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A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates (3.0 m, 4.1 m) while a constant force acts on it. The force has magnitude 2.4 N and is directed at a counterclockwise angle of 100° from the positive direction of the x axis. How much work is done by the force on the coin during the displacement?

  • Physics - ,

    Take the "dot product" of the force vector and the displacement vector. If i is the x unit vector and j is the y unit vector, the force vector is
    F = 2.4 sin 100 i + 2.4 cos 100 j
    The displacement vector is
    deltaR = 3.0 i + 4.1 j

    W = F . (deltaR)
    = 7.2 sin 100 + 9.84 cos 100

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