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# Momentum and Collisions

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## Momentum and Collisions Answer Key

Instructions: Read each question carefully. Choose the answer that best fits the question. Short answer response questions must be responded to in complete sentences. If the question involves calculations, you must show all your math work.

1.
Ball A is a 1.50 kg ball moving at 8.00 m/s south. It strikes Ball B, a 2.00 kg ball moving at 3.00 m/s south. The velocity of Ball B after the collision is 4.50 m/s south.

What is the momentum of Ball B after the collision?
1. 9
2. 15
3. 2.25
4. None of the Above
2.
Ball A is a 1.50 kg ball moving at 8.00 m/s south. It strikes Ball B, a 2.00 kg ball moving at 3.00 m/s south. The velocity of Ball B after the collision is 4.50 m/s south.

What is the momentum of Ball A before the collision and after the collision?
1. 12 before the collision, 12 after the collision
2. 18 before the collision, 12 after the collision
3. 12 before the collision, 9 after the collision
4. 20 before the collision, 0 after the collision
3.
A truck on a freeway is going 50 m/s. If it has a momentum of 100 kg*m/s, what is the mass of the truck?
1. 4 kg
2. 2 kg
3. 10 kg
4. 6 kg
4.
The sum of all the external forces on a system of particles is zero. Which of the
following must be true of the system?
1. The total mechanical energy is constant.
2. The total potential energy is constant.
3. The total kinetic energy is constant.
4. The total linear momentum is constant.
5. It is in static equilibrium.
5.
In the collision pictured below, the black box (62kg), moves at a velocity of 13m/s and hits the grey box (62kg).

A.
What is the momentum of the black box when it collides with the grey box?
• $p_"black"=mv=62kg*13m/s=806N$
B.
What is the velocity and momentum of the grey box after the collision?
• Since both masses are equal, the velocity of the grey box after the elastic collision is the same as the black box's velocity before the collision, 13m/s. Because of the Law of Conservation of Momentum, the momentum transfers from the black box to the grey box equaling 806N.
C.
What kind of collision is this depicting?
• This is a picture of an elastic collision with equal masses.
6.
In the perfectly elastic collision pictured below, the black sphere (23kg), moves at an initial velocity of 17m/s, and the grey sphere (41kg), moves at initial velocity of -7m/s.

A.
What is the velocity of the black sphere as it moves away from the grey sphere?
• $v'_"black"=((m_"black"-m_"grey")/(m_"black"+m_"grey"))(v_"black")=((23kg-41kg)/(23kg+41kg))(17m/s)=-4.78m/s$
B.
What is the velocity of the grey sphere as it moves away from the black sphere?
• $v'_"grey"=((2m_"black")(v_"black"))/((m_"black"+m_"grey"))=((2*23kg)(17m/s))/(23kg+41kg)=12.22m/s$
C.
What is the momentum of each sphere before impact?
• $p_"black"=m_"black"*v_"black"=23kg*17m/s=391N$

$p_"grey"=m_"grey"*v_"grey"=41kg*7m/s=287N$
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