Explanation Given: The mass of the collar is 20 kg . The uncompressed length of the springs is 1 m . The speed of the collar is 2 m/s at s = 0 . The stiffness of the spring is k A = 50 N/m and k B = 100 N/m . Write the formula for work done by spring on thecollar. U S = 1 2 k s 2 (I) Here, k is the stiffness of the spring and s is the compression length of the spring. Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (II) Here, m is the mass of the object and v is the velocity of the object. Write the formula for Principle of Work and Energy. T 1 + ∑ U 1 − 2 = T 2 (III) Here, T 1 is initial kinetic energy, T 2 is final kinetic energy and ∑ U 1 − 2 is total work done by all the forces on the collar. Conclusion: Calculate the work done by spring A . Substitute 50 N/m for k in Equation (I). U S A = 1 2 × 50 N/m × s 2 = 25 s 2 J Calculate the work done by spring B . Substitute 100 N/m for k in Equation (I). U S B = 1 2 × 100 N/m × s 2 = 50 s 2 J Calculate the total work done by the springs. ∑ U 1 − 2 = − U S A − U S B Substitute 25 s 2 for U S A and 50 s 2 for U S B

14th Edition

ISBN: 9780133976717

Author: HIBBELER, Russell C.

Publisher: Pearson Education

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Chapter 14.3, Problem 29P

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Themaximum compression of spring due to back and forth motion of collar.

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Chapter 14.3, Problem 28P

Chapter 14.3, Problem 30P

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Chapter 14 Solutions

Engineering Mechanics Dynamics

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