A block of mass m slides on a circular track of radius r whose wall and floor both have coefficient of kinetic friction \mu with the block. The size of the block is small compared to the radius of the track. The floor lies in a horizontal plane and the wall is vertical. The block is in constant contact with both the wall and the floor. The block has initial speed v_{0}.
a. Let the block have kinetic energy E after traveling through an angle \theta. Derive an expression for \frac{d E}{d \theta} in terms of g, r, \mu, m and E.
b. Suppose the block circles the track exactly once before coming to a halt. Determine v_{0} in terms of g, r, and \mu.