Explanation Given data: Compression length of the spring is 0.062 m. Speed of the object horizontally is 1.5 m s . Formula used: Write the expression for total mechanical energy. E = 1 2 m v 2 + 1 2 I ω 2 + m g h + 1 2 k x 2 (1) Here, E is the total mechanical energy, m is the mass, v is the velocity, I is the moment of inertia, ω is the angular speed, g is the acceleration due to gravity with the value 9.8 m s 2 , h is the height, k is the spring constant, and x is the displacement of the spring. Write the expression for angular frequency. ω = k m (2) Explanation: For the final mechanical energy, Substitute E f for E , v f for v , ω f for ω , h f for h and x f for x in equation (1), E f = 1 2 m v f 2 + 1 2 I ω f 2 + m g h f + 1 2 k x f 2 (3) For the initial mechanical energy, Substitute E 0 for E , v 0 for v , ω 0 for ω , h 0 for h and x 0 for x in equation (1), E 0 = 1 2 m v 0 2 + 1 2 I ω 0 2 + m g h 0 + 1 2 k x 0 2 (4) According to conservation of energy, initial mechanical energy is same as final mechanical energy, E f = E 0 Equate equations (3) and (4), 1 2 m v f 2 + 1 2 I ω f 2 + m g h f + 1 2 k x f 2 = 1 2 m v 0 2 + 1 2 I ω 0 2 + m g h 0 + 1 2 k x 0 2 (5) The initial velocity of the block is zero, since the block starts from rest, that is, v 0 = 0 m s

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ISBN: 9781119326342

Author: CUTNELL

Publisher: WILEY

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Chapter 10, Problem 37P

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Angular frequency.

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