Force and potential energy of a particle

[dkgojackets]

Homework Statement

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.

Homework Equations

work-energy theorem, PE = mgh

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?

 

[radou]

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

 

[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.

 

[radou]

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.

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

 

[dkgojackets]

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

So it is the same as the work done?

 

[radou]

So it is the same as the work done?

Yes, it is.

 

[dkgojackets]

Ack, but negative. Got it now.