# What is the work done by a hiker who is climbing up a hill

1. May 5, 2007

### Weave

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
$$W=\int_{a}^{b}F dx$$

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 $$W=Fdelta x$$
$$delta x$$ can be obtained from f(b)-f(a).
If the force is not constant we do
$$W=\int_{f(a)}^{f(b)}F dx$$
Right?

Last edited: May 5, 2007
2. May 5, 2007

### turdferguson

Is the elevation a function of x? Neglecting friction, work would just be $$mgdeltax$$

3. May 5, 2007

### Weave

I am not sure, my Prof. said that the equation is just the equation of the hill.

4. May 5, 2007

### rootX

Shoudn't it be $$W=\int_{a}^{b}F dx$$
instead of $$W=\int_{f(a)}^{f(b)}F dx$$?
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.

5. May 5, 2007

### Weave

So how about the equation of the hill- f(x)?

6. May 5, 2007

so..........

7. May 5, 2007

### rootX

:shy:
I dunn know, I was just guesing

8. May 5, 2007

### husky88

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