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

2022
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418

Pages:

1
Author:

Lamghari6kx

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 12. FBD top block: Note that, since φ s = tan −1 µ s = tan −1 ( 0.40 ) = 21.8° > 15°, no motion will impend if P = 0, with or without cable AB. (a) With cable, impending motion of bottom block requires impending slip between blocks, so F1 = µ s N ΣFy′ = 0: N1 − W1 cos15° = 0, N1 = W1 cos15° = 189.515 N F1 = µ s N1 = ( 0.40 )W1 cos15° = 0.38637 W1 F1 = 75.806 N FBD bottom block: ΣFx′ = 0: T − F1 − W1 sin15° = 0 T = 75.806 N + 50.780 N = 126.586 N ( ) W2 = ( 30 kg ) 9.81 m/s 2 = 294.3 N ΣFy = 0 : N 2 − (189.515 N ) cos (15° ) − 294.3 N + ( 75.806 N ) sin15° = 0 N 2 = 457.74 N F2 = µ s N 2 = ( 0.40 )( 457.74 N ) = 183.096 N FBD block: ΣFx = 0: − P + (189.515 N ) + ( 75.806 N ) cos15° + 126.586 N + 183.096 N = 0 P = 361 N (b) Without cable, blocks remain together ΣFy = 0: N − W1 − W2 = 0 N = 196.2 N + 294.3 N = 490.5 N F = µ s N = ( 0.40 )( 490.5 N ) = 196.2 N ΣFx = 0: − P + 196.2 N = 0 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. P = 196.2 N

COSMOS Chapter 8 Solution 12

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