1. Chapter 9 – Momentum and its Conservation

2. 9.1 HW Quiz Define Impulse Define Momentum
What is the Impulse-Momentum Theorem
What impact does the impulse-momentum theorem have on auto safety?

3. 9.1 Impulse and Momentum

4. 9.1 Impulse and Momentum
When a bat strikes a ball the magnitude of the force exerted on the ball is not constant.
The magnitude rises to a maximum value and then returns to zero when the ball leaves the bat.

5. 9.1 Impulse and Momentum
Even though the contact time may be quite short, the maximum force can be quite large
Since the time of the collision is very short, we consider the average force. (not instantaneous)

6. 9.1 Impulse and Momentum
If a ball is to be hit well, both the size of the force and the time of contact are important
We bring together the average force and the time of contact, calling the product impulse

7. Impulse = FΔt Definition of Impulse:
9.1 Impulse and Momentum
Definition of Impulse:
The impulse of a force is the product of the average force, F, and the time interval, Δt, during which the force acts:
Impulse = FΔt
Impulse is a vector quantity and has the same direction as the average force.
SI Unit of Impulse: Newton · second (N · s)

8. 9.1 Impulse and Momentum
Vi = 0
A large impulse produces a large response, that is, the ball leaves the bat with a large velocity
However a more massive the ball has more inertia, so it resists acceleration and has less velocity after leaving the bat
Both mass and velocity play a role in how an object responds to a given impulse

9. p = mv Definition of Linear Momentum:
9.1 Impulse and Momentum
Definition of Linear Momentum:
The linear momentum, p, of an object is the product of the object’s mass, m, and velocity, v:
p = mv
Linear momentum is a vector quantity that points in the same direction as the velocity.
SI Unit of Momentum: kilogram · meter/second (kg · m/s)

10. ( ) 9.1 Impulse and Momentum
When the velocity of an object changes from vi to vf during a time interval Δt, the average acceleration is given by: a =
vf - vi Δt
But, by Newton’s second law:
F = ma
Substituting for a:
F = m (
vf - vi Δt )
equals
F =
mvf - mvi Δt
The numerator on the right side is the change in momentum

11. FΔt = mvf - mvi or: FΔt = mΔv
9.1 Impulse and Momentum
Impulse-Momentum Theorem:
When a net force, F, acts on an object, the impulse of the net force is equal to the change in the momentum of the object:
FΔt = mvf mvi
final momentum
initial momentum
impulse
Impulse = Change in momentum
or: FΔt = mΔv

12. 9.1 Impulse and Momentum
FΔt = mvf mvi
to minimize the effect of the force on an object involved in a collision, the time must be increased
to maximize the effect of the force on an object involved in a collision, the time must be decreased

13. 9.1 Impulse and Momentum
Air bags in a car extend the time required to stop the momentum of the driver and passenger.

14. 9.1 Impulse and Momentum
Padding a potential impact area can be observed in gymnasiums (underneath the basketball hoops)

15. Catching a foul ball at a baseball game
9.1 Impulse and Momentum
Catching a foul ball at a baseball game
Egg toss

16. 9.1 Impulse and Momentum
A kg vehicle traveling at 94 km/h (26 m/s) can be stopped in 21 s by gently applying the brakes. It can be stopped in 3.8 s if the driver slams on the brakes, or in 0.22 s if it hits a concrete wall. What average force is exerted on the vehicle in each of these stops?

17. 9.1 Impulse and Momentum
A baseball (m = .14 kg) has an initial velocity of vi = -38 m/s as it approaches a bat. The direction of approach has been chosen as the negative direction. The bat applies a force to the ball and the ball departs from the bat with a velocity of vf = +58 m/s.
a) Determine the impulse applied to the ball by the bat.
b) Assuming that the time of contact is 1.6 x 10-3 s, find the average net force exerted on the ball by the bat.

18. Rebounding requires a large impulse
9.1 Impulse and Momentum
Rebounding requires a large impulse
Thus, a hailstone of the same mass as a raindrop can dent a car because its change in velocity is much greater
(Also, because a liquid changes shape, the time of impact is increased, further reducing the force.)

