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!

Computing work from a vector field

  1. Dec 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Picture is attached. I am trying to find the work done by F (gradient vector field) in moving an object from point A to point B along the path C1.


    2. Relevant equations

    Work = the line integral of F along the curve C of F dot dr.

    3. The attempt at a solution

    Just not sure how to compute work from a graph instead of a function!
     

    Attached Files:

  2. jcsd
  3. Dec 10, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, C3 looks like a circle but the others are just random squiggles. Obviously you can't integrate along a path if you don't know the exact path.

    What you can do is hope that [itex]F\cdot dr[/itex] (which you don't tell us) is an "exact differential" (i.e. that this force field is conservative). If it is then the integral (work done) along the path depends only on the endpoints and not the path between them. Then you can do it in either of two ways: integrate along horizontal and vertical lines between the endpoints or find an anti-derivative os [itex]F\cdot dr[/itex] and evaluate at the endpoints.
     
  4. Dec 10, 2007 #3
    It is given that the force field is a gradient vector field/conservative. What do you mean by "integrate along horizontal and vertical lines between the endpoints"?
     
  5. Dec 10, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I mean exactly what I said! For example, for C1 it appears that the integration is from (1, 3/2) to (3 1/2, 2 1/2) so you could just do an integration for x= 1 to 3 and then y= 3/2 to 5/2.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?