Explanation Given: The mass of the block A is m A = 10 kg . The mass of the block B is m B = 15 kg . The stiffness of the spring is k = 5 kN/m . Initially the spring is compressed to s = 200 mm and at rest. Write the principle of conservation of energy. T 1 + V 1 = T 2 + V 2 (I) Here, T 1 , T 2 is the initial and final kinetic energy and V 1 , V 2 is the initial and final potential energy. Write the formula for kinetic energy. T = 1 2 m A v A 2 + 1 2 m B v B 2 (II) Here, m is the mass, v is the velocity and the suffixes A , B indicates blocks A and B . Here, the motion occurs only at the datum. Hence the gravitational potential energy becomes zero. V g = 0 The total potential energy ( V ) is equal to the elastic potential energy ( V e ) . V = V e Write the formula for elastic potential energy ( V e ) . V e = V = 1 2 k s 2 (III) Here, k is the stiffness of the spring and s is the change in length of the spring. Write the principle of conservation of linear momentum. ∑ m v 1 = ∑ m v 2 (IV) Here, m is the mass of the freight car, v is the velocity of the freight car, the suffixes 1 , 2 indicates the initial and final stages. Conclusion: According to law of conservation of energy: At initial: Calculate the initial kinetic energy. When the blocks are at rest the kinetic energy becomes zero. T 1 = 0 Calculate the initial elastic potential energy. Substitute 5 kN/m for k and 200 mm for s in Equation (III). V 1 = 1 2 ( 5 kN/m × 1000 N 1 kN ) ( 200 mm × 1 m 1000 mm ) 2 = 100 J At final: Calculate the final kinetic energy. Substitute 10 kg for m A and 15 kg for m B in Equation (II). T 2 = 1 2 ( 10 kg ) ( v A ) 2 + 1 2 ( 15 kg ) ( v B ) 2 = 5 v A 2 + 7.5 v B 2 When the stretched spring is released from rest, the spring becomes unstretched and the elastic potential energy of the spring is zero. V 2 = 0 J Calculate the speed of the blocks

15th Edition

ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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Chapter 15, Problem 10FP

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Chapter 15 Solutions

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The speed of the both blocks A and B .

Solution Summary: The author explains the principle of conservation of energy and the suffixes A,B indicates blocks.

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Chapter 15 Solutions