A solid ball is released from rest down inclines of various inclination angles $\theta$  but through a fixed vertical height h. the coefficient of static and kinetic friction are both equal to $\mu$ . Which of the following graphs best represents the total kinetic energy K of the ball at the bottom of the incline as a function of the angle  $\theta$ of the incline ?  

The ball rolls without slipping so long as $\theta$  is less than some critical angle. For  $\theta$ less than the critical angle no energy is lost in friction. For $\theta$  greater than the critical angle the ball will slip and energy will be lost due to friction. If the angle is 900 the ball falls straight down and there is no friction, so no energy us lost. There must then be some angle where the most energy is lost in friction.