Function describing Potential Energy

[JC91]

Hi, can someone please help me on this problem. I'm not sure what to do with the equation given. I tried taking the derivative, partial, and anti and nothing seems to be working. Can someone please give me a hint on how to start this problem.

Thanks in advance.

Suppose the following function describes the potential energy of a point mass (m=3 kg) at various locations in the xy plane:

U(x,y)=x2 - y2 + 32
(Units omitted; you may assume [x], [y] = m and = J.)

a.) Find a general function vector F(x,y) and then use it to find