# Force and potential energy

1. Dec 19, 2006

### dkgojackets

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

A conservative force F(x) = bx + a acts on a 2.61 kg particle, where x is in meters, b = 6.3 N/m, and a = 4 N. Calculate the change in potential energy of the particle as it moves along the x-axis from x1 = .749 m to x2 = 4.81 m.

2. Relevant equations

work-energy theorem, PE = mgh

3. The attempt at a solution

My first thought was simply 0, since it was going along the x-axis and therefore no change in PEg and no springs or such, but that was wrong. I solved that the work done by the force = 87.3556 J. I also solved initial kinetic energy if the final speed was 16.8 m/s, which was 280.9676. KEi + W = KEf. Where does the potential fall in?

2. Dec 19, 2006

For a conservative force, what is the relation between the force and its potential?

3. Dec 19, 2006

### dkgojackets

I remember doing potential energy diagrams...and force is the negative derivative of one. So potential is the integral of force? That's what I did to determine the total work done, though.

4. Dec 19, 2006

Right, that's all you have to do. Find the potential and calculate the change.

5. Dec 19, 2006

### dkgojackets

So it is the same as the work done?

6. Dec 19, 2006

Yes, it is.

7. Dec 19, 2006

### dkgojackets

Ack, but negative. Got it now.