Question

Use Einstein's velocity addition rule and the principle of momentum conservation to explain why you can't use the formula p=mv to find the momentum of an object that is moving relativistically, and show that the correct formula for relativistic momentum is actually p = γmv. Use the following bullet points as a guide for what points to cover in your essay. First imagine you have two objects, A and B, that are moving in the same direction relative to you but with different speeds. Object B is ahead of object A, but the separation between them is narrowing because object A is faster. Now suppose object A catches up to object B and they collide. They keep going in the same direction after the collision but with new speeds. What is the total non-relativistic momentum before and after the collision? Now suppose the collision is taking place aboard a moving train that you are observing from the ground. Let u be the speed of the train relative to you. Use Einstein's velocity addition rule to add the train's motion to the motions of objects A and B to find their speeds relative to you. What is the total non-relativistic momentum before and after the collision, now with the motion of the train taken into account? If you set them equal to each other, does the speed of the train u just cancel out? You should have found that when you use the non-relativistic formula for momentum, the train motion did not cancel out. Explain why this implies that non-relativistic momentum is not conserved on the moving train. Now show that u does cancel out when you use the relativistic formula for total momentum before and after the collision between objects A and B on the moving train. Explain why this implies that relativistic momentum is conserved.

Answer 1

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