Potential Function of a Conservative Force

[bmb2009]

Homework Statement

Given a conservative force with the Force given as F=y^2(i)+2xy(j), what is the potential function related to it.

Homework Equations

-dU/dx = F

The Attempt at a Solution

I know I have to integrate the components but I don't know how... since the (i) direction was differentiated with respect to x would I just treat the y as constant and say F=xy^2(i)+xy^2(j) + c ?

 

[fzero]

You're on the right track, but remember that the potential is a scalar function. You've written down a result that is a vector and for some reason called it F. It might help to explicitly write down the components of F in terms of the partial derivatives of U.

 

[bmb2009]

So would it just be U(x,y)=xy^2 + xy^2 = 2xy^2 + c because it's a scalar?

 

[LCKurtz]

So would it just be U(x,y)=xy^2 + xy^2 = 2xy^2 + c because it's a scalar?

Close, but no. Remember, you are looking for a scalar function $U(x,y)$ such that $\nabla U = \vec F$. So you need $U_x = y^2$ and $U_y = 2xy$. Start by taking the anti-partial derivative of the first one with respect to $x$ by holding $y$ constant, as you asked in your original post. Don't forget when you do that your "constant" of integration will be a function of $y$. Them make the second equation work.