COSMOS Chapter 8 Solution 128 - Edubirdie

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

2021
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277

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1
Author:

Sean Horton

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 128. ΣFn = 0: ∆θ ∆N − T + (T + ∆T )  sin =0 2 ∆N = ( 2T + ∆T ) sin or ΣFt = 0: ∆θ (T + ∆T ) − T  cos − ∆F = 0 2 or ∆F = ∆T cos Impending slipping: ∆F = µ s ∆N So In limit as So and ∆T cos ∆θ 2 ∆θ 2 ∆θ ∆θ sin ∆θ = µ s 2T sin + µ s ∆T 2 2 2 ∆θ → 0: dT = µ sTdθ , or dT = µ s dθ T dT T2 β ∫ T1 T = ∫ 0 µ s dθ ; ln T2 = µs β T1 or T2 = T1e µs β Note: Nothing above depends on the shape of the surface, except it is assumed to be a smooth curve. 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.

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