Fourth six weeks reviewFourth six weeks review

Frames of ReferenceFrames of Reference

Object or point from which motion is Object or point from which motion is determineddetermined

Most common isMost common is

EarthEarth Motion is a changeMotion is a change

in in positionposition relativerelative to to

a frame of referencea frame of reference

What is motion?What is motion? If you are standing in one place, and your If you are standing in one place, and your

friend walks by you, are you moving friend walks by you, are you moving relative to your friend?relative to your friend? Is your friend moving relative to you?Is your friend moving relative to you? Is either of you moving relative to the Is either of you moving relative to the

earth?earth?

Answer:Answer: You are moving relative to your friend, and your friend is You are moving relative to your friend, and your friend is

moving relative to you!moving relative to you! You (the Joker) are not moving relative to the earth, but You (the Joker) are not moving relative to the earth, but

your friend is. You are both moving relative to the sun!your friend is. You are both moving relative to the sun!Who is movingWho is movingrelative to therelative to thecomputercomputerscreen?screen?

SpeedSpeed

Speed = Distance ÷ TimeSpeed = Distance ÷ Time

D_ D_

S TS T

Example: A car travels 300km in 6 Example: A car travels 300km in 6 hours. What is the speed of the car?hours. What is the speed of the car?

Answer:Answer:

Speed = distance ÷ timeSpeed = distance ÷ time Speed = 300km ÷ 6 hoursSpeed = 300km ÷ 6 hours Speed = 50km/hrSpeed = 50km/hr

More practiceMore practice

1. How far can a plane travel if it flies 1. How far can a plane travel if it flies 800km/hr for 9 hours?800km/hr for 9 hours?

2. How long does it take a ship to go 500 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?km if it travels at a speed of 50km/hr?

AnswerAnswer

1. 1. DD SS T T

DD800800 9 9

800km 800km ▪ 9hrs = 7200km ▪ 9hrs = 7200km hrhr

AnswerAnswer

2. 2. DD SS T T 500 500 5050 T T

500km ÷ 500km ÷ 50km50km = 10 hrs = 10 hrs hrhr

VelocityVelocity

Speed in a given direction.Speed in a given direction.

What is the velocity of a boat that What is the velocity of a boat that travels from St. Peter to Mankato travels from St. Peter to Mankato (10 miles) in 15 minutes?(10 miles) in 15 minutes?

AnswerAnswer

Speed = distance ÷ timeSpeed = distance ÷ time Speed = 10 miles ÷ 15 Speed = 10 miles ÷ 15

minutesminutes Speed = 0.67 mi/minSpeed = 0.67 mi/min Velocity = 0.67 mi/min SouthVelocity = 0.67 mi/min South

Distance-time graphsDistance-time graphs

D (m)D (m) T (sec) T (sec)

00 00

55 77

10101414

15152121

Was your graph a straight Was your graph a straight line?line?

A A distance-time graphdistance-time graph which is which is a a straight linestraight line indicates indicates constant speedconstant speed..

In constant speed, the object In constant speed, the object does not speed up or slow does not speed up or slow down. The acceleration is zero.down. The acceleration is zero.

0 1 2 3 4 5

Was your graph a curve?Was your graph a curve?

A graph that A graph that curvescurves on a on a distance-time graphdistance-time graph shows shows that the object is that the object is acceleratingaccelerating

Distance-time graphsDistance-time graphs

Describe the motion of the object as Describe the motion of the object as shown in the shown in the

graph.graph.From 0-8 sec, constant speed:(25 m/sec);From 8-12 sec, no motion;From 12-16 sec, acceleration;From 16-20 sec, constant speed

What does your graph look What does your graph look like?like?

Constant speedConstant speed will be a will be a horizontal horizontal line on a speed time line on a speed time graph. graph.

If the speed If the speed decreasesdecreases, the line , the line will slant will slant downdown..

If the speed If the speed increasesincreases, the line , the line will slant will slant upup..

AccelerationAcceleration

Change in velocityChange in velocity Can be change in speed Can be change in speed oror direction direction

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T

∆ ∆VV aa tt

Acceleration problemAcceleration problem

A roller coaster’s velocity at A roller coaster’s velocity at the top of a hill is 10m/s. Two the top of a hill is 10m/s. Two seconds later it reaches the seconds later it reaches the bottom of the hill with a bottom of the hill with a velocity of 26m/s. What is velocity of 26m/s. What is the acceleration of the roller the acceleration of the roller coaster?coaster?

