Explanation Given: The mass of the block ( A ) is 12 lb . The mass of the block B and C is 15 lb . Initially all the blocks are at rest. At final the motion of all the blocks momentarily stopped. Draw the free body diagram of the blocks as shown in Figure (1). From Figure (1). Write the formula for maximum displacement ( y ) of the block ( A ) at middle of the blocks B and C . D E = y Write the formula for displacement of the blocks B and C . s = F D − F E (I) Write the formula to calculate the work done by the weight of the block ( W ) . U W = W s (II) Here, W is the weight of the block and s is the displacement. Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (III) Here, m is the mass of the object and v is the velocity of the block. Write the formula for Principle of Work and Energy. T 1 + ∑ U = T 2 (IV) 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 block. Conclusion: Refer Figure (1). Calculate the displacement of the blocks B and C . Use Pythagoras theorem to calculate F D . F D = F E 2 + D E 2 = 4 2 + y 2 Substitute 4 2 + y 2 for F D and 4 ft for F E in Equation (I). s = 4 2 + y 2 − 4 ft Calculate the work done by block A Substitute 12 lb for W and y for s in Equation (II). U W ( A ) = 12 lb ( y ) = 12 y Calculate the work done by blocks B and C . Substitute 15 lb for W and 4 2 + y 2 − 4 ft for s in Equation (II). U W ( B and C ) = 2 × 15 lb ( 4 2 + y 2 − 4 ft ) = 2 ( 15 ) ( 4 2 + y 2 − 4 ) Calculate total work done on the block ( ∑ U ) . ∑ U = U W ( A ) − U W ( B and C ) Substitute 12 y for U W ( A ) and 2 ( 15 ) ( 4 2 + y 2 − 4 ) for U W ( B and C )

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.3, Problem 18P

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The maximum displacement due to the block (A) at the middle between the blocks B and C .

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Chapter 14 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The maximum displacement due to the block ( A ) at the middle between the blocks B and C .

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