(a) To determine Speed of the wheel at the bottom Explanation Consider a wheel with mass m and radius r rolling down through a inclined plane of height h . Initially, the wheel 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 wheel, g is the acceleration due to gravity and h is the height of the inclined plane. 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 wheel, I is the rotational inertia and ω is the angular velocity of the wheel. 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 wheel. Write the energy conservation equation. U = K E (IV) Substitute (I) and (III) in (IV) and write in terms of v . m g h = 1 2 m v 2 + 1 2 I ( v r ) 2 v 2 = m g h 1 2 ( m + I r 2 ) v = m g h 1 2 ( m + I r 2 ) (V) Conclusion: Substitute 9.8 m / s 2 for g and 29 (b) To determine Correct statement regarding the mass of the wheel.

4th Edition

ISBN: 9780134988559

Author: Wolfson, Richard

Publisher: Pearson Education,

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Chapter 10, Problem 43E

(a)

To determine

Speed of the wheel at the bottom

(b)

To determine

Correct statement regarding the mass of the wheel.

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Chapter 10, Problem 42E

Chapter 10, Problem 44E

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