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Math Help - applied work problem

  1. #1
    ggw
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    applied work problem

    a force F with 8N has direction vector 5i+9j-3k. the force pushes an object on a ramp in a straight line from the point (2,3,0) to the point (4,9,15), where the coordinates are measured in meters. Find the amount of work done by the force
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ggw View Post
    a force F with 8N has direction vector 5i+9j-3k. the force pushes an object on a ramp in a straight line from the point (2,3,0) to the point (4,9,15), where the coordinates are measured in meters. Find the amount of work done by the force
    First the displacement of the object is
    (4, 9, 15) - (2, 3, 0) = (2, 6, 15)
    which has a magnitude of sqrt(2^2 + 6^2 + 15^2) = 16.278820596

    The magnitude of the direction vector of the force is
    sqrt(5^2 + 9^2 + 3^2) = 10.723805295
    The angle between the force and the displacement is
    cos(t) = (5i + 9j - 3k) (dot) (2i + 6j + 15k)/(|5i + 9j - 3k|*|2i + 6j + 15k|)

    cos(t) = (10 + 54 - 45)/(10.723805295*16.278820596) = 0.108838299

    W = F (dot) s = |F|*|s|*cos(t) = (8 N)*(16.278820596 m)*0.108838299 = 14.174073147 J

    Thus W = 14 J.

    -Dan
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