circular motion

Question

The coefficient of static friction for a stone on a turntable is .40 . The stone is .25 m from the center of the turntable. What is the maximum speed with which the stone can travel before it begins to slide on the turntable?

Answer 1

The stone will stay on the turntable as long as the centripetal force is not more than the maximum static frictional force. Let's see if we can figure out the maximum speed by setting those two forces equal to each other:

F_f = F_c

µmg = mv²/r

Since the mass is on both sides, we can cancel it out.

µg = v²/r

(0.40)(9.8) = v²/(0.25)

Multiplying both sides by 0.25, we get 0.98 = v² and if we take the square root, we will get that v = 0.99 m/s. I hope this helps!