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

2020
Views:

265

Pages:

2
Author:

Andrioliwbf

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 134. First reduce the given force system to a force-couple at the origin at B. 15   8 Have ΣF : − ( 79.2 lb ) k − ( 51 lb )  i + j = R 17   17 (a) ∴ R = − ( 24.0 lb ) i − ( 45.0 lb ) j − ( 79.2 lb ) k and R = 94.2 lb ΣM B : rA/B M RB Have × FA + M A + M B = M RB i j k 15   8 = 0 −20 0 − 660k − 714  i + j  = 1584i − 660k − 42 ( 8i + 15 j) 17 17   0 0 −79.2 ∴ M RB = (1248 lb ⋅ in.) i − ( 630 lb ⋅ in.) j − ( 660 lb ⋅ in.) k (b) Have M1 = λ R ⋅ M OR = λR = R R −24.0i − 45.0 j − 79.2k ⋅ (1248 lb ⋅ in.) i − ( 630 lb ⋅ in.) j − ( 660 lb ⋅ in.) k  94.2 = 537.89 lb ⋅ in. . COSMOS: Complete Online Solutions Manual Organization System M1 = M 1λ R and = − (137.044 lb ⋅ in.) i − ( 256.96 lb ⋅ in.) j − ( 452.24 lb ⋅ in.) k Then pitch p = or p = 5.71 in. (c) M1 537.89 lb ⋅ in. = = 5.7101 in. 94.2 lb R Have M RB = M1 + M 2 ∴ M 2 = M RB − M1 = (1248i − 630 j − 660k ) − ( −137.044i − 256.96 j − 452.24k ) = (1385.04 lb ⋅ in.) i − ( 373.04 lb ⋅ in.) j − ( 207.76 lb ⋅ in.) k Require M 2 = rQ/B × R i j k 1385.04i − 373.04 j − 207.76k = x 0 z −24 −45 −79.2 = ( 45z ) i − ( 24 z ) j + ( 79.2 x ) j − ( 45x ) k From i: From k: 1385.04 = 45z −207.76 = −45x ∴ z = 30.779 in. ∴ x = 4.6169 in. ∴ The axis of the wrench intersects the xz-plane at x = 4.62 in., z = 30.8 in. .