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

2024
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214

Pages:

1
Author:

lankstoetp14

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 137. FBD Collar: Stretch of spring x = AB − a = a −a cosθ  a   1  − a  = (1.5 kN/m )( 0.5 m )  − 1 Fs = k  θ θ cos cos      1  = ( 0.75 kN )  − 1 = ( 750 N )( sec θ − 1) θ cos   Fs cosθ − W + N = 0 ΣFy = 0: W = N + ( 750 N ) (1 − cosθ ) or Impending slip: F = µ s N (F must be +, but N may be positive or negative) Fs sin θ − F = 0 ΣFx = 0: or F = Fs sin θ = ( 750 N )( tan θ − sin θ ) (a) θ = 20°: F = ( 750 N )( tan 20° − sin 20° ) = 16.4626 N Impending motion: (Note: for N = F µs 16.4626 N = 41.156 N 0.4 = N < 41.156 N, motion will occur, equilibrium for N > 41.156) W = N + ( 750 N )(1 − cos 20° ) = N + 45.231 N But So equilibrium for W ≤ 4.07 N and W ≥ 86.4 N W (b) θ = 30°: F = ( 750 N )( tan 30° − sin 30° ) = 58.013 N Impending motion: N = F µs = 58.013 = 145.032 N 0.4 W = N + ( 750 N )(1 − cos 30° ) = N ± 145.03 N = −44.55 N ( impossible ) , 245.51 N Equilibrium for W ≥ 246 N 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.

COSMOS Chapter 8 Solution 137

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