Suppose that a long cart is moving at a constant relativistic speed with respect to the ground. Sand is falling on it from negligible height(from the same place and zero horizontal velocity with respect to ground). A person standing just beside the place from where sand falls, pushes the cart with a force in order to make it move with a constant velocity. Also a force is exerted on the person's feet by the ground so that he stays at rest in the ground frame. Now apparently the cart gains energy, so the person must loose energy, as a result he keeps loosing mass. In the ground frame, the person's momentum is zero, hence constant, so the force that the ground exerts on the person and the force that the cart exerts on the person are equal. But if we view the situation in the cart's frame(which moves with a constant velocity and hence is inertial), then the person loses mass and moves with a constant velocity, as a result the person's momentum keeps changing with time, so the force that the cart exerts on the person and the force that the ground exerts on the person must not be equal. Now which of the two forces, the force that ground exerts on person, or the force that the cart exerts on the person should come out to be equal in both frames? Why so?
$\begingroup$
$\endgroup$
2
-
$\begingroup$ You seem to be neglecting that sand you've mentioned earlier in your question, the cart cannot possibly have a constant force acting on it since it is gaining mass in its own frame and thus also doesn't have a constant momentum. $\endgroup$– TriatticusCommented May 30, 2022 at 20:05
-
$\begingroup$ @Triatticus In the cart's frame, the velocity of cart is zero, so its momentum is zero. But the sand that will fall will have a momentum and in order to counteract that momentum, we need a force and it will turn out to be constant(i suppose) on solving, assuming that the rate at which sand falls is constant $dm/dt=\sigma$ in the ground frame(note that this is not the rate of increase of mass of the cart). $\endgroup$– Wizard0001Commented May 30, 2022 at 21:11
Add a comment
|