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

2024
Views:

153

Pages:

2
Author:

Bettottifof

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 129. First, reduce the given force system to a force-couple system at the origin. Have ΣF : ( 2P ) i − ( P ) j + ( P ) j = R ∴ R = ( 2P ) i Have ΣM O : Σ ( rO × F ) = M OR M OR i j k i j k = Pa 2 2 2.5 + 0 0 4 = Pa ( −1.5i + 5j − 6k ) 2 −1 0 0 1 0 R = 2Pi (a) or Magnitude of R = 2P Direction of R : θ x = 0°, θ y = −90°, θ z = 90° (b) Have M1 = λ R ⋅ M OR λR = R R = i ⋅ ( −1.5Pai + 5Paj − 6Pak ) = −1.5Pa and pitch . P= M1 −1.5Pa = = −0.75a R 2P or P = −0.75a COSMOS: Complete Online Solutions Manual Organization System M OR = M1 + M 2 (c) Have ∴ M 2 = M OR − M1 = ( 5Pa ) j − ( 6Pa ) k Require M 2 = rQ/O × R ( 5Pa ) j − ( 6Pa ) k = ( yj + zk ) × ( 2Pi ) = − ( 2Py ) k + ( 2Pz ) j From i : 5Pa = 2Pz ∴ z = 2.5a From k : − 6Pa = −2Py ∴ y = 3a ∴ The axis of the wrench is parallel to the x-axis and intersects the yz-plane at y = 3a, z = 2.5a .

COSMOS Chapter 3 Solution 129

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