A railcar of negligible mass contains of loose gravel that is initially piled in a…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A railcar of negligible mass contains M=150kg of loose gravel that is initially piled in a heap at the railcar’s left end. The railcar sits on a horizontal, frictionless track and is initially at rest. A conveyor belt inside the railcar slowly transfers the gravel from the left end to the right end, a distance L=4.0m away, at a constant rate so that a mass m has been moved at any instant.
Ignore any gravel that is momentarily in transit above the floor of the railcar. Let x=0 be the left end of the railcar and let x increase toward the right end.
(1) Derive an expression for the x-coordinate of the center of mass of the gravel as a function of the transferred mass m (where 0≤m≤M).
(2) Sketch qualitatively how the x-coordinate of the center of mass changes with m from 0 to M. Clearly indicate the initial and final values on your sketch.
(3) Determine the total horizontal displacement of the railcar relative to the ground after all the gravel has been transferred. Express your answer in meters.
(4) Explain, in terms of external forces, why the railcar undergoes the displacement you found even though no gravel leaves the railcar.