Download - Momentum
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Impulse and Momentum
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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?
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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
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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
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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.
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Impulsive Force
A large force exerted during a small time interval is called an impulsive force.
Keeping with the tennis racket and ball:
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Momentum
The momentum of a particle is defined as
We can write Newtons second law in terms of momentum:
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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.)
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Impulse-Momentum Theorem
The importance of the impulse-momentum theorem is this:
An impulse delivered to a particle changes the particles momentum.
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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?
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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?
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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
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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?
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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:
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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!
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Conservation of Momentum
An isolated system is one for which the net external force is zero.
Then
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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?
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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
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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?
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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
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For next day
Study for the midterm!
For the day after that, read the rest of chapter 9.
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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?
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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?
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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.
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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.
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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.
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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?
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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?
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For next day
Read Chapter 10, sections 10.1 10.5. This is the beginning of our discussion of energy, and is very important.