AnswerAnswer

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T a = a = 26m/s – 10m/s26m/s – 10m/s

2 s2 sa = a = 16m/s16m/s

2s2sa = 8m/s/s or 8m/sa = 8m/s/s or 8m/s22

More acceleration problemsMore acceleration problems

1. A car accelerates at a rate of 1. A car accelerates at a rate of 20mi/hr/s. How long does it take to 20mi/hr/s. How long does it take to reach a speed of 80 mi/hr?reach a speed of 80 mi/hr?

2. A car travels at 60 miles per hour 2. A car travels at 60 miles per hour around a curve. Is the car around a curve. Is the car accelerating?accelerating?

3. A car travels in a straight line at 3. A car travels in a straight line at 60mi/hr. Is the car accelerating?60mi/hr. Is the car accelerating?

Answers:Answers:

1. 1. ∆V ∆V 80mi/hr80mi/hr

a ta t 20mi/hr/s20mi/hr/s t t

4sec = t4sec = t

2. yes! Because it’s changing direction!2. yes! Because it’s changing direction!

3. no! It’s not changing speed or 3. no! It’s not changing speed or direction!direction!

DecelerationDeceleration

Negative accelerationNegative acceleration Example: A car slows from Example: A car slows from

60mi/hr to 20mi/hr in 4 60mi/hr to 20mi/hr in 4 seconds. What is its seconds. What is its acceleration?acceleration?

Answer:Answer:

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T Acceleration = Acceleration = Vf – ViVf – Vi

tt a = a = 20mi/hr – 60mi/hr20mi/hr – 60mi/hr

4 s4 sa = a = -40mi/hr-40mi/hr

4s4sa = -10mi/hr/sa = -10mi/hr/s

MomentumMomentum

Momentum = Mass x Momentum = Mass x VelocityVelocity

Which has more Which has more momentum: a 300lb football momentum: a 300lb football player moving at 5m/s or a player moving at 5m/s or a 200lb quarterback moving 200lb quarterback moving at 10m/s?at 10m/s?

Answer:Answer: Momentum of the 300lb player isMomentum of the 300lb player is

(300 lbs/2.2 lbs) x 5 m/s= 681.8 kg-(300 lbs/2.2 lbs) x 5 m/s= 681.8 kg-m/sm/s

Momentum of the quarterback isMomentum of the quarterback is (200lbs/2.2 lbs) x 10m/s = 909.1 kg-(200lbs/2.2 lbs) x 10m/s = 909.1 kg-

m/sm/s

The quarterback has a greater momentum!The quarterback has a greater momentum!

Inelastic collisionInelastic collision

Elastic collisionElastic collision

Two dimensional Two dimensional collisioncollision

Momentum problemsMomentum problems

2 cars are heading east, car A is 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 30mi/hr, car B is traveling 60mi/hr. Each car weighs traveling 60mi/hr. Each car weighs 2000lbs.2000lbs.What is the momentum of car A?What is the momentum of car A?What is the momentum of car B?What is the momentum of car B? If car B crashes into car A, what If car B crashes into car A, what is the total momentum?is the total momentum?

Answers:Answers: P=mvP=mv Car A’s momentum = 30mi/hr x Car A’s momentum = 30mi/hr x

(2000lbs/2.2lbs)(2000lbs/2.2lbs)

PPAA = 27272.73 kg-mi/hr east = 27272.73 kg-mi/hr east Car B’s momentum = 60mi/hr x Car B’s momentum = 60mi/hr x

(2000lbs/2.2lbs)(2000lbs/2.2lbs) PPBB = 54545.46 = 54545.46 kg-mi/hr eastkg-mi/hr east

Total momentum = PTotal momentum = PAA + P + PBB

= 27272.73 + 54545.46= 27272.73 + 54545.46

= 81818.19 kg-mi/hr east= 81818.19 kg-mi/hr east

Another momentum Another momentum problem!problem!

Car X is traveling 30mi/hr east, Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. car Y is traveling 60mi/hr west. Each car weighs 2000lbs.Each car weighs 2000lbs.What is the momentum of car X?What is the momentum of car X?What is the momentum of car Y?What is the momentum of car Y? If car X crashes into car Y, what If car X crashes into car Y, what is the total momentum?is the total momentum?

