Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    W=∫[itex]\vec{F}[/itex][itex]\cdot[/itex]d[itex]\vec{l}[/itex]

    3. The attempt at a solution

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

    d[itex]\vec{l}[/itex]=dx[itex]\hat{i}[/itex]+dy[itex]\hat{j}[/itex]
    [itex]\vec{F}[/itex]=-αxy2[itex]\hat{j}[/itex]

    Since it's the dot product,
    [itex]\vec{F}[/itex][itex]\cdot[/itex]d[itex]\vec{l}[/itex]=dx+-αxy2dy.

    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

    User Avatar
    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.

    AM
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook