Question

No violation of the law of the conservation of momentum for an isolated system has
ever been found. A consequence of the conservation of momentum is that the center of mass of
an isolated system does not change. Einstein pointed out an apparent violation of the rule that the
center of mass does not change for an isolated system. He carried out a thought experiment in
which a pulse of light is emitted from the left wall of a railroad car, which is initially at rest,
travels to the right wall of the railroad car and is absorbed. The railroad car of mass M and length
L is on frictionless tracks. Let the energy of the emitted light moving to the right be E. According
to Maxwell’s equations, light also carries momentum p = E/c, where c is the speed of light.
(a) [4] Find the velocity of the railroad car V immediately after the light pulse is emitted.
(b) [4] What happens to the railroad car once the light is absorbed? Explain your answer.
(c) [4] What is the displacement of the railroad car?
(d) [4] This problem is analogous to the problem of a person moving from the back to the front
of a canoe, which is initially at rest. In that case the center of mass does not move. What can you
say about the present case?

Answer 1

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