The coefficient of static friction for a stone on a turntable is .32. The stone is .35 m from the center of the turntable.

Question

What is the maximum speed with which the stone can travel before it begins to slide on the turntable? (The answer is 1.0 m/s I just don't know how to get there)

Answer 1

The only force acting on the stone in the direction of motion (say, along the radius of the turntable so the "r" dimension). In the y-dimension (up and down) are the normal force and gravity, respectively. Since the object is moving in a circle then a=v^2/r. Using Newtons 2nd law independently in the r-dimension and y-dimension

∑F = ma ∑F = ma

fr=m(v^2/r) Fn-mg=m(0)

mu*Fn=m(v^2/r) Fn=mg

Substitute mg for Fn

mu*(mg)=m(v^2/r)

cancel out m from both sides and rearrange for v

√(mu*g*r)=v

√(.32*9.8*.35)=v

1.0m/s=v