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

2023
Views:

277

Pages:

1
Author:

Quintin Ware

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 32. FBD Plate: Assume reactions as shown, at ends of sleeves, FA = µ s N A , For impending slip FB = µ s N B P sin θ − µ s N A − µ s N B = 0 ΣFx = 0: N A + N B = 2.5 P sin θ ΣFy = 0: N A − N B − P cosθ = 0, Solving: N A = ΣM B = 0: P ( 2.5sin θ + cosθ ) , 2 N A − N B = P cosθ NB = P ( 2.5sin θ − cosθ ) (1) 2 ( 23.5 in.) P sin θ − (16 in.) N A + (1 in.) FA = 0 ( 23.5 in.) P sin θ P − 16 in. − 0.4 (1 in.)  ( 2.5sin θ + cosθ ) = 0 2 4sin θ − 7.8cosθ = 0, (2) θ = 62.9° For θ > 62.9°, the panel will be self locking, ∴ motion for θ ≤ 62.9°. As θ decreases, N B will reverse direction at 2.5sin θ − cosθ = 0, (see equ. 1) or at θ = 21.8°. So for θ ≤ 21.8° ΣFx = 0 : P sin θ − µ s ( N A + N B ) = 0 N A + N B = 2.5 P sin θ ΣFy = 0: N A + N B − P cosθ = 0, ∴ 2.5sin θ = cosθ , N A + N B = P cosθ θ = 21.8° So impending motion for 21.8° ≤ θ ≤ 62.9° W 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.