1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trouble w/ Vector Dot Product
Loading...