Explanation Write the expression for total energy of the block before the release and after the release using work energy theorem. K i + W s + W g = K f (I) Here, K i is the initial kinetic energy, W s is the work done by the spring, W g is the work done by the gravity on the block, and K f is the final kinetic energy of the block. Write the expression for initial kinetic energy of the block. K i = 1 2 m v i 2 (II) Here, K i is the initial kinetic energy of the block, m is the mass of the block, and v i is the initial velocity of the block. Write the expression for initial kinetic energy of the block. K f = 1 2 m v f 2 (III) Here, K f is the initial kinetic energy of the block, and v f is the final velocity of the block. Write the expression for work done by the spring on the block. W s = 1 2 k x sp, i 2 − 1 2 k x sp, f 2 (IV) Here W s is the work done by the spring on the block, 1 2 k x sp, i 2 is the initial energy of the block, and 1 2 k x sp, f 2 is the final energy of the block. Write the expression for work done by the gravity on the block. W g = m g sin θ ( d + x ) (V) Here, W g is the work done by the gravity on the block, m is the mass of the ball, g is the acceleration due to gravity, and sin θ ( d + x ) is the distance block moves against the gravity. Use equation (II), (III), (IV), and (V) in equation (I). 1 2 m v i 2 + ( 1 2 k x sp, i 2 − 1 2 k x sp, f 2 ) + m g sin θ ( d + x ) = 1 2 m v f 2 (VI) Since the initial velocity of the block and the final velocity of the block is zero, the spring displaces an initial distance of x , and the angle between the horizontal and the inclined plane in which the block moves is 20.0 ° , the above equation is reduced to 1 2 m v 2 + ( 0 − 1 2 k x 2 ) + m g sin θ ( d + x ) = 0 (VII) Divide the equation (VII) by m and rearrange

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

5th Edition

ISBN: 9781133422013

Author: Raymond A. Serway; John W. Jewett

Publisher: Cengage Learning

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Chapter 6, Problem 62P

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The distance the spring is compressed when the block comes to rest momentarily.

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Chapter 6, Problem 61P

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