University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

218

Pages:

1
Author:

Caroline Mcfarland

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 33. FBD Plate: Assuming reactions as shown, at ends of sleeves, For impending slip FB = µ s FB P sin θ − µ s ( N A + N B ) = 0 ΣFx = 0: ΣFy = 0: FA = µ s N A , N A + N B = 2.5 P sin θ (1) N A − N B = P cosθ (2) N A − N B − P cosθ = 0, NA = Solving: P ( 2.5sin θ + cosθ ) , 2 NB = P ( 2.5sin θ − cosθ ) 2 Note that, for θ < 21.8°, N B becomes negative, so we must change equ. 2 to N A + N B = P cosθ , ( 2′ ) but equ. (1) does not change. Solving (1) and ( 2′ ) gives P cosθ = 2.5P sin θ , or θ = 21.8°, so the lower limit for impending slip is θ = 21.8°. For θ ≥ 21.8°, the forces are as shown, and ΣM B = 0: ( 23.5 in.) P sin θ + xP cosθ + (1 in.) FA − (16 in.) N A = 0 P + x P cosθ + 0.4 (1 in.) − (16 in.)  ( 2.5sin θ + cosθ ) = 0 2 x 4sin θ − ( 7.8 in.) − x  cosθ = 0, tan θ = 1.950 − 4 in. ( 23.5 in.) P sin θ or (a) For x = 4 in., tan θ = 1.950, θ = 43.5°. For θ > 43.5° self locking ∴ impending motion for 21.8° ≤ θ ≤ 43.5° W (b) As x increases from 4 in., the upper bound for θ decreases, becoming 21.8° ( tan θ = 0.4000 ) when x = ( 4 in.)(1.950 − 0.400 ) = 6.2 in. Thus xmax = 6.20 in. W at which θ must equal 21.8°. Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.

COSMOS Chapter 8 Solution 33

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