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

2024
Views:

486

Pages:

1
Author:

lankstoetp12

COSMOS: Complete Online Solutions Manual Organization System Chapter 8, Solution 43. FBD A: For impending motion A must start up and C down the incline. Since the normal force between A and B is less than that between B and C, and the friction coefficients are the same, Fmax will be reached first between A and B, and B and C will stay together. ΣFy = 0: Impending slip: ΣFx = 0: N1 − ( 4 lb ) cos 30° = 0, F1 = µ s N1 = 2 3µ s lb T − ( 4 lb ) sin 30° − 2 3µ s lb = 0 ( FBD B and C: N1 = 2 3 lb ) T = 2 1 + 3µ s lb ΣFy = 0: N 2 − 2 3 lb − ( 3 lb + 8 lb ) cos 30° = 0 N2 = Impending slip: ΣFx = 0: (1) 15 3 lb 2 15 3µ s lb 2  15   3  µs  lb − ( 3 + 8) lbsin 30° = 0 T +  2 3 +   2  F2 = µ s N 2 =  11 19  3µ s  lb T = − 2 2  FBD B: Equating (1) and (2): ( (2) ) 4 1 + 3µ s lb = 11 − 19 3µ s 23 3 µ s = 7, µ s min = 0.1757 W To check slip reasoning above: ΣFy = 0: N3 − 2 3 lb − ( 3 lb ) cos 30° = 0, F3max = µ s N3 = ΣFx = 0: N3 = 7 3 lb 2 7 3µ s 2 − ( 3 lb ) sin 30° + 2 3µ s lb − F3 = 0 F3 = 2 3 ( 0.1757 ) lb − 3 lb = − 0.891 lb 2 F3 < F3max , OK 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.