1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Vector calculus

  1. May 25, 2010 #1
    1. The problem statement, all variables and given/known data

    A force is applied to a particle, defined by:

    F(x,y)= (y^2, 2xy) << This is a verticle bracket with the y^2 ontop of the 2xy

    The path of the particle is straight. The particle moves from (-1,2) to (1,3)

    i) Calculate the work that the force F does as the particle moves along the path C by evaluating the appropreate line integral directly

    I dont know where to start with this. I know that work: w = fd so to get the distance i must do some integration, but how do you integrate a vector like that?

    Can somone please help!? - would be much appreciated

    Many thanks
  2. jcsd
  3. May 25, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What do you mean by that? Force is a vector, not a fraction???
    w = fd only works for constant forces along straight lines. Perhaps you mean

    [tex] W = \int_C \vec F \cdot d\vec R[/tex]
  4. May 25, 2010 #3
    Hi there! thanks for your help

    sorry about the fraction thing.. what i ment was that it is a vector but written vertically not horizontally... so still a vector but not (y^2, 2xy) .. Im damn useless at LaTeX so i cant make it with a large bracket and the y^2 at the top and the 2xy at the bottom.. hope that makes sense

    Also i was only making a guess with the w=fd thing, im sure your expression is what im looking for as it uses vectors.

    What would be the next logical thing to do with it?

    Thanks again
  5. May 25, 2010 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Click on the formula below to see the LaTeX for writing the column vector.

    [tex]\textbf{F} = \begin{pmatrix} y^2 \\ 2xy \end{pmatrix}[/tex]
  6. May 26, 2010 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Parameterize the line as

    [tex]\vec R(t) = \langle x(t), y(t), z(t)\rangle[/tex]

    and use

    [tex]\int_C \vec F \cdot d\vec R = \int_a^b \vec F(t)\cdot \frac {d\vec R}{dt}\, dt[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook