# Potential Energy and Force

1. Jun 19, 2007

### kiwikahuna

1. The problem statement, all variables and given/known data
A potential energy funtion for a two dimensional force is of the form
U = ax^3y + bx
where a =10.51 J/m^4 and b = -8 J/m.
Find the magnitude of the force that acts at the point (x,y) for x =93, y =68

2. Relevant equations
F(x) = dU/dx

3. The attempt at a solution
Given the PE function, I know that I have to take the derivative to find Force but I am confused as to how to do this with it being in 2-d. There are two variables, x and y. Help please.

2. Jun 20, 2007

### malawi_glenn

if

U = ax^3y + bx

then you want to differentiate this with respect to x and then y, you just when you differentiate with respect to x treat ALL the others as constants. And the same way with the y.

$$\dfrac{dU}{dx} = 3ayx^{3y-1} + b$$

now you try