Introduction to Classical Mechanics · Problem 12.15
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 grab the front of the cart and pull on it to keep it moving at constant speed v (while running with it). What force does your hand apply to the cart? (Assume that the cart is made of the most rigid material possible.) Calculate this force in both the ground frame and the cart frame (your frame), and show that the results are equal.