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Homework Help: Trouble w/ Vector Dot Product

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    A cutting tool under microprocessor control has several forces acting on it. One force is [itex]\vec{F}[/itex]=-αxy2[itex]\hat{j}[/itex], a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α=2.50 N/m3. Consider the displacement of the tool from the origin to the point x=3.00m, y=3.00m.

    (a) Calculate the work done on the tool by [itex]\vec{F}[/itex] if this displacement is along the straight line y=x that connects these two points.

    2. Relevant equations


    3. The attempt at a solution

    I'm trying to use the equation above, so here's what I know:


    Since it's the dot product,

    I'm confused as to why the right side of that equation is equal to -αy3dy, as the textbook solution suggests. Any help is appreciated.
  2. jcsd
  3. Oct 24, 2011 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    If x = y then [itex]-axy^2 = -ay^3[/itex]

    The dot product of the two vectors is:

    [itex]\vec{a} \cdot \vec{b} = ab\cos\theta[/itex]

    where [itex]\theta[/itex] is the angle between the two vectors.

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