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Net Work Done on an Object by 3 Forces

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Figure 7-30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.70 N, F2 = 5.31 N, and F3 = 9.69 N, and the indicated angles are θ2 = 50.8° and θ3 = 39.6°. What is the net work done on the canister by the three forces during the first 6.80 m of displacement?


    2. Relevant equations

    I didn't really use equations other than things that are obvious.

    W = Fd


    3. The attempt at a solution

    I found the x components of F2 and F3 and got 3.35608 and 7.46627 respectively. Since they are opposite of each other, I found the difference which was 4.11019.

    Then, since it seems as though F1 and the difference of F2 and F3 forms a 90 degree angle, I used Pythagorean theorem to find the overall force. That came out to be 4.91769.

    I plugged it into W=Fd and got 33.4403.

    I'm not sure where I went wrong. Any help would be appreciated.
     
  2. jcsd
  3. Oct 15, 2009 #2

    berkeman

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    Staff: Mentor

    Without a diagram, it's a little hard to check your work. Can you attach a PDF or JPEG of your problem?
     
  4. Oct 15, 2009 #3
  5. Oct 16, 2009 #4

    berkeman

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    Staff: Mentor

    Theta 2 and theta 3 are not opposite. Does that help?

    This type of problem is usually best done by adding force components in the x and y directions (rectangular coordinates). After you get the resultant force vector in rectangular coordinates, you can convert that to polar coordinates (magnitude and direction) if needed, as it is in this problem.
     
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