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Homework Help: What is the work done by a hiker who is climbing up a hill

  1. May 5, 2007 #1
    1. The problem statement, all variables and given/known data
    A hiker of mass(m) climbs up a hill( the equation of the hill is f(x), what is the work done on the interval [a,b]

    2. Relevant equations
    [tex] W=\int_{a}^{b}F dx[/tex]

    3. The attempt at a solution
    So for this problem I wanted to make sure. We would do:
    Assuming Force is constant, we would have [tex]W=Fdelta x[/tex]
    [tex]delta x[/tex] can be obtained from f(b)-f(a).
    If the force is not constant we do
    [tex] W=\int_{f(a)}^{f(b)}F dx[/tex]
    Last edited: May 5, 2007
  2. jcsd
  3. May 5, 2007 #2
    Is the elevation a function of x? Neglecting friction, work would just be [tex]mgdeltax[/tex]
  4. May 5, 2007 #3
    I am not sure, my Prof. said that the equation is just the equation of the hill.
  5. May 5, 2007 #4
    Shoudn't it be [tex] W=\int_{a}^{b}F dx[/tex]
    instead of [tex] W=\int_{f(a)}^{f(b)}F dx[/tex]?
    Because work is just area under the force-displacement graph.

    I think, for x, x is the horizontal distance and f(x) is the vertical distance.
  6. May 5, 2007 #5
    So how about the equation of the hill- f(x)?
  7. May 5, 2007 #6
  8. May 5, 2007 #7
    I dunn know, I was just guesing
  9. May 5, 2007 #8
    My guess is that the force is constant. I would agree with turdferguson.
    Work done depends only on the change in elevation.
    So W=mg*delta x
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