A solid uniform marble and a block of ice, each with the same mass, start from r

Question

A solid uniform marble and a block of ice, each with the same mass, start from rest at the same height H above the bottom of a hill and move down it. The marble rolls without slipping, and the ice slides without friction. (a) Find the speed of each of these objects when they reach the bottom of the hill. (b) Which object is moving faster at the bottom, the block of ice or the marble? (c) Which object has more kinectic energy at the bottom, the block of ice or the marble? Pls try to give the explanation..thanks

Explanation / Answer

for marble, take distance traveled down ramp to be x = H/sintheta ( H is hight of ramp, sin is incline) v =(2gx) for ice, a=g*sin theta, therefore acceleration for a rolling sphere is less than thatof an object rolling without friction because some energy goes intothe rotational energy of the marble the objects have the same potential energy because totalpotential enery added to the systems are equal, even though the icehas greater velocity, the marble has energy stored in its angularmomentum equal to the difference. :)

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