MomentumMomentum

What is momentum?What is momentum?Momentum is the quantity of motion.Momentum is the quantity of motion.

If an object is in motion, it has momentumIf an object is in motion, it has momentum

MassMass in motion in motion

Momentum is dependent on 2 things: Momentum is dependent on 2 things: – How much “stuff” is moving, How much “stuff” is moving, Mass, Mass,

measured in kgmeasured in kg– How fast the stuff is moving, How fast the stuff is moving, Velocity, Velocity,

measured in m/smeasured in m/s

Calculating MomentumCalculating Momentum

Momentum is a vector quantity.Momentum is a vector quantity.

Momentum = mass x velocityMomentum = mass x velocity

p = m x vp = m x v

An object can have a large An object can have a large momentum if it has either a large momentum if it has either a large mass and/or a high speed.mass and/or a high speed.

Determining momentumDetermining momentumA small sports car and a large A small sports car and a large delivery truck are traveling at the delivery truck are traveling at the same speed. Which has more same speed. Which has more momentum?momentum?If the car is to have the same If the car is to have the same momentum as the truck, what about momentum as the truck, what about the car must be changed?the car must be changed?If the truck is at rest, what is its If the truck is at rest, what is its momentum?momentum?

Sample ProblemsSample ProblemsDetermine the momentum of a ...Determine the momentum of a ...

1)1)A 60-kg halfback moving eastward at 9 m/s.A 60-kg halfback moving eastward at 9 m/s.

Answer: 540 kg m/s eastAnswer: 540 kg m/s east

2) A 1000-kg car moving northward at 20 m/s.2) A 1000-kg car moving northward at 20 m/s.

Answer: 20000 kg m/s northAnswer: 20000 kg m/s north

3) A 40-kg freshman moving southward at 2 3) A 40-kg freshman moving southward at 2 m/s.m/s.

Answer: 80 kg m/s southAnswer: 80 kg m/s south

Changing momentumChanging momentum

In order to change the momentum of In order to change the momentum of an object, the velocity must be an object, the velocity must be changed (if the mass remains the changed (if the mass remains the same).same).

Any change in velocity is called Any change in velocity is called acceleration.acceleration.

Newton’s second law states that any Newton’s second law states that any acceleration requires a force. acceleration requires a force.

Changing momentum (continued)Changing momentum (continued)

F = m x a (Newton’s 2F = m x a (Newton’s 2ndnd law) law)

a = a = v v

tt

F = F = mm v v

tt

FF t = m t = m vv

What is impulse?What is impulse?

FF t is called an impulse. t is called an impulse.

Impulse is a change in momentum.Impulse is a change in momentum.

Impulse is a force applied over a time Impulse is a force applied over a time interval.interval.

Impulse is measured in NImpulse is measured in N..s. s.

What is the relationship between What is the relationship between momentum and impulse?momentum and impulse?

If two objects have the same If two objects have the same momentum, the same impulse is momentum, the same impulse is required to change that momentum.required to change that momentum.

A large force can be applied over a A large force can be applied over a small time interval small time interval

oror

A small force can be applied over a A small force can be applied over a large time interval.large time interval.

Applications of ImpulseApplications of Impulse

If you were to attempt to catch a If you were to attempt to catch a baseball with your bare hand, you baseball with your bare hand, you would probably move your hand would probably move your hand backward as you catch the ball. backward as you catch the ball. Why?Why?

How do airbags or padded How do airbags or padded dashboards assist in protecting dashboards assist in protecting drivers in a crash?drivers in a crash?

Discussion QuestionsDiscussion Questions1.1. Would you try to stop a 150 lb (68 Would you try to stop a 150 lb (68

kg) cannonball fired towards you at kg) cannonball fired towards you at 30 mph (48 km/hr)? Why not? How 30 mph (48 km/hr)? Why not? How does this compare with trying to does this compare with trying to brace yourself in a car collision?brace yourself in a car collision?

2.2. Show mathematically why a 36,000 Show mathematically why a 36,000 kg truck traveling 0.89 m/s has the kg truck traveling 0.89 m/s has the same momentum as a 1800 kg SUV same momentum as a 1800 kg SUV traveling at 18 m/s.traveling at 18 m/s.

Discussion QuestionsDiscussion Questions3.3. During the egg throwing demonstration, During the egg throwing demonstration,

which egg experienced the greater which egg experienced the greater impulse? Which egg experienced the impulse? Which egg experienced the greater force of impact? Which egg greater force of impact? Which egg experienced the greater time of impact?experienced the greater time of impact?

4.4. Describe three other examples where Describe three other examples where momentum is reduced by applying a momentum is reduced by applying a smaller collision force over a longer smaller collision force over a longer impact time.impact time.

