(a) Explanation Given information: The Weight of block B ( W B ) is 10 lb. The Weight of wedge A ( W A ) is 5 lb. The compressive load ( P ) is 50 lb. Calculation: Find the mass of wedge A ( m A ) using the relation: m A = W A g Here, g is the acceleration due to gravity. Substitute 5 lb for W A and 32.2 ft/s 2 for g . m A = 5 32.2 = 0.1553 lb .s 2 ft Find the mass of block B ( m B ) using the relation: m B = W B g Substitute 10 lb for W B and 32.2 ft/s 2 for g . m B = 10 32.2 = 0.3106 lb .s 2 ft Sketch the free body and kinetic diagram of Wedge A as shown in Figure (1). Refer Figure (1). Apply Newton’s law of motion along x - axis: Σ F x = m a x − 10 + N A B sin ( 8 ° ) = − m A a A Here, N A B is the force of between wedge A and block B and a A is the acceleration of wedge A . Substitute 0.1553 lb .s 2 ft for m A . − 10 + N A B sin ( 8 ° ) = − m A a A − 10 + N A B sin ( 8 ° ) = − ( 0.1553 ) a A 0.1392 N A B + 0.1553 a A = 10 (1) Apply Newton’s law of motion along y - axis: Σ F y = m a y N A − 5 − N A B cos ( 8 ° ) = 0 N A − 0.9903 N A B = 5 (2) Here, N A is the normal force on block A . Sketch the free body and kinetic diagram of block B as shown in Figure (2). (b) To determine Find the force between A and B .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 12.1, Problem 12.21P

(a)

To determine

Find the acceleration of block B.

(b)

To determine

Find the force between A and B.

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Chapter 12.1, Problem 12.20P

Chapter 12.1, Problem 12.22P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the acceleration of block B .

Solution Summary: The author calculates the mass of wedge A using Newton's law of motion along x - axis.