A train, of mass m, comes into a station travelling slightly too fast to stop in time before it hits the buffers at the end of the track. The buffers are effectively metal plates attached to a spring which obeys Hooke's law with a spring constant k. The trains wheels lock and it skids along the horizontal rails with sparks flying so that at the point that the train first touches the buffers it has a speed v. If the maximum compression of the spring in the buffers is 1m what is the minimum coefficient of kinetic friction between the locked wheels of the train and the rails for the buffers to be able to stop it given that the gravitational field is g?
W = 1/2kx^2
KE = 1/2mv^2
W = [tex]\mu[/tex]mgh
The Attempt at a Solution
I've tried using the Work Energy Theorem like so:
[tex]\mu[/tex]mgh - 1/2kx^2 = 0 - 1/2mv^2
But I have no idea what directions to take, or even if I'm using the right formula.