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Brian Cohen
Brian Cohen asked in Science & MathematicsPhysics · 7 years ago

Can someone help me with moments produced in a 3D force system?

A 3D force F=180kN is applied at point A (4, 5, 2) and directed towards point B (6, 1, 6). Point C has x, y and z coordinates of (-2, 5, -2).

What are the three components of the moment produced by F about the point C?

1 Answer

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  • EM
    Lv 7
    7 years ago
    Favorite Answer

    AB = <6 - 4, 1 - 5, 6 - 2> = <2, -4, 4>

    ||AB|| = sqrt[2² + (-4)² + 4²] = 6

    F = 180 <2/6, -4/6, 4/6> = <60, -120, 120> kN

    Assuming length units of meters,

    r = CA = <4 - (-2), 5 - 5, 2 - (-2)> = <6, 0, 4> m

    τ = r x F

    τ = <6, 0, 4> m x <60, -120, 120> kN

    τ = <(0)(120) - (4)(-120), (4)(60) - (6)(120), (6)(-120) - (0)(60)> kN-m

    τ = <480, -480, -720> kN-m

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