an object starts from rest and there is a net

force doing work on it, the work done will be equal to the of the object.

• In equation form:

𝐹𝑑=12𝑚𝑣2

Work-Energy Theorem

Work-energy theorem• Gain or reduction of energy is the result of work.• In equation form: work change in kinetic

energy (W K).• Doubling speed of an object requires times

the work.

Work-Energy Theorem• Applies to decreasing speed:

– reducing the speed of an object or bringing it to a halt

Example: Applying the brakes to slow a moving car, work is done on it (the friction force supplied by the brakes distance).

The work done in bringing a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is

A. actually less.B. about the same.C. twice.D. None of the above.

Work-Energy TheoremCHECK YOUR NEIGHBOR

Chapter 7 big idea: “Conservation of Energy”

• A system of particles has a total energy, E.• If the system is isolated, meaning that there

is no work or heat being added or removed from the system, then:

• This means the energy is “conserved”; it doesn’t change over .

• This is also the first law of thermodynamics; “You can’t get something for nothing.”

Discussion Question on Conservation of Energy

• An object is flying through the air with nothing touching it.

• Neglect air resistance.• Is energy of the object conserved?A. YesB. No

v

Discussion Question

• A 1 kg object is dropped from rest a height of 3 m above the ground.

• Just before it hits the ground, what is its kinetic energy? [Neglect air resistance.]

A. 3 JB. 15 JC. 30 JD. 90 JE. 150 J v

Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then

A. energy is not conserved.B. 10 joules go to warming the bow. C. 10 joules go to warming the target.D. 10 joules are mysteriously missing.

A situation to ponder…CHECK YOUR NEIGHBOR

Machines

• (Force distance)input (force distance)output

Principles of a machine:

• Conservation of energy concept: input output

• Input force input distance Output force output

distance

Simplest machine:• Lever

– rotates on a point of support called the fulcrum

– allows force over a large distance and force over a short distance

Efficiency• Percentage of work put into a machine that is

converted into useful work output• In equation form:

Efficiency

Discussion Question

• When the useful energy output of a machine is 100 J, and total energy input is 200 J, what is the efficiency?

A. 25%B. 50%C. 75%D. 100%E. 200%

Recycled Energy• Re-employment of

energy that otherwise would be wasted.

• Edison used heat from his power plant in New York City to heat buildings.

• Typical power plants waste about of their energy to because they are built away from buildings and other places that use heat.

Sources of EnergyExample:• Photovoltaic cells

on rooftops catch the solar energy and convert it to electricity.

More energy from the Sun hits Earth in 1 hour than all of the energy consumed by humans in an entire year!

Sources of EnergyConcentrated energy

• Nuclear power– stored in uranium and plutonium– doesn’t pollute our atmosphere

– creates radioactive waste which, if stored near humans, can be toxic.

PHY205H1S Physics of Everyday Life

Chapter 8: Rotation

• Circular Motion• Rotational Inertia• Torque• Centre of Mass and

Centre of Gravity• Centripetal Force• Centrifugal Force• Angular Momentum

Circular Motion – Rotational Speed

• Rotational (angular) speed is the number of radians of angle per unit of time (symbol ).

Tangential speed Radial Distance Rotational Speed

• All parts of a rigid merry-go-round or turntable turn about the axis of rotation in the same amount of time.

• So, all parts have the same .

Discussion Question• The rotational speed on the outer edge of a

rotating roulette wheel isA. less than toward the centre.B. the same as toward the centre.C. greater than toward the centre.

Roulette wheel image from http://yourfamilyfinances.com/2012/09/01/payday-loans-debt-trap/ ]

• The tangential speed on the outer edge of a rotating roulette wheel is

A. less than toward the centre.B. the same as toward the centre.C. greater than toward the centre.

Roulette wheel image from http://yourfamilyfinances.com/2012/09/01/payday-loans-debt-trap/ ]

Discussion Question

Rolling Without Slipping Under normal driving

conditions, the portion of the rolling wheel that contacts the surface is stationary, not sliding

In this case the speed of the centre of the wheel is:

If your car is accelerating or decelerating or turning, it is of the road on the wheels that provides the net force which accelerates the car

where C = circumference [m] and T = Period [s]

𝑣=𝐶𝑇

Discussion Question• The circumference of the tires on your car is

0.9 m.• The onboard computer in your car measures

that your tires rotate 10 times per second.• What is the speed as displayed on your

speedometer?A. 0.09 m/sB. 0.11 m/sC. 0.9 m/sD. 1.1 m/sE. 9 m/s

Rotational Inertia• An object rotating about

an axis tends to remain rotating about the same axis at the same rotational speed unless interfered with by some external influence.

• The property of an object to resist changes in its rotational state of motion is called

(symbol I).

[Image downloaded Jan.10, 2013 from http://images.yourdictionary.com/grindstone ]

Rotational InertiaDepends upon:• of object.• of mass

around axis of rotation.– The greater the distance

between an object’s mass concentration and the axis, the greater the rotational inertia.

Rotational InertiaWhich pencil has the largest

rotational inertia?

A. The pencil rotated around an axis passing through it.

B. The pencil rotated around a vertical axis passing through centre.

C. The pencil rotated around vertical axis passing through the end.

Torque

• The tendency of a force to cause is called torque.

• Torque depends upon three factors:– of the force– The in which it acts– The point at which it is applied on the object

Image by John Zdralek, retrieved Jan.10 2013 from http://en.wikipedia.org/wiki/File:1980_c1980_Torque_wrench,_140ft-lbs_19.36m-kg,_nominally_14-20in,_.5in_socket_drive,_Craftsman_44641_WF,_Sears_dtl.jpg ]

TorqueConsider the common experience of pushing open a door. Shown is a top view of a door hinged on the left. Four pushing forces are shown, all of equal strength. Which of these will be most effective at opening the door?

A. F1

B. F2

C. F3

D. F4

Torque lever arm force

Torque• The equation for Torque is

• The is the perpendicular distance between the line along which the force is applied, and the rotation axis.

Suppose the girl on the left suddenly is handed a bag of apples weighing 50 N. Where should she sit order to balance, assuming the boy does not move?

A. 1 m from pivotB. 1.5 m from pivotC. 2 m from pivotD. 2.5 m from pivot

Rotational InertiaCHECK YOUR NEIGHBOR

• Centre of mass is the average position of all the that makes up the object.

• Centre of gravity (CG) is the average position of distribution. – Since weight and mass are proportional, centre of

gravity and centre of mass usually refer to the same point of an object.

Centripetal Acceleration

A car is traveling East at a constant speed of 100 km/hr. Without speeding up of slowing down, it is turning left, following the curve in the highway. What is the direction of the acceleration?

N

A.NorthB.EastC.North-EastD.North-WestE.None; the acceleration is zero.

E

S

W

Centripetal Force• Any force directed toward a fixed

is called a force.• Centripetal means “centre-seeking” or

“toward the centre.”

Example: To whirl a tin can at the end of a string, you pull the string toward the centre and exert a centripetal force to keep the can moving in a circle.

Centripetal Force• Depends upon

– mass of object, m.– tangential speed of the object, v.– radius of the circle, r.

• In equation form:

𝐹=❑❑

Suppose you double the speed at which you round a bend in the curve, by what factor must the centripetal force change to prevent you from skidding?

A. DoubleB. Four timesC. HalfD. One-quarter

Centripetal ForceCHECK YOUR NEIGHBOR

Centrifugal Force• Although centripetal force is centre directed, an

occupant inside a rotating system seems to experience an outward force.

• This apparent outward force is called force.

• Centrifugal means “centre-fleeing” or “away from the centre.”

[Image downloaded Jan.10 2013 from http://www.et.byu.edu/~wanderto/homealgaeproject/Harvesting%20Algae.html ]

Rotating Reference Frames• Centrifugal force in a

is a force in its own right – feels as real as any other force, e.g. gravity.

• Example:– The bug at the bottom of the can experiences

a pull toward the bottom of the can.

Angular Momentum• The “inertia of rotation” of rotating objects is

called angular momentum.– This is analogous to “inertia of motion”, which was

momentum.• Angular momentum

rotational inertia rotational velocity

– This is analogous toLinear momentum mass velocity

𝐿=¿

𝑝=𝑚𝑣

Conservation of Angular Momentum

The law of conservation of angular momentum states:If no external net torque acts on a rotating

system, the angular momentum of that system remains constant.

Analogous to the law of conservation of linear momentum:If no external force acts on a system, the total linear

momentum of that system remains constant.

Your professor is rotating at some rotational speed ω with some rotational inertia set partly by the fact that he is holding masses in his outstretched arms.

Suppose by pulling the weights inward, the rotational inertia of the professor reduces to half its original value. By what factor would his rotational speed change?

A. DoubleB. Three timesC. HalfD. One-quarter

Angular MomentumCHECK YOUR NEIGHBOR

Conservation of Angular MomentumExample:• When the professor pulls the weights

inward, his rotational speed !

Before Class 4 on Monday• Please read Chapters 13 and 14, or at least watch

the 20-minute pre-class video for class 4• Pre-class reading quiz on chapters 13 and 14 is due

Monday by 10:00am • Midterm Test in 1 week: Wednesday 1-3 in EX310 (last

name A-M), EX320 (last name N-Z)• Test will begin promptly at 1:10 and will be 1 hour and 50

minutes long.• Please bring a calculator, and, if you wish, a a 8.5x11” aid

sheet upon which you may write anything you wish on both sides

• Test will cover Hewitt chapters 2-5, 7, 8, 13 and 14, and will include some multiple choice and some short-answer