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 $\theta$ with the horizontal as shown in Figure $\mathrm{P} 10.48$. The coefficient of kinetic friction between block and incline is $\mu .$ (a) Use energy methods to show that the block's speed as a function of position $d$ down the incline is $v=\sqrt{\frac{4 M g d(\sin \theta-\mu \cos \theta)}{m+2 M}}$ (b) Find the magnitude of the acceleration of the block in terms of $\mu, m, M, g,$ and $\theta .$