1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Work - Line Integral

  1. Jun 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I have exam tomorrow and there's a problem I don't know how to do.

    Consider the curve C1 (x=-y^2+3y) and C2 (x=0), both defined for y[itex]\in[/itex][0,3].
    Calculate the work done by F(x,y)=(x,y^2) along the curve C=C1UC2 (retrograde direction).

    2. Relevant equations

    3. The attempt at a solution

    The solution given is 0. I really don't know how to get it. Thanks!
  2. jcsd
  3. Jun 21, 2012 #2


    Staff: Mentor

    When you traverse the curve do you wind up at your staring point? if so then the work is zero by definition, right?
  4. Jun 21, 2012 #3
    This is not true in general. (If you have a conservative force then it is true; this force happens to be conservative, but how would you show that?)

    You could parametrize the two separate trajectories as some r(t)=(x(t),y(t))

    Then use ∫f(r(t))*r'(t)dt on each curve.
  5. Jun 21, 2012 #4
    How do I do it for C2? I think this is the biggest problem for me.
  6. Jun 21, 2012 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You need to show your work before you can receive help here.
  7. Jun 21, 2012 #6
    Hint: Organize your work, write C2:, and then write notes for that region, like r(t)=(0,y(t)), F(x,y)=F(0,y)=... You'll have to decide on the rest of the parametrization for r(t) is, that is, what do you think y(t) should be. Decide on a and b in t=a...b. Et cetera; good luck!
  8. Jun 22, 2012 #7


    User Avatar
    Science Advisor

    As algebrat suggests, following on what jedishrfu said (hopefully jedishrfu had already noted, but forgot to say, that the force is conservative) the simplest way to do that is show that the force is conservative. portugese, do you know how to do that?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook