A child rolls a 0.600-kg basketball up a long ramp. The

Solution 84P Step 1: Initially, the energy possessed by the ball was purely Kinetic. Once it climbs the ramp, the kinetic energy will be converted to potential energy and some amount of work done due to frictional force. So, we can write, KE initialW fPE top We know that, KE = ½ mv + ½ I 2 initial Where, m - mass of the basket ball v - initial velocity of the ball I - moment of inertia of the ball - Angular velocity of the ball 2 Where, ½ mv = translational kinetic energy 2 ½ I = Rotational kinetic energy of the ball We know that, I = mr for the basketball since, it is considered as a hollow sphere. Angular velocity of the ball, = v/r Where, r - radius of the ball 2 2 2 2 Then, ½ I = ½ × × mr × (v/r) = mv 2 2 2 Therefore, KE initial mv + mv = mv Therefore, mv = mgh - W --------------------- (1) f Where, g - acceleration due to gravity h - maximum vertical height of the ball in the ramp