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Math Help - Work of force not working out

  1. #1
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    Work of force not working out

    I have a question about work done by force:

    If a 10N (newton) force acting in the direction of vector (1,1) moves an object from P =(-2,1) to Q=(5,6) calculate the work done. Distance measured in metres.

    I did vector PQ
    Q-P = (5,6) - (-2,1) = (7,5)
    Absolute value PQ = sqrt7^2 + 5^2 = sqrt74

    vector (1,1) is a 45 degree angle or 1/sqrt2

    next, work = (force)(QP)(1/sqrt2)
    10sqrt74(1/sqrt2)

    Im getting 5sqrt148 but the correct answer is 60sqrt2
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  2. #2
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    The problem is that work is actually equal to the dot product of force with displacement. That is,

    W=\mathbf{F}\cdot\mathbf{d}=\left(\dfrac{10}{\sqrt  {2}}\langle 1,1\rangle\right)\cdot\langle 7,5\rangle=\dots

    What do you get when you do that?
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  3. #3
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    so i'd do the dot product of (10/sqrt2,10/sqrt2).(7,5)?

    I got the answer doing that.
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  4. #4
    A Plied Mathematician
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    That'd work, too (pun intended).
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