Answers:Answers: P=mvP=mv Car X’s momentum = 30mi/hr x Car X’s momentum = 30mi/hr x

(2000lbs/2.2 lbs)(2000lbs/2.2 lbs)

Px = 27272.73 kg-mi/hr eastPx = 27272.73 kg-mi/hr east Car Y’s momentum = 60mi/hr x Car Y’s momentum = 60mi/hr x

(2000lbs/2.2lbs)(2000lbs/2.2lbs)

PPYY = 54545.45 kg-mi/hr west = 54545.45 kg-mi/hr west Total momentum = PTotal momentum = PYY - P - PX X

= 54545.45-27272.73= 54545.45-27272.73

= 27272.72 kg-mi/hr west= 27272.72 kg-mi/hr west

FORCEFORCE = Any = Any pushpush or or pullpull which which causes something to causes something to movemove or or change its change its speedspeed or or directiondirection

What is a Force?What is a Force?

Forces can be Forces can be BALANCEDBALANCED or or UNBALANCEDUNBALANCED

Balanced forces are Balanced forces are equalequal in size in size and opposite in directionand opposite in direction

Unbalanced forces are Unbalanced forces are notnot equal equal in size and/or opposite in in size and/or opposite in direction. If the forces on an direction. If the forces on an object are UNBALANCED, we say object are UNBALANCED, we say a a NETNET force results. force results.

Amusement Park Forces

What is a Force?What is a Force?

First LawFirst Law: An object at : An object at restrest stays stays at rest or an object in motion, at rest or an object in motion, stays in motion (in the same stays in motion (in the same direction/at the same speed) direction/at the same speed) unless acted upon by an unless acted upon by an unbalanced unbalanced forceforce

Also called the Also called the law of inertialaw of inertia

Newtons’s 1Newtons’s 1stst Law and Law and YouYou

Don’t let this be you. Wear seat belts.Don’t let this be you. Wear seat belts.

Because of inertia, objects (including you) Because of inertia, objects (including you) resist changes in their motion. When the resist changes in their motion. When the car going 80 km/hour is stopped by the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 brick wall, your body keeps moving at 80 m/hour.m/hour.

Examples of Newton’s Examples of Newton’s 11stst LawLaw

Why then, do we observe Why then, do we observe every day objects in motion every day objects in motion slowing down and becoming slowing down and becoming motionless seemingly motionless seemingly without an outside force?without an outside force?

It’s a force we sometimes cannot see It’s a force we sometimes cannot see – friction.– friction.

Friction is a force Friction is a force that occurs when that occurs when 2 surfaces 2 surfaces oppose each oppose each other.other.

Types of frictionTypes of friction

Static-Static- Friction that acts on Friction that acts on something that is not movingsomething that is not moving

SlidingSliding- Force resulting when - Force resulting when pushing or pulling an object over pushing or pulling an object over a surface.a surface.

RollingRolling- Contact is reduced - Contact is reduced because of rollers or wheels or because of rollers or wheels or ball bearingsball bearings

FluidFluid- Resistance from a “liquid” - Resistance from a “liquid” or air.or air.

22ndnd Law Law

Second lawSecond law: The : The greater the greater the forceforce applied to an applied to an object, the more object, the more the object will the object will accelerateaccelerate. It takes . It takes more force to more force to accelerate an accelerate an object with a lot of object with a lot of mass than to mass than to accelerate accelerate something with something with very little mass.very little mass.

The player in black had more acceleration thus he hit with a

greater amount of force

22ndnd Law Law

When mass is in kilograms and When mass is in kilograms and acceleration is in m/s/s, the unit of acceleration is in m/s/s, the unit of force is in newtons (N).force is in newtons (N).

One newton is equal to the force One newton is equal to the force required to accelerate one kilogram required to accelerate one kilogram of mass at one meter/second/second.of mass at one meter/second/second.

22ndnd Law (F = m x a) Law (F = m x a) How much force is needed to accelerate a

1400 kilogram car 2 meters per second/per second?

Write the formulaWrite the formula F = m x a Fill in given numbers and unitsFill in given numbers and units F = 1400 kg x 2 meters per second/second Solve for the unknownSolve for the unknown 2800 kg-meters/second/second or 2800 N

Newton’s 2Newton’s 2ndnd Law Law proves that different masses proves that different masses accelerate to the earth at the same rate, but with accelerate to the earth at the same rate, but with different forces.different forces.

We know that We know that objects with objects with different masses different masses accelerate to the accelerate to the ground at the same ground at the same rate.rate.

