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Which person exerted a force perpendicular to displacement?

  1. Feb 28, 2015 #1
    1. The problem statement, all variables and given/known data

    Jack and Jill are maneuvering a 3570kg boat near a dock. Initially the boat's position is [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png2,0,9[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngm [Broken] and its speed is 4.6m[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngs. [Broken] As the boat moves to position [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png12,0,0[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngm, [Broken] Jack exerts a force of [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png-80,0,290[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngN, [Broken] and Jill exerts a force [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png0,240,0[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngN. [Broken]

    How much work does Jack do?

    WJack= -3410 J

    How much work does Jill do?

    WJill= 0 J

    The second part of the question asks... Which person exerted a force perpendicular to the displacement of the boat?
    a) Neither Jack nor Jill.
    b) Both Jack and Jill.
    c) Jill
    d) Jack.

    I was able to find the Work correctly but not I am just having a little trouble with the second part.


    2. Relevant equations

    W=Fd



    3. The attempt at a solution

    At first, I thought it was Jack since Jack is the only person exerting Work. But then I thought Jill because she's exerting force, but just in the wrong direction (perpendicular?) so her work is 0. I only have one shot at this, is my reasoning ok for saying its Jill?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 28, 2015 #2
    Hi there,

    Firstly I took the difference between the starting and finishing vectors to get a movement vector of (10, 0, -9). Then there is the vector of force that Jill exerts (0, 240, 0).

    Two vectors are perpendicular if their dot product is zero. So in this case the dot product is (10x0)+(0x240)+(-9x0) = 0+0+0 = 0.

    So I'd say that yes, Jill's force vector is perpendicular to the displacement of the boat.

    Steven Thomas.
     
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