Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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12a0001     Conservation of momentum for colliding cars on a track.     12a0001
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Question

 

You do an experiment with colliding cars on a low-friction track. Car 1 of mass 0.5 kg is moving in the direction at a speed of 2 m/s when it collides with Car 2 of mass 1.0 kg which is at rest. After the collision, Car 1 rebounds and moves to the right with a speed of 0.67 m/s. Define the system as Car 1.

  1. What is the change in the momentum of the system as a result of the collision?
  2. What objects in the surroundings interact with the system during the collision and what is the change in the momentum of the surroundings?
  3. What is the velocity of Car 2 after the collision?

 



Solution

 

(a) Begin by drawing a picture of the situation.


Figure: The momentum of Cars 1 and 2 before and after the collision.

Define the system. In this case, the system is Car 1. The initial momentum of Car 1 is

The final momentum of Cart 1 is

To find the change in momentum of Car 1, sketch a picture of the initial momentum and final momentum drawn tail to tail. The change in momentum is drawn from the head of the initial momentum to the head of the final momentum, as shown below.


Figure: The change in momentum of Car 1.

The change in momentum can also be calculated algebraically.

Note that the change in the momentum of Car 1 is to the right, which is consistent with the picture.

(b) The only objects that interact with the system during the collision are Earth (gravitational interaction), the track, and Car 2. The picture below shows the forces on Car 1 during the interaction.


Figure: A free body diagram for Car 1.

The upward force by the track on Car 1 balances the downward gravitational force by Earth on Car 1. Thus, the net external force on Car 1 is force by Car 2 on Car 1 during the collision. Thus, the only object in the surroundings that contributes to the net external force on Car 1 is Car 2.

According to Conservation of Momentum,

Since the system is Car 1 and the surroundings is Car 2 (remember Car 2 exerts the only external unbalanced force on Car 1), then

The change in momentum of Car 2 is the same in magnitude but opposite in direction as the change in momentum of Car 1, so it points to the left.


Figure: The change in momentum of Car 2.

(c) The final velocity of Car 2 can be found from its momentum.

Car 2's final velocity is to the left, as expected.