2) Two carts are shown just before they collide. Four students are discussing th

Question

2) Two carts are shown just before they collide. Four students are discussing the situation. Anna: ''After the collision, the carts will stick together and move off to the left. Cart B has more speed, and its speed is going to determine which cart dominates in the collision.'' Bob: ''I think they will stick together and move off to the right because Cart A is heavier. It?s like when a truck hits a car. The truck is going win no matter which one is moving faster.'' Carlo: ''1 think the speed and the mass compensate, and the carts are going to be at rest after the collision.'' David: ''The carts must have the same momentum after the collision as before the collision, and the only way that this can happen is if they keep the same speeds. All the collision does is change their directions, so that Cart A will be moving to the left at 3 m/s and Cart B will be moving to the right at 4 m/s.'' Which of these students, if any, do you agree with? Explain your reasoning. Anna _________ Bob _______ Carlo __________ David ________ None of them________

Explanation / Answer

David is right.

From the conservation of momentum,

momentum of cart A before collision + momentum of cart B before collision = momentum of cart A after collision + momentum of cart B after collision

That is,

mAi vAi + mBi vBi = mAf vAf + mBf vBf

4 * 3 + 3 * 4 = mAf vAf + mBf vBf

The only way for it to happen is, they retain their individual speed (obviously mass is going to remain unchanged). The direction is going to change because of the impact of the collision.

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