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A solid uniform spherical stone starts moving from rest atthe top of a hill. At the bottom of the hill the ground curvesupward, launching the stone vertically a distance $H$ below itsstart. How high will the stone go (a) if there is no friction on the hill and (b) if there is enough friction on the hill for the stone to roll without slipping? (c) Why do you get two different answers even though the stone starts with the same gravitational potential energy in both cases?

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a) $H$b) $\frac{5 H}{7}$c) In part (b) the stone ends up with rotational kinetic energy.

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

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Simon Fraser University

Hope College

University of Winnipeg

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in the first part of this question, we are going to kill. Play the high court by the stone when there is no friction sold. Decide is it using the law of conservation of energy? We can, right. MGH equals to one by two and we're square. So call it equating one hear mg etches the potential energy at the top and one over two m with square Is the candidate energy at the bottom using the same law we can also right. MGH equals to one by to him with square. That's quality quite into here. Captain alleges the launching distance off the storm. No comparing equating one into weekend right Somalis equals two capitalists. So this is the answer The first part of this question in part B. We have to kill clad the high court by the stone when that is friction. So let's decide. Is Jeff In order to complete this height, let me write few equations. Weak ones, too. Our omega No, let's ride the moment off. Initial for the stone I calls to two by five m r Square No looks, right. Equation Using the law of conservation of energy M g H F equals to one by two and we square. Let's call it a quiet and three using the same law we can also right. MGH equals to one by do and we're squared plus one. But I do Iomega Square. Let's call it equation for hear potential energy is equal Lento Translation. Kinetic Energy plus Rotation. Canada Energy. Now setting the value off I and Omega from these equations into equating four we can get MGH equals to one by to him, we square last one by two in tow to buy five more square Into Me by our old square. This is your plan to five by seven MGH You call stolen by doing we square. Let's call it equation. Five. No comparing equation three and five. We can right Jeff equals two 5.7 edge. Let's come toward the third part of this question. As in second cast, the potential energy is converted into both translation. Kinetic energy and the rotation Kinetic energy. That's why, and she's granted an edge of so I know the ocean

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