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Calculation of work involving unit vectors

  1. Nov 2, 2013 #1
    1. The problem statement, all variables and given/known data

    A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j
    How much work does the force you apply do on the grocery cart?

    2. Relevant equations

    3. The attempt at a solution

    I was assuming all I needed to do was do F*d for the i unit vector and j unit vector like so:
    W = (F*d)i + (F*d)j = (30*-9)i + (-40*-3)j = (-270J)i + (120J)j

    But according to the answer book, the final work has no unit vectors involved and it is the sum of those two calculated works.

    -270J + 120J = -150J

    How come the unit vectors are not included in the answer? Also, how come we can simply sum up the x and y W's and works like that? I know it has something to do with work being a scalar...
  2. jcsd
  3. Nov 2, 2013 #2
    Dot product gives you a scalar quantity. Also- i.i=1 not i.
  4. Nov 2, 2013 #3


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    Science Advisor
    Homework Helper

    hi bakakun028! welcome to pf! :smile:

    yes, work done is always a scalar quantity (an ordinary number) :wink:
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