The rotor(gravitron) physics problem?

Question

If r=2m and v=7m/s when the floor drops away, what is the minimum coefficient of friction?


when i tryed this problem i got .1 but i think it is wrong because i dont know how to work out the problem

Answer 1

The force due tot he rotational motion on a mass m on the wall of teh drum is:

F = mv^2/r where v = speed of rotation and r = radius of drum

Now teh object has a force W = -mg where g = acceleration due to gravity pulling it down along the drum. The force of friction is

f = uN = uF = umv^2/r whrere u = coefficient of friction.

If mass does not slip, then f -mg = 0 or mg = umv^2/r

So u = rg/v^2 = 2*9.8/(7^2) = 19.6/49 = 0.4