Chapter 10, Problem 92CP

A cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cord’s free end is connected to a block of mass M. The block starts from rest and then slides down an incline that makes an angle θ with the horizontal as show n in Figure P10.48. The coefficient of kinetic friction between block and incline is μ. (a) Use energy methods to show that the block’s speed as a function of position d down the incline is

$v=\sqrt{\frac{4Mgd(\sin \theta -\mu \cos \theta )}{m+2M}}$

(b) Find the magnitude of the acceleration of the block in terms of μ, m, M, g, and θ.

Figure P10.48