1. Chapter 6
Impulse and Momentum

2. There are many situations when the
force on an object is not constant.

3. DEFINITION OF IMPULSE
The impulse of a force is the product of the average
force and the time interval during which the force acts:
Impulse is a vector quantity and has the same direction
as the average force.

5. DEFINITION OF LINEAR MOMENTUM
The linear momentum of an object is the product
of the object’s mass times its velocity:
Linear momentum is a vector quantity and has the same
direction as the velocity.

6. Do these objects have the same momenta?
Can these objects have the same momenta?

8. IMPULSE-MOMENTUM THEOREM
When a net force acts on an object, the impulse of
this force is equal to the change in the momentum
of the object
impulse
final momentum
initial momentum

9. Example 2 A Rain Storm
Rain comes down with a velocity of -15 m/s and hits the
roof of a car. The mass of rain per second that strikes
the roof of the car is kg/s. Assuming that rain comes
to rest upon striking the car, find the average force
exerted by the rain on the roof.

10. Conceptual Example 3 Hailstones Versus Raindrops
Instead of rain, suppose hail is falling. Unlike rain, hail usually
bounces off the roof of the car.
If hail fell instead of rain, would the force be smaller than,
equal to, or greater than that calculated in Example 2? Explain.

11. Explain the physics (Impulse – momentum theorem) behind air bags

12. Compare change of momentum for each egg if they were dropped from the same height. Compare impulses applied to each. Explain why one egg breaks and the other one doesn’t

13. Why do we instinctively squat
when landing after a jump? (Explain the physics of this instinct).

14. Ping-Pong Lab revisited

15. Conservation of Momentum
Collisions

16. Momentum is conserved
In the absence of friction, air resistance and other external forces.
The only forces that are exerted on the objects are the action-reaction pairs

17. Collisions

18. Types of collisions
(Nearly) elastic
Inelastic
Perfectly inelastic

19. Perfectly inelastic Objects collide – ‘stick together’ and move as one
MOMENTUM IS CONSERVED

20. Example 1
A 1500 kg car traveling at 15.0 m/s to the south collides with a 4500 kg truck that is initially at rest at a stoplight. The car and truck stick together and move together after the collision. What is the final velocity of the two-vehicle mass?

21. Example 2
A 1.50 × 104 kg railroad car moving at 7.00 m/s to the north collides with and sticks to another railroad car of the same mass that is moving in the same direction at 1.50 m/s. What is the velocity of the joined cars after the collision?

22. Is KE conserved in PIC?
A 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target. a. What is the final velocity of the combined mass?
b. Was KE of the system conserved?

23. Elastic Collisions
Objects collide and move separately without any damage or loss of momentum or KE.
Note: some energy is converted into sound (negligible compared to KE of the balls) + there is friction, but we look at the very short moment – right before and right after the collision. So, we can disregard any loss of energy and consider this collision (nearly) elastic.

24. Example 1 Find the velocity of the second marble after the collision.
A kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a kg marble moving to the left at cm/s. After the collision, the first marble moves to the left at 18.0 cm/s.
Find the velocity of the second marble after the collision.
Verify your answer by calculating the total kinetic energy before and after the collision.

25. Example 1
A kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a kg marble moving to the left at cm/s. After the collision, the first marble moves to the left at 31.5 cm/s.

26. Example 1
A kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a kg marble moving to the left at cm/s. After the collision, the first marble moves to the left at 18.0 cm/s.
Verify your answer by calculating the total kinetic energy before and after the collision.

27. Inelastic collisions
Most of every day collisions: car accidents, bumping into a table (door, wall, or whatever you prefer to bump into)
Objects do not lock together and move (rest) separately.
Momentum is conserved.
Energy is lost

28. Collisions lab