# Work done by General Variable force

1. Mar 10, 2012

### 1MileCrash

1. The problem statement, all variables and given/known data

The force on a particle is directed along an x-axis and is given by F = F0(x/x0 - 1).

Find the work done by the force in moving the particle from x = 0 to x = 2x0
2. Relevant equations

3. The attempt at a solution

It looks like the force is a recurrence relation or something...

$W = \int^{2x_{0}}_{0} F_{0}(x/x_{0}-1) dx$

I don't really understand.. unless I just take x0 to be the lower limit of integration, 0, and then 2x0 is just also 0, leaving me integrating from 0 to 0... which is just 0, but that seems to render this an absurdly stupid question.

Last edited: Mar 10, 2012
2. Mar 10, 2012

### ehild

F0 and x0 are undetermined constant.

ehild

3. Mar 10, 2012

### 1MileCrash

So x0 is could not be described as lower limit of integration? I see it as integrating from original x position to two times original x position, which in this case is 0 to 0, which means the integral is 0?

How do you view it?

4. Mar 10, 2012

### ehild

X0 is just a number and the upper limit of integration is 2X0, the lover limit is zero.

Yes, the integral is 0. The antiderivative is F0(x2/(2x0)-x), which returns 0 between the limits.

ehild