copyright © by holt, rinehart and winston. all rights reserved. concept check – momentum (3) an...

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Concept Check – Momentum (3)

An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (assume that the rain falls vertically into the box)

1. speeds up2. maintains constant speed3. slows down4. stops immediately


Concept Check – Momentum (3)

An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (assume that the rain falls vertically into the box)

1. speeds up2. maintains constant speed3. slows down4. stops immediately

Since the rain falls in vertically, the mass increases. Since the

mass of the box slowly increasesincreases with the added rain, its velocity

has to decreasedecrease so that the momentum of the cart doesn’t change.


Concept Check – Momentum and Collisions

The driver of a car is going to crash. Would it be better to crash into a brick wall or a hay stack?

1. brick wall2. hay stack3. both options would cause equal damage4. can’t tell without knowing the initial velocity

?



The driver of a car is going to crash. Would it be better to crash into a brick wall or a hay stack?

1. brick wall2. hay stack3. both options would cause equal damage4. can’t tell without knowing the initial velocity

Either way, the car will undergo the samesame change in momentum. To decrease the force of impact, increase the time of impact. The hay stack will allow the momentum to change over a slightly slightly longer timelonger time, reducing the force of impactforce of impact.

?



A small car and a large truck collide head-on. Which one experiences the larger force?

1. the car2. the truck3. they both have the same force4. can’t tell without knowing the final velocities



A small car and a large truck collide head-on. Which one experiences the larger force?

1. the car2. the truck3. they both have the same force4. can’t tell without knowing the final velocities

According to Newton’s 3rd Law, the force on the car is equalequal to the force on the truck. There is only one interaction.


Concept Check – Momentum and Collisions (2)

A small car and a large truck collide head-on. Which one experiences the larger impulse?

1. the car2. the truck3. they both have the same impulse4. can’t tell without knowing the final velocities


Concept Check – Momentum and Collisions (2)

A small car and a large truck collide head-on. Which one experiences the larger impulse?

1. the car2. the truck3. they both have the same impulse4. can’t tell without knowing the final velocities

According to Newton’s 3rd Law, the force on the car is equalequal to the force on the truck. If the forces are equal, the impulses are also equal.



A small car and a large truck collide head-on. Which one has the larger change in momentum?

1. the car2. the truck3. they both have the same change in momentum4. can’t tell without knowing the final velocities



A small car and a large truck collide head-on. Which one has the larger change in momentum?

1. the car2. the truck3. they both have the same change in momentum4. can’t tell without knowing the final velocities

Each experiences the same impulseimpulse. According to the Impulse-Momentum Theorem, the impulse is equal to the change in momentum. Therefore, each has the same change in momentum.


Momentum is Conserved

The Law of Conservation of Momentum:

The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

Pi = Pf

m1v1,i + m2v2,i = m1v1,f + m2v2,f

total initial momentum = total final momentum


Sample Problem

Conservation of MomentumA 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right,what is the final velocity of the boat?


Collisions

Perfectly inelastic collision

Conservation of momentum for a perfectly inelastic collision:

m1v1,i + m2v2,i = (m1 + m2)vf

total initial momentum = total final momentu

Kinetic energy is not conserved in an inelastic collision!


Sample Problem

Perfectly Inelastic CollisionsTwo clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of 0.250 kg and an initial velocity of 3.00 m/s to the left. What is velocity of the two clay balls after they are stuck together?


Elastic Collisions

Elastic Collision

A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision.

Momentum Is Conserved in an Elastic Collision

1 1, 2 2, 1 1, 2 2,

2 2 2 21 1, 2 2, 1 1, 2 2,

1 1 1 1

2 2 2 2

i i f f

i i f f

m v m v m v m v

m v m v m v m v


Sample Problem

Elastic CollisionsA 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on collision with a 0.030 kg shooter marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface. What is the velocity of the 0.030 kg marble after the collision?

copyright © by holt, rinehart and winston. all rights reserved. concept check – momentum (3) an...

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