1. 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 up 2. maintains constant speed 3. slows down 4. stops immediately

2. 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 up 2. maintains constant speed 3. slows down 4. stops immediately increases decrease Since the rain falls in vertically, the mass increases. Since the mass of the box slowly increases with the added rain, its velocity has to decrease so that the momentum of the cart doesn’t change.

3. Copyright © by Holt, Rinehart and Winston. All rights reserved. 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 wall 2. hay stack 3. both options would cause equal damage 4. can’t tell without knowing the initial velocity ?

4. Copyright © by Holt, Rinehart and Winston. All rights reserved. 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 wall 2. hay stack 3. both options would cause equal damage 4. can’t tell without knowing the initial velocity same slightly longer timeforce of impact Either way, the car will undergo the same 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 longer time, reducing the force of impact. ?

5. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions A small car and a large truck collide head-on. Which one experiences the larger force? 1. the car 2. the truck 3. they both have the same force 4. can’t tell without knowing the final velocities

6. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions A small car and a large truck collide head-on. Which one experiences the larger force? 1. the car 2. the truck 3. they both have the same force 4. can’t tell without knowing the final velocities equal According to Newton’s 3 rd Law, the force on the car is equal to the force on the truck. There is only one interaction.

7. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions (2) A small car and a large truck collide head-on. Which one experiences the larger impulse? 1. the car 2. the truck 3. they both have the same impulse 4. can’t tell without knowing the final velocities

8. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions (2) A small car and a large truck collide head-on. Which one experiences the larger impulse? 1. the car 2. the truck 3. they both have the same impulse 4. can’t tell without knowing the final velocities equal According to Newton’s 3 rd Law, the force on the car is equal to the force on the truck. If the forces are equal, the impulses are also equal.

9. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions A small car and a large truck collide head-on. Which one has the larger change in momentum? 1. the car 2. the truck 3. they both have the same change in momentum 4. can’t tell without knowing the final velocities

10. Copyright © by Holt, Rinehart and Winston. All rights reserved. Concept Check – Momentum and Collisions A small car and a large truck collide head-on. Which one has the larger change in momentum? 1. the car 2. the truck 3. they both have the same change in momentum 4. can’t tell without knowing the final velocities impulse Each experiences the same impulse. According to the Impulse- Momentum Theorem, the impulse is equal to the change in momentum. Therefore, each has the same change in momentum.

11. Copyright © by Holt, Rinehart and Winston. All rights reserved. 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. P i = P f m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f total initial momentum = total final momentum

12. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem Conservation of Momentum A 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?

13. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem, continued Conservation of Momentum 1. Define Given: m 1 = 76 kgm 2 = 45 kg v 1,i = 0v 2,i = 0 v 1,f = +2.5 m/s (to the right) Unknown: v 2,f = ? 2. Plan Choose an equation or situation: Because the total momentum of an isolated system remains constant, the total initial momentum of the boater and the boat will be equal to the total final momentum of the boater and the boat. P i = P f m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f

14. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem, continued Conservation of Momentum 2. Plan, continued Because the boater and the boat are initially at rest, the total initial momentum of the system is equal to zero. Therefore, the final momentum of the system must also be equal to zero. 0 = m 1 v 1,f + m 2 v 2,f Rearrange the equation to solve for the final velocity of the boat. 3. Calculate Substitute the values into the equation and solve:

15. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem, continued Conservation of Momentum 4. Evaluate The negative sign for v 2,f indicates that the boat is moving to the left, in the direction opposite the motion of the boater. Therefore, v 2,f = 4.2 m/s, to the left

16. Copyright © by Holt, Rinehart and Winston. All rights reserved. Collisions Perfectly inelastic collision Conservation of momentum for a perfectly inelastic collision: m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f total initial momentum = total final momentu Kinetic energy is not conserved in an inelastic collision!

17. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem Perfectly Inelastic Collisions Two 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?

18. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem, continued Perfectly Inelastic Collisions Use the equation for a perfectly inelastic collision to calculate the final velocity. Substitute the values into the equation and solve: Calculate the final velocity.

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

20. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem Elastic Collisions A 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?

21. Copyright © by Holt, Rinehart and Winston. All rights reserved. Sample Problem, continued Substitute the values into the equation and solve: The rearranged conservation-of-momentum equation will allow you to isolate and solve for the final velocity.