Practice Problem #1Practice Problem #1

A 0.50 kg football is thrown with a A 0.50 kg football is thrown with a velocity of 15 m/s to the right. A velocity of 15 m/s to the right. A stationary receiver catches the ball stationary receiver catches the ball and brings it to rest in 0.020 s. What and brings it to rest in 0.020 s. What is the force exerted on the receiver?is the force exerted on the receiver?

Practice Problem #2Practice Problem #2A 0.40 kg soccer ball approaches a player A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. horizontally with a velocity of 18 m/s to the north. The player strikes the ball and causes it to move The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the What impulse was delivered to the ball by the player?player?

Law of Conservation of MomentumLaw of Conservation of Momentum

The Law of Conservation of The Law of Conservation of Momentum states that if no net force Momentum states that if no net force acts on a system, the momentum of acts on a system, the momentum of the system cannot change.the system cannot change.

This means that the momentum This means that the momentum before a collision is equal to the before a collision is equal to the momentum after a collision.momentum after a collision.

Law of Conservation of Momentum Law of Conservation of Momentum (continued)(continued)

The equation for the law of The equation for the law of conservation of momentum:conservation of momentum:

ppA1A1 + p + pB1B1 = p = pA2A2 + p + pB2B2

The momentum gained by object B is The momentum gained by object B is equal to the momentum lost by equal to the momentum lost by object Aobject A

Momentum is conserved if:Momentum is conserved if:The system is closed (no gain or loss in The system is closed (no gain or loss in mass)mass)

Only internal forces are involved (forces Only internal forces are involved (forces outside the system are external forces-outside the system are external forces-althoughalthough there will always be some interaction with outside there will always be some interaction with outside

forces they are usually small and can be ignoredforces they are usually small and can be ignored))

There must be collisions (the objects can There must be collisions (the objects can come apart or remain stuck together)come apart or remain stuck together)

Sample ProblemSample Problem

A 2275 kg car going 28 m/s rear ends A 2275 kg car going 28 m/s rear ends a 875 kg car going 16 m/s on ice in a 875 kg car going 16 m/s on ice in the same direction. The two cars the same direction. The two cars stick together. How fast does the stick together. How fast does the wreckage move immediately after wreckage move immediately after the collision?the collision?

Calculating the AnswerCalculating the Answer

ppA1A1+ p+ pB1B1 = p = pA2A2 + p + pB2B2

mvmvA1A1 + mv + mvB1B1 = (m = (mAA + m + mBB)v)v22

(2275)(28) + (875)(16) = (2275+875)x(2275)(28) + (875)(16) = (2275+875)x

X = 25 m/sX = 25 m/s

Sample Problem #2Sample Problem #2

John has a mass of 200.0 kg and is John has a mass of 200.0 kg and is riding in a 100kg bumper car at riding in a 100kg bumper car at

10.0 m/s. If he collides with Melinda 10.0 m/s. If he collides with Melinda who has a mass of 25 kg and is at who has a mass of 25 kg and is at rest, what is Melinda’s velocity after rest, what is Melinda’s velocity after the collision if John continues ahead the collision if John continues ahead at a speed of 4.12 m/s after the at a speed of 4.12 m/s after the collision?collision?

Calculating the AnswerCalculating the Answer

ppA1A1+ p+ pB1B1 = p = pA2A2 + p + pB2B2

(300.0)(10.0) + (125)(0) = (300.0)(4.12) + (125)x(300.0)(10.0) + (125)(0) = (300.0)(4.12) + (125)x

X = 14.1 m/sX = 14.1 m/s

Recoil ProblemRecoil Problem

An astronaut at rest in space fires a An astronaut at rest in space fires a thruster pistol that expels 35 g of gas thruster pistol that expels 35 g of gas at 875 m/s. The combined mass of at 875 m/s. The combined mass of the astronaut and pistol is 84 kg. the astronaut and pistol is 84 kg. How fast and in what direction is the How fast and in what direction is the astronaut moving after firing the astronaut moving after firing the pistol?pistol?

Calculating the AnswerCalculating the AnswerppA1A1 + p + pB1B1 = p = pA2A2 + p + pB2B2

(m(mAA + m + mBB)v)v11 = mv = mvAA + mv + mvBB

(84)(0) = (.035)(875) + (84)x(84)(0) = (.035)(875) + (84)x

X = -.36 m/s (the direction is opposite to X = -.36 m/s (the direction is opposite to that of the gas leaving the pistol)that of the gas leaving the pistol)

HomeworkHomework

Complete problems 7-12 on p. 210 Complete problems 7-12 on p. 210 and 13-15 on p. 214and 13-15 on p. 214