19. 9.1 Impulse and Momentum
Define momentum of an object.
Momentum is the ratio of change in velocity of an object to the time over which the change happens.
Momentum is the product of the average force on an object and the time interval over which it acts.
Momentum of an object is equal to the mass of the object times the object’s velocity.
Momentum of an object is equal to the mass of the object times the change in the object’s velocity.

20. 9.1 Impulse and Momentum
Mark and Steve are playing cricket. Mark hits the ball with an average force of 6000 N and the ball snaps away from the bat in 0.2 ms. Steve hits the same ball with an average force of 3000 N and the ball snaps away in 0.4 ms. Which of the following statements about the impulse given to the ball in both the shots is true?
Impulse given to the ball by Mark is twice the impulse given by Steve.
Impulse given to the ball by Mark is four times the impulse given by Steve.
Impulse given to the ball by Mark is the same as the impulse given by Steve.
Impulse given to the ball by Mark is half the impulse given by Steve.

21. 9.1 Impulse and Momentum
A 1500-kg car hits a wall with a velocity of 20 m/s and immediately comes to rest. What is the final momentum of the car?
(1500 kg)(20 m/s)
(1500 kg)(–20 m/s)
0 kg·m/s
(1500 kg)(20 m/s)2

22. 9.1 Impulse and Momentum
Can the momentum of a bicycle and a car be the same?

23. 9.1 Impulse and Momentum
A 0.50 kg object is at rest. A 3.00 N force to the right acts on the object during a time interval of 1.50 s.
What is the velocity of the object at the end of this interval?
b) At the end of the interval, a constant force of 4.00 N to the left is applied for 3.00 s. What is the velocity at the end of the 3.00 s?

24. 9.1 Impulse and Momentum
A 1.50 kg toy car has a starting velocity of 0 m/s. Consider the graph below to answer the following:
-What is its velocity at 5 s?
-What is its speed at 9 s?
-What is its velocity at 12 s?
-What is its velocity at 7 s?

25. 9.1 Impulse and Momentum
A .500 kg ball is dropped from rest at a point 1.20 m above the floor. The ball rebounds straight upward to a height of m. What is the magnitude and direction of the impulse applied to the ball by the floor?

26. 9.2 Conservation of Momentum
A collision is an interaction between two objects which have made contact with each other
In a collision, there is a force on both objects which causes an acceleration of both objects.

27. 9.2 Conservation of Momentum
The rightward moving seven-ball experiences a leftward force which causes it to slow down; the eight-ball experiences a rightward force which causes it to speed up

28. 9.2 Conservation of Momentum

29. under certain circumstances momentum is a conserved quantity
9.2 Conservation of Momentum
under certain circumstances momentum is a conserved quantity
– a quantity that remains unchanged as a
system evolves.
System – a set of objects that interact with each other
Closed system – a system that does not gain or lose mass
Two types of forces can act on a system of objects
Internal – forces the objects in the system exert on each other
External – forces exerted on the objects from a source external to the system

30. 9.2 Conservation of Momentum
isolated system - the net external force acting on the system is zero (no system on Earth can be completely isolated)
The momentum of each ball may change as a result of the collision (each departing with a velocity different than what it started with)
The sum of their momenta is found to be the same before as after the collision
Sum of momenta before:
mAvAi + mBvBi
Sum of momenta after:
mAvAf + mBvBf =

31. momentum before = momentum after
9.2 Conservation of Momentum
Law of Conservation of Momentum:
The total linear momentum of a closed, isolated system remains constant (is conserved).
m1v1i + m2v2i = m1v1f + m2v2f
momentum before = momentum after

32. There is no net external force during the collision.
9.2 Conservation of Momentum
Frictionless Pool Table (Two-ball system)
There is no net external force during the collision.
The total momentum of this two-ball system IS conserved.

33. Frictionless Pool Table (Two-ball system)
9.2 Conservation of Momentum
Frictionless Pool Table (Two-ball system)
The instant before the balls collide, a hole opens in the table beneath them.
During the collision, an external force causes the balls to accelerate downward causing a change in the total momentum.
Total momentum of this two-ball system is NOT conserved.

34. The force applied by ball 2 causes a net external force.
9.2 Conservation of Momentum
Frictionless Pool Table (One-ball system)
The force applied by ball 2 causes a net external force.
The total momentum of the system is NOT conserved.

35. 9.2 Conservation of Momentum
A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?

