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/2.  (a) Using conservation of energy (assuming no friction between cart and axles), and assuming pure rolling motion (no slipping), show that the acceleration of the cart along the incline is

(b)  Note that the x component of acceleration of the ball released by the cart is g sin .  Thus, the x component of the cart's acceleration is smaller than that of the ball by the factor M/(M + 2m).  Use this fact and kinematic equations to show that the ball overshoots the cart by an amount x, where

and vyi is the initial speed of the ball imparted to it by the spring in the cart.  

(c) Show that the distance d that the ball travels measured along the incline is

Figure P10.89

an axis through its center is I. The spool is placed on a rough horizontal surface so that it rolls without slipping when a force T acting to the right is applied to the free end of the thread. Show that the magnitude of the frictional force exerted by the surface on the spool is given by

Determine the direction of the force of friction.

Figure P10.90

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