Results 1 to 2 of 2

Thread: finding work by integrals

  1. #1
    s7b
    s7b is offline
    Junior Member
    Joined
    Jan 2009
    Posts
    58

    finding work by integrals

    Find the work done by the force F from (0,0,0) to (1,1,1) over the following path:

    The path of the line segment from (0,0,0) to (1,1,0) followed by the line segment from (1,1,0) to (1,1,1) where the Force F=(1/(x^2+1))j


    How do I set up this integral??
    Please help me out if you know how!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Work done by variable force

    Hello s7b
    Quote Originally Posted by s7b View Post
    Find the work done by the force F from (0,0,0) to (1,1,1) over the following path:

    The path of the line segment from (0,0,0) to (1,1,0) followed by the line segment from (1,1,0) to (1,1,1) where the Force F=(1/(x^2+1))j


    How do I set up this integral??
    Please help me out if you know how!
    The first line segment is in the plane $\displaystyle z=0$; the force is in the direction of the $\displaystyle y$-axis, and it moves along the line $\displaystyle y = x$ in the plane from $\displaystyle (0,0)$ to $\displaystyle (1,1)$. So as the point of application of the force moves from $\displaystyle (x,y)$ to $\displaystyle (x+\delta x,y+\delta y), \delta y = \delta x \Rightarrow$ work done = $\displaystyle F\delta y = F\delta x$.

    To find the work done, then, you'll need to evaluate $\displaystyle \int_0^1F\,dx$, where $\displaystyle F = \frac{1}{x^2+1}$

    The second part of the movement is parallel to the $\displaystyle z$-axis, and is therefore at right angles to the force. So it does a zero amount of work.

    Grandad
    Last edited by Grandad; Mar 23rd 2009 at 02:21 PM. Reason: Corrected solution
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. WHY Integrals work...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 20th 2010, 01:34 PM
  2. How To Work Out Integrals?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 9th 2009, 09:21 AM
  3. Integrals and work
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Sep 14th 2008, 07:38 PM
  4. Work and Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 13th 2008, 07:19 PM
  5. Integrals and work again
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 11th 2007, 02:24 PM

Search Tags


/mathhelpforum @mathhelpforum