Confusing Force function

DrummingAtom

1. The problem statement, all variables and given/known data
The force on a particle is directed along an x axis and given by [tex] F = F_0(\frac {x}{x_0} -1) [/tex]. Find the work done by the force in moving the particle from x = 0 to [tex] x = 2x_0 [/tex]


2. Relevant equations
F=ma, W=Fd, etc.


3. The attempt at a solution
I don't even know how to interpret that function. Does the [tex] x_0 [/tex] mean the initial position? Does [tex] F_0 [/tex] mean the initial force? I'm so confused. Any help would be appreciated.

tiny-tim

Hi DrummingAtom!

(try using the X₂ tag just above the Reply box )
That's right …

a "0" subscript always means a constant (usually the value at t = 0).

(oh … except in relativity, where x₀ means time! )

DrummingAtom

I'm still confused on this one. So, if _{x0 F0} are constants then how would the graph of this function look? Because they want you to graph F(x) before integrating. I mean what do you pick for your constant in a situation like this? I know it's going to be a linear function.

collinsmark

It doesn't really matter, as long as x₀ is not 0 (otherwise you'll have a divide by zero problem). But if you want to make your life easier, put it on the positive x-axis somewhere. I suggest putting it at x = 1. That way you'll integrate from 0 to 2. But don't label you x-axis with '1' and '2'; rather label you x-axis to go from

0....x₀...2x₀...3x₀...

Now when you consider your graph's labels, you are integrating from 0 to 2x₀, as the problem specifies!

The y-axis is F. So where does F₀ fit into your graph? I'll let you do that.