Minimum coefficient of static friction

Question

An amusement park ride consists of a vertical cylinder that rotates about its axis. The radius of the cylinder is 2.5m and rotates at a constant speed of 15 m/s. What is the minimum coefficient of static friction between the rider's back and the wall required to keep the rider from slipping?

Answer 1

Calculate the centripetal force F_c on the rider.  That will have the same magnitude as the normal force N exerted by the cylinder wall against the rider.  Use that to express the static friction f, set the static friction equal to the weight, and then solve  for μ.

 

N = F_c = mv²/r

 

f = μN = μmv²/r

 

μmv²/r = mg

 

μ = rg/v² = (2.5)(9.8)/(15²) ≅ 0.109