(a) Explanation Given information: The weight ( W A ) of block A is 200 lb. The weight ( W B ) of block B is 350 lb. The static friction ( μ s ) between block A and the incline is 0.25. The kinetic friction ( μ k ) between block A and the incline is 0.20. Calculation: Assume at T = 175 lb , the Block B in equilibrium. Find the required friction force ( F r e q ) to maintain block A in equilibrium. Sketch the free body diagram of the block A as shown in Figure (1). Refer Figure (1), Consider equilibrium along x -axis (consider the direction of forces along x -axis are positive) Σ F x = 0 T − 200 sin 30 ° − F r e q = 0 Substitute 175 lb for T . 175 − 200 sin 30 ° − F r e q = 0 175 − 100 − F r e q = 0 F r e q = 75 lb Find the normal force ( N ) on the block A . Consider equilibrium along y -axis. (Consider the direction of forces along y -axis is positive). Σ F y = 0 N − 200 cos 30 ° = 0 N = 173.2 lb Find the actual friction force ( F M ) on the block A using the equation: F M = μ s N Substitute 0.25 for μ s and 173.2 lb for N . F M = 0.25 × 173.2 = 43.3 N Since F r e q > F M , blocks will move ( A up and B down). Write the general equation of mass ( m ) of the blocks. m = W g Here, W is the mass of the block and g is the acceleration due to gravity. The acceleration ( a B ) of block B is the half of the acceleration ( a A ) of block A . Sketch the free body diagram and kinetic diagram of the block A shown in Figure (2). Here, N is the normal force on the block A , F is the friction force between block A and incline, T is the tension in the rope, and m A is the mass of the block A . Refer Figure (2), Find the friction force ( F ) on block A using the equation: F = μ k N Substitute 0.20 for μ k and 173.2 N for N . F = ( 0.20 ) ( 173.2 ) = 34.64 lb Apply Newton’s law of equation along x -axis (Consider positive along x -axis). Σ F x = m A a A − 200 sin 30 ° − 34 (b) To determine The tension in the cable.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 12.1, Problem 12.14P

(a)

To determine

The acceleration of each block.

(b)

To determine

The tension in the cable.

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Chapter 12.1, Problem 12.13P

Chapter 12.1, Problem 12.15P

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

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