Momentum

Impulse and Momentum

Reading Quiz: Question 1

1. a force that is applied at a random time.

2. a force that is applied very suddenly.

3. the area under the force curve in a force-versus-time graph.

4. the time interval that a force lasts.

2%

37%

48%

13%

What is impulse?

Reading Quiz: Question 2

1. always.

2. if the system is isolated.

3. if the forces are conservative.

4. never; its just an approximation

44%

51%

4%

1%

The total momentum of a system is conserved

Reading Quiz: Question 3

1. The net force.

2. The impulse.

3. The momentum.

4. Nothing in particular.

34%

56%

10%

0%

The quantity

is equal to

Momentum and Impulse

Think about the collision between a tennis ball and a racket. Its not instantaneous the collision takes time.

The ball compresses, the strings bend.

Collision times depend on the materials, but typically have durations of 1 to 10 ms.

Impulsive Force

A large force exerted during a small time interval is called an impulsive force.

Keeping with the tennis racket and ball:

Momentum

The momentum of a particle is defined as

We can write Newtons second law in terms of momentum:

Impulse

Lets define a quantity called the impulse:

Its related to the change of a particles momentum by the impulse-momentum theorem:

(Actually, this is just Newtons 2nd law; see text for derivation.)

Impulse-Momentum Theorem

The importance of the impulse-momentum theorem is this:

An impulse delivered to a particle changes the particles momentum.

ConcepTest 1

1. -30 kg m/s

2. 0 kg m/s

3. 10 kg m/s

4. 20 kg m/s

5. 30 kg m/s

37%

0%

17%

5%

41%

What is the carts change in momentum?

ConcepTest 2

1. The clay ball exerts a larger impulse because it sticks.

2. The rubber ball exerts a larger impulse because it bounces.

3. They exert equal impulses because they have equal momenta.

4. Neither exerts an impulse on the wall because the wall doesnt move.

11%

35%

48%

5%

A 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds. The rubber ball bounces, the clay ball sticks. Which ball exerts a larger impulse on the wall?

ConcepTest 3

1. 0 m/s

2. 0.5 m/s to the left

3. 0.5 m/s to the right

4. 1.0 m/s to the left

5. 1.0 m/s to the right

22%

8%

14%

36%

20%

A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse due to the force shown in the graph. What is the objects speed and direction after the impulse?

Fx (N)

t (s)

0.5 s 2

-2

Example: A bouncing ball

A 100 g rubber ball is dropped from a height of 2.00 m onto a hard floor. The figure shows the force that the floor exerts on the ball. How high does the ball bounce?

Conservation of Momentum

We need to extend our concept of momentum to a system of many particles.

Its easy enough: the total momentum of the system is just the sum of each particles momentum:

Conservation of Momentum

Take the derivative of the total momentum and use Newtons second law (Fk = dpk/dt):

Each force acting on a single particle can be either an internal force or an external force.

But the internal forces will all cancel!

Newtons 2nd law for the system as a whole!

Conservation of Momentum

An isolated system is one for which the net external force is zero.

Then

ConcepTest 4

1. No; the inertial mass of Earth is so large that the planet's change in motion is imperceptible.

2. Yes; because of its much larger inertial mass, however, the change in momentum of Earth is much less than that of all the jumping people.

3. Yes; Earth recoils, like a rifle firing a bullet, with a change in momentum equal to and opposite that of the people.

4. It depends.

20%

41%

35%

4%

Suppose the entire population of the world gathers in one spot and, at the sounding of a prearranged signal, everyone jumps up. While all the people are in the air, does Earth gain momentum in the opposite direction?

ConcepTest 5

1. increases.

2. does not change.

3. decreases.

6%

25%

70%

Suppose rain falls vertically into an open cart rolling along a straight horizontal track with negligible friction. As a result of the accumulating water, the speed of the cart

ConcepTest 6

1. 6 m/s

2. 3 m/s

3. 1.5 m/s

4. 1.0 m/s

5. It stops

0%

0%

0%

0%

0%

Consider my skateboard rolling across the table. Suppose it has a mass of 1 kg, and the textbook also has a mass of 1 kg. If it starts moving at 3 m/s, how fast does it go after I gently place the textbook on it?

ConcepTest 7

1. hit the other car.

2. hit the wall.

3. hit either one-it makes no difference.

4. consult your lecture notes.

25%

39%

36%

0%

Think fast! You've just driven around a curve in a narrow, one-way street at 25 mph when you notice a car identical to yours coming straight toward you at 25 mph. You have only two options: hitting the other car head on or swerving into a massive concrete wall, also head on. In the split second before the impact, you decide to

For next day

Study for the midterm!

For the day after that, read the rest of chapter 9.

ConcepTest 8

1. Yes

2. No

3. It depends

48%

28%

24%

As you release a ball, it falls gaining speed and momentum. Is momentum conserved?

ConcepTest 9

1. Yes

2. No

3. It depends

0%

0%

0%

Two particles collide, one of which was initially moving and the other initially at rest. Is it possible for both particles to be at rest after the collision?

Inelastic Collisions

A collision in which two objects stick together and move with a common final velocity is called a perfectly inelastic collision.

E.g., a ball of clay hitting the floor or a bullet embedding itself in wood.

Example: Football collision

Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30.

Explosions

An explosion is the opposite of a collision.

The particles of the system move apart from each other after a brief, intense interaction.

The explosive forces are all internal, so momentum should be conserved.

Example: Rocket explosion

A 1500 kg weather rocket accelerates upward at 10 m/s2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal the light fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the heavier fragment just after the explosion?

Example: A 2D collision

One billiard ball is shot east at 2.0 m/s. A second, identical billiard ball is shot west at 1.0 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90 and sending it north at 1.41 m/s. What are the speed and direction of the first ball after the collision?

For next day

Read Chapter 10, sections 10.1 10.5. This is the beginning of our discussion of energy, and is very important.