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8 April, 23:51

Find the Cartesian components of force PP acting in the x, y, and z directions given P=50.0 NP=50.0 N, α=143.5∘α=143.5∘, β = 70.0∘β = 70.0∘, and γ=60.9∘γ=60.9∘. Recall that αα is the angle between the vector and the x axis, ββ is the angle between the vector and the y axis, and γγ is the angle between the vector and the z axis.

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  1. 9 April, 02:31
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    vec (F) = [ - 40.193 i + 17.101 j + 24.317 k ]

    Explanation:

    Given:

    -The force P = 50.0 N

    - Angle with x-axis α = 143.5

    - Angle with y-axis β = 70.0

    - Angle with z-axis γ = 60.9

    Find:

    Find the Cartesian components of force P acting in the x, y, and z directions,

    Solution:

    - The Force vector in the Cartesian coordinate system is given by the dot product of the Force P and the unit vector in its direction.

    F. unit (u) = vec (F)

    - Where, the unit vector is defined as:

    unit (u) = [ cos (α) i + cos (β) j + cos (γ) k ]

    - Using the given unit angles α, β, and γ compute unit (u):

    unit (u) = [ cos (143.5) i + cos (70) j + cos (60.9) k ]

    unit (u) = [ - 0.80386 i + 0.34202 j + 0.48634 k ]

    - The force vector is:

    vec (F) = 50.[ - 0.80386 i + 0.34202 j + 0.48634 k ]

    vec (F) = [ - 40.193 i + 17.101 j + 24.317 k ]
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