Finding the coefficient of static friction

[rm_girl]

Homework Statement

So a hot wheel was put on a linear track, and one end of the track is slowly lifted until the cart starts to move. The height of the one end is measured as 6.45cm and distance (or hypotenuse) is 189.5cm
mass of hot wheel is 45.7 g

Homework Equations

PE = mgh
KE = 1/2mv2
W_f = F_fd
Ff = μmg

The Attempt at a Solution

So I was thinking of using PE = KE + Wf, but the car doesn't move, so I can't have KE in there. If that's the case, do I just set up the equation as PE = Wf ? and find the coefficient of static friction from there?

 

[haruspex]

This is a very strange question. Friction between the ramp and wheels has nothing to do with it - the wheels will roll, not slide. The initial resistance to motion comes from friction in the axles and, perhaps, rolling resistance in the wheels. To calculate the coefficient of friction in the axles the ratio of the wheel radius to axle radius is needed. Rolling resistance is a property of the wheel rubber, and I'm not sure of the details of that.
If we ignore all that and treat the cart as a wheelless block, this is a statics question, so energy is irrelevant. Just consider the forces at their limits prior to movement.