Problems $13\mathrm{.}37$ through $13\mathrm{.}39$

A railcar with an overall mass of $75,000kg$ traveling with a speed $v_i$ is approaching a barrier

equipped with a bumper consisting of a nonlinear spring whose force vs$.$ compression law is given

by $F_s=x^3,$ where $=640{10}^6\frac{N}{m^3}$ and $x$ is the compression of the bumper.

Problem $13\mathrm{.}38$ I Treating the system as a particle, assuming that the contact between railcar

and rails is frictionless, and letting $v_i=6k\frac{m}{h},$ determine the bumper compression necessary to

bring the railcar to a stop.