However, because of However, because of the 2the 2ndnd Law we know Law we know that they don’t hit that they don’t hit the ground with the the ground with the same force.same force.

F = maF = ma

98 N = 10 kg x 9.8 m/s/s98 N = 10 kg x 9.8 m/s/s

F = maF = ma

9.8 N = 1 kg x 9.8 9.8 N = 1 kg x 9.8 m/s/sm/s/s

Examples of Newton’s Examples of Newton’s 2nd Law2nd Law

Check Your Check Your UnderstandingUnderstanding

1. What acceleration will result when a 12 N net force 1. What acceleration will result when a 12 N net force applied to a 3 kg object? A 6 kg object?applied to a 3 kg object? A 6 kg object?

   2. A net force of 16 N causes a mass to accelerate at a rate 2. A net force of 16 N causes a mass to accelerate at a rate

of 5 m/sof 5 m/s22. Determine the mass.. Determine the mass.

3. How much force is needed to accelerate a 66 kg skier 1 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?m/sec/sec?

4. What is the force on a 1000 kg elevator that is falling 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?freely at 9.8 m/sec/sec?

Check Your Check Your UnderstandingUnderstanding

1. What acceleration will result when a 12 N net force applied to a 3 1. What acceleration will result when a 12 N net force applied to a 3 kg object? kg object?

12 N = 3 kg x 4 m/s/s12 N = 3 kg x 4 m/s/s

   2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s22. .

Determine the mass.Determine the mass. 16 N = 3.2 kg x 5 m/s/s16 N = 3.2 kg x 5 m/s/s

   3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?

66 kg-m/sec/sec or 66 N66 kg-m/sec/sec or 66 N

4. What is the force on a 1000 kg elevator that is falling freely at 9.8 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?m/sec/sec?

 9800 kg-m/sec/sec or 9800 N9800 kg-m/sec/sec or 9800 N

Third lawThird law: : For For every every actionaction force, there force, there is an is an equalequal and and oppositeopposite reactionreaction force. force. (Forces are (Forces are always always paired)paired)

33rdrd Law Law

There are two There are two forces resulting forces resulting from this from this interaction - a interaction - a force on the chair force on the chair and a force on your and a force on your body. These two body. These two forces are called forces are called actionaction and and reactionreaction forces.forces.

33rdrd Law Law

Flying gracefully Flying gracefully through the air, through the air, birds depend on birds depend on Newton’s third Newton’s third law of motion. As law of motion. As the birds push the birds push down on the air down on the air with their wings, with their wings, the air pushes the air pushes their wings up their wings up and gives them and gives them lift.lift.

Examples of Newton’s 3Examples of Newton’s 3rdrd LawLaw

GRAVITYGRAVITY: An : An attractionattraction force force between all between all massesmasses

Newton’s universal law of Newton’s universal law of gravitationgravitation: Every : Every objectobject in the in the universe universe exertsexerts a gravitational a gravitational attraction to attraction to allall other objects other objects in the universein the universe

The amount of gravitational The amount of gravitational force depends upon the force depends upon the massmass of the objects and the of the objects and the distancedistance between the objectsbetween the objects

What is Gravity?What is Gravity?

The The greatergreater the mass, the the mass, the greater the greater the forceforce

The greater the The greater the distancedistance, the , the lessless the force the force

Acceleration due to gravity = 9.8 Acceleration due to gravity = 9.8 m/s/s or 9.8 m/sm/s/s or 9.8 m/s22

What is Gravity?What is Gravity?

Gravity in Space

WeightWeight is a measure of the is a measure of the gravitational forcegravitational force between two between two objectsobjects

The greater the mass the The greater the mass the greater the force (weight)greater the force (weight)

Measured in units called Measured in units called NewtonsNewtons (N) (N)

WeightlessnessWeightlessness – – freefree from the effects of from the effects of gravitygravity

Air resistanceAir resistance: The force of : The force of airair exerted on a exerted on a fallingfalling object object

The air pushes The air pushes upup as gravity pulls as gravity pulls downdown

Dependent upon the Dependent upon the sizesize and and speedspeed of of the objectthe object

When the air resistance When the air resistance equalsequals the the force of gravity, force of gravity, terminal velocityterminal velocity is is reachedreached

Terminal velocity is the Terminal velocity is the highesthighest velocity that an object will reach as it velocity that an object will reach as it fallsfalls