Question about Circular Motion and Gravitation? (must know about centripetal forces and inertia and such.)?

Question

1) A 2.00 x 10^3 kg car rounds a circular term of radius 20.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.70, how fast can the car go without skidding?


2) A wooden bucket filled with water has a mass of 75 kg and is attached to a rope that is wound around a cylinder with a radius of 0.075 m. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicularly to the crank handle is required to raise the bucket?


Answer both or one of the questions. Any help you can give would be greatly appreciated! I really can't get these two. >.<

Answer 1

First you need to know that the centrifugal force on the car is m*v^2/r, and that the frictional force is k*m*g. When the centrifugal force exceeds the frictional force, the car will skid, so no skidding occurs if:

m*v^2/r < k*m*g

solve for v:

v < √[k*g*r]

note that the mass doesn't matter.

Part 2) is a torque-balance condition. Torque is F * R; the torque on the cylinder from the bucket is

Tb = m*g*Rcyl

The torque on the cylinder from the crank is

Tcrnk = Fcrnk * Rcrnk

The weight will rise if the crank torque exceeds the bucket torque:

Fcrnk * Rcrnk > m*g*Rcyl

Fcrnk > m*g*Rcyl/Rcrnk