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!

Line integral setup

  1. Sep 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A squirrel weighing 1.2 pounds climbed a cylindrical tree by following the helical path

    [itex]x = \cos{t}, y = \sin{t}, z = 4t, 0 \leq t \leq 8 \pi [/itex]
    (distance measured in feet)

    How much work did it do?

    2. Relevant equations

    [itex]\int_{C} \vec{F} \cdot d\vec{r}[/itex]

    3. The attempt at a solution
    I've defined a curve [itex]C[/itex] by the vector

    [itex]\vec{r}(t) = \cos{t} \vec{i} + \sin{t} \vec{j} + 4t \vec{k}[/itex],
    [itex]0 \leq t \leq 8 \pi[/itex]

    I'm not sure where to go from here. Specifically, I don't know how to use the weight of the squirrel. Every other problem I've worked on explicitly gave me a vector field to work with.

    I know the bounds of the integral will be from 0 to 8π, and that r'(t) will be used.

    Thanks in advance!
     
  2. jcsd
  3. Sep 15, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The squirrel's weight points straight down. Try ##\vec F = \langle 0,0,-1.2\rangle##. And remember the line integral gives the work done by the force. You should be able to check your answer by comparing the change in potential energy.
     
  4. Sep 16, 2012 #3
    Got it, thanks.

    So I should get my answer with the following integral:

    [itex]W = \int^{8\pi}_{0} (0\vec{i} + 0\vec{j} - 1.2\vec{k}) \cdot (-\sin{t}\vec{i} + \cos{t}\vec{j} + 4\vec{k}) dt ?[/itex]

    This isn't for a physics course, and we haven't learned anything about potential energy. If the integral's setup is right, though, I can't take it from there.
     
  5. Sep 16, 2012 #4
    I'm not still new at line integrals so take this with a grain of salt.
    Take the dot product inside the integral, and integrate the answer.


    Potential energy close to the earth is [itex]E_p=mgh[/itex] so [itex]W=mgΔh[/itex] with m being mass, g gravitational acceleration and h is the heigth.
     
  6. Sep 16, 2012 #5
    Sorry, I meant I can take it from there. Thanks though!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Line integral setup
  1. Double Integral Setup (Replies: 8)

Loading...