COSMOS Chapter 3 Solution 130 | Michigan State University - Edubirdie

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

2019
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476

Pages:

1
Author:

hivalye6w

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 130. First, reduce the given force system to a force-couple at the origin. ΣF : Pi − Pi − Pk = R Have ∴ R = − Pk ΣM O : − P ( 3a ) k − P ( 3a ) j + P ( −ai + 3aj) = MOR Have ∴ MOR = Pa ( −i − 3k ) Then let vectors ( R, M1 ) represent the components of the wrench, where their directions are the same. R = − Pk or Magnitude of R = P (a) Direction of R : θ x = 90°, θ y = 90°, θ z = −180° M1 = λ R ⋅ M OR (b) Have = −k ⋅  Pa ( −i − 3k )  = 3Pa and pitch (c) Have P= M1 3Pa = = 3a R P or P = 3a M OR = M1 + M 2 ∴ M 2 = M OR − M1 = Pa ( −i − 3k ) − ( −3Pak ) = − Pai Require M 2 = rQ/O × R − Pai = ( xi + yj) × ( − P ) k = Pxj − Pyi From i : − Pa = − Py or y =a j: x = 0 ∴ The axis of the wrench is parallel to the z-axis and intersects the xy plane at x = 0, y = a .

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