A ball is rolling along at speed without slipping on a horizontal surface when it comes to a hill that rises at a constant angle above the horizontal. In which case will it go higher up the hill: if the hill has enough friction to prevent slipping or if the hill is perfectly smooth? Justify your answers in both cases in terms of energy conservation and in terms of Newton’s second law.

Solution 19DQ When the hill has friction, Let m be the mass, v be its speed, I be the moment of inertia and is the angular speed of the ball. Since the ball is in horizontal surface, initial potential energy is zero. Total energy when it is moving on the horizontal surface, 1 2 1 2 E i mv2 i + 2 …..(1) Let h be the distance moved by the ball upward the hill. Therefore, final energy, 1 2 1 2 E f mgh + mv 2 1 + 2 1 …..(2) When the hill has no friction, Initial energy, 1 2 1 2 E i mv2...