COSMOS Chapter 8 Solution 127 - Edubirdie

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

2024
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249

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1
Author:

bratrochanter

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 127. FBD wrench Note: EC = ( 0.20 m ) , sin 75° EA = EC − 0.03 m θ = 75° so β = 285° = 4.9742 rad ΣM E = 0:  0.20 m   0.20 m  − 0.03 m  F −  cos 75° − 0.03 m  T = 0   sin 75°   sin 75°  T = 7.5056 F ΣFx = 0: N sin 75° + F cos 75° − T = 0 Impending slip: N =  sin 75°  , so F =  + cos 75°  = T = 7.5056 F µs  µs  F sin 75° µs + cos 75° = 7.5056 µ s = 0.1333 Must still check impending slip of belt on pipe FBD small portion of belt at A ΣFn = 0: N1 − N 2 = 0 Impending slip F1 = µ s N1, F2 = µ s N 2 F1 = F2 = F so ΣFt = 0: 2 F − TA = 0, TA = 2 F Impending slip of belt on pipe T = TAe µ s β or µ s = 1 β ln T 1 7.5056 = = 0.2659 ln 2F 4.9742 2 This controls, so for self locking, 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. µ s min = 0.267

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