# Potential energy to force

1. Mar 8, 2016

### muhammed_oli

1. The problem statement, all variables and given/known data
The potential energy function for a system of particles is given by
U(x) = −4x^3 + 3x^2 + 8x,
where x is the position of one particle in the system.
(a) Determine the force Fx on the particle as a function of x.

2. Relevant equations
du/dx[U(x)] = Fx

3. The attempt at a solution
-12x^2+6x+8

webassign says this is wrong, what am I missing? Just did a problem like this where I was given the potential energy equation and had to find the force. In that case there was both x and y forces and had to take partial derivatives of each. This is frustrating me :(

2. Mar 8, 2016

### Orodruin

Staff Emeritus
Recheck the relation between force and potential.

3. Mar 8, 2016

### muhammed_oli

hm -dU/dx = Force(x) ?

4. Mar 8, 2016

### Orodruin

Staff Emeritus
Yes.

5. Mar 8, 2016

### muhammed_oli

awesome, thank you

6. Mar 8, 2016

### j.clarke238

Force is equal to $- \frac{dU(x)}{dx}$, in one dimension.
This is so that if you have a minimum in your potential $\frac{dU(x)}{dx} >0$, the force will be restorative and tend to bring you back to that equillibrium. I.e. the force is in the opposite direction to the displacement of your object.
Conversely, if you have a maximum in your potential energy curve the force will push you away.

TLDR: times your answer by -1 and see if 'webassign' likes you for it.