36. 9.2 Conservation of Momentum
Starting from rest, two skaters push off against each other on smooth level ice, where friction is negligible. As figure (a) shows, one is a woman (mw = 54 kg), and one is a man (mm = 88 kg). Part (b) of the drawing shows that the woman moves away with a velocity of vf1 = +2.5 m/s. Find the recoil velocity vf2 of the man.

37. A rocket, containing fuel at rest in some reference frame.
9.2 Conservation of Momentum
A rocket, containing fuel at rest in some reference frame.
In the same reference frame, the rocket fires and gases are expelled at high speed out the rear. The total vector momentum remains zero.

38. 9.2 Conservation of Momentum
A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun is pushed backward and the bullet is pushed forward. The acceleration of the recoiling gun is ...
a) greater than the acceleration of the bullet
b) smaller than the acceleration of the bullet
c) the same size as the acceleration of the bullet

39. 9.2 Conservation of Momentum
Calculate the recoil velocity of a 5.0 kg rifle that shoots a kg bullet at a speed of 120 m/s.

40. 9.2 Conservation of Momentum

41. 9.2 Conservation of Momentum
A thread holds a 2.0 kg cart and a 5.0 kg cart together. After the thread is burned, a compressed spring pushes the carts apart, giving the 2.0 kg cart a speed of 0.30 m/s to the left. What is the velocity of the 5.0 kg cart?
A 15.0 g rubber bullet travels at a velocity of 100 m/s, hits a stationary 10.0 kg concrete block resting on a frictionless surface, and ricochets in the opposite direction with a velocity of -80 m/s. How fast will the concrete block be moving?

42. 9.2 Conservation of Momentum
A 30.0 g bullet strikes a 6.0 kg stationary piece of lumber and embeds itself in the wood. The piece of lumber and bullet fly off together at 5.0 m/s. What is the original speed of the bullet?
A 1.00 kg ball that is traveling at 8.0 m/s collides head on with a 1.50 kg ball moving in the opposite direction at a speed of 12.0 m/s. The 1.00 kg ball bounces backward at 15.0 m/s after the collision. Find the speed of the second ball after the collision.

43. 9.2 Conservation of Momentum
An astronaut at rest in space fires a thruster pistol that expels .035 kg of hot gas at 875 m/s. The combined mass of the astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing the pistol?

44. 9.2 Conservation of Momentum
Movies often show someone firing a gun loaded with blanks. In a blank cartridge the lead bullet is removed, and the end of the shell casing is crimped shut to prevent the gunpowder from spilling out. When a gun fires a blank, is the recoil greater than, the same as, or less than when the gun fires a standard bullet?

45. Momentum is conserved in two-dimensional collisions as well
9.2 Conservation of Momentum
Momentum is conserved in two-dimensional collisions as well
x-component momentum conserved
y-component momentum conserved

46. 9.2 Conservation of Momentum
A 1325 kg car, C, moving north at 27.0 m/s, collides with a 2165 kg car, D, moving east at m/s. The two cars are stuck together. In what direction and with what speed do they move after the collision?

47. 9.2 Conservation of Momentum
High-speed stroboscopic photographs show the head of a kg golf club traveling at 55.0 m/s just before it strikes a kg golf ball at rest on a tee. After the collision, the club travels (in the same direction) at m/s. What is the speed of the ball after impact?

48. 9.2 Conservation of Momentum
A 55 kg pole-vaulter falls from rest from a height of 5.0 m onto a foam-rubber pad. The pole- vaulter comes to rest 0.3 s after landing on the pad.
Calculate the athlete’s velocity just before landing on the pad.
Calculate the average force exerted on the pole-vaulter due to the collision

49. 9.2 Conservation of Momentum
A 65.0 kg ice skater moving forward with a velocity of 2.50 m/s throws a kg snowball forward with a velocity of 32.0 m/s.
What is the velocity of the skater after throwing the snowball. Disregard friction.
A second skater initially at rest with a mass of 60.0 kg catches the snowball. What is the velocity of the second skater?

50. 9.2 Chapter 9 Vocabulary impulse momentum impulse-momentum theorem
closed system
isolated system
internal forces
external forces
law of conservation of momentum

51. 9.1 Impulse and Momentum
Bend your knees while landing to increase the time, thus reducing the force.