Explanation A marble can be considered as a solid sphere with mass m and radius r Initially, the marble will have a potential energy. As it rolls down, the potential energy is transformed into linear and rotational kinetic energy. Write the equation for potential energy U = m g h (I) Here U is the potential energy, m is the mass of the marble, g is the acceleration due to gravity and h is the height from the bottom. Write the equation for kinetic energy. K E = 1 2 m v 2 + 1 2 I ω 2 (II) Here v is the velocity of the marble, I is the rotational inertia and ω is the angular velocity of the marble. Substitute ω = v r in (II) K E = 1 2 m v 2 + 1 2 I ( v r ) 2 (III) Here r is the radius of the marble. Write the equation for rotational inertia of a solid sphere I = 2 5 m r 2 (IV) Substitute (IV) in (III) K E = 1 2 m v 2 + 1 2 ( 2 5 m r 2 ) ( v r ) 2 = 1 2 m v 2 + 1 5 m v 2 = 7 10 m v 2 (V) Write the energy conservation equation

4th Edition

ISBN: 9780134988559

Author: Wolfson, Richard

Publisher: Pearson Education,

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Chapter 10, Problem 41E

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Speed of the marble at the bottom.

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Chapter 10, Problem 40E

Chapter 10, Problem 42E

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