Coefficent of kinetic friction

[spiegalr]

Homework Statement

A train, of mass m, comes into a station traveling 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?

Homework Equations

W = 1/2kx^2
KE = 1/2mv^2
W = $$\mu$$mgh

The Attempt at a Solution

I've tried using the Work Energy Theorem like so:
$$\mu$$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.
Thanks!

 

[tiny-tim]

Welcome to PF!

Hi spiegalr! Welcome to PF!

Hint: what is the work done by the force of friction?

 

[tomcue]

Hello, it seems like you are on the right track with using the Work Energy Theorem to solve this problem. To find the minimum coefficient of kinetic friction, we need to consider the forces acting on the train and use the equations you have provided.

First, let's consider the forces acting on the train as it skids along the rails. The only two forces acting on the train are the force of gravity (mg) and the frictional force (Ff). Since the train is locked, there is no normal force acting on it. Therefore, the net force on the train is simply the frictional force, which can be written as:

Fnet = Ff = \mumg

Next, we can use the Work Energy Theorem to relate the work done by the frictional force to the change in kinetic energy of the train. We can write this as:

W = \mumgh - 1/2kx^2 = \mumg(1m) - 1/2mv^2

Since the train is coming to a stop, we can set the final kinetic energy to be zero. Solving for the coefficient of kinetic friction, we get:

\mu = (1/2kx^2)/(mg)

Substituting in the given values and solving, we get:

\mu = (1/2k(1m)^2)/(mg) = 1/(2kg)

Therefore, the minimum coefficient of kinetic friction needed for the buffers to stop the train is 1/(2kg), where k is the spring constant and g is the gravitational field. I hope this helps!