and (b) Reflect: Its translational kinetic energy at the base of the hill is Its total kinetic energy is 20.9 J. This equals its final potential energy: 9.50. Set Up: The marble is a solid sphere and has Since the marble rolls without slipping, The block of ice has only translational kinetic energy. At the bottom of the hill, the marble has speed and the block has speed Use coordinates where is upward and at the bottom of the hill. Then and for each object. Solve: (a) Conservation of energy gives so marble: so and block of ice: and (b) The ice is moving faster at the bottom. (c) For each object, They have the same kinetic energy at the bottom. 9.51. Set Up: The solid cylinder has and the solid sphere has for each. Use coordinates where is upward and at the bottom of the hill. Then and for each object. Let the maximum heights h be and Solve: (a) Conservation of energy gives so cylinder: and sphere: and (b) The cylinder has a larger and hence more initial kinetic energy. (c)
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