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27 July, 17:43

A particle moves along a straight path through a displacement d = 2.5i + cj while a force F = 8.5i + - 8.5j acts on it. The displacement is measured in meters and the force is measured in Newtons. (Other forces also act on the particle.) What is the value of c if the work done by F on the particle is zero?

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  1. 27 July, 18:09
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    Work is defined as the scalar product of force and distance

    W=F•d

    Given that

    F = 8.5i + - 8.5j. + * -=-

    F=8.5i-8.5j

    d = 2.5i + cj

    If the work in the practice is zero, then W=0

    therefore,

    W=F•ds

    0=F•ds

    0 = (8.5i - 8.5j) • (2.5i + cj)

    Note that

    i. i=j. j=k. k=1

    i. j=j. i=k. i=i. k=j. k=k. j=0

    So applying this

    0 = (8.5i - 8.5j) • (2.5i + cj)

    0 = (8.5*2.5i. i + 8.5*ci. j - 8.5*2.5j. i-8.5*cj. j)

    0=21.25-8.5c

    Therefore,

    8.5c=21.25

    c=21.25/8.5

    c=2.5
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