Introduction to Classical Mechanics · Problem 12.14
Relativity (Dynamics) — Morin
Physics — Mechanics · relativistic-rocket-motion
Problem
A long cart moves at relativistic speed v. Sand is dropped into the cart at a rate dm/dt=σ in the ground frame. Assume that you stand on the ground next to where the sand falls in, and you push on the cart to keep it moving at constant speed v. What is the force between your feet and the ground? Calculate this force in both the ground frame (your frame) and the cart frame, and show that the results are equal.