Explanation Given info: The radius of hemispherical bowl is R . Explanation: Formula to calculate the initial potential energy of the sliding mass, U i = m g h i U i is the initial potential energy of the sliding mass m is the identical masses g is gravitational acceleration h i is initial height of sliding mass Substitute R for h i to find U i , U i = m g ( R ) = m g R Formula to calculate the initial kinetic energy of the system, K i = 1 2 m v i 2 K i is the initial kinetic energy of the sliding mass m is the identical masses v i is the initial velocity of sliding mass Both masses are at rest initially. Therefore, the initial kinetic energy of the sliding mass is zero. K i = 0 Formula to calculate the final potential energy of the system, U f = m g h f U f is final potential energy of the system when sliding mass reaches at bottom m is the identical masses g is gravitational acceleration h f is final height of sliding mass Both masses reach at the bottom point. Therefore final height of both masses is zero. Therefore, U f = 0 Formula to calculate the final kinetic energy of the sliding mass, K f = 1 2 m v f 2 K f is the final kinetic energy of the sliding mass m is the identical masses v f is the final velocity of the sliding mass Expression for law of conservation of energy, U i + K i = U f + K f Substitute m g R for U i , 0 for K i , 0 for U f and 1 2 m v f 2 for K f to find v f . m g R + 0 = 0 + 1 2 m v f 2 v f 2 = 2 g R v f = 2 g R Thus, the final velocity of the sliding mass is 2 g R

14th Edition

ISBN: 9780133969290

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Chapter 8, Problem 8.82P

To determine

The height above the bottom of the bowl they will go after colliding.

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Chapter 8, Problem 8.81P

Chapter 8, Problem 8.83P

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Chapter 8 Solutions

University Physics (14th Edition)

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The height above the bottom of the bowl they will go after colliding.

Solution Summary: The author explains that the height above the bottom of the bowl they will go after colliding is R/4.

The height above the bottom of the bowl they will go after colliding.

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Chapter 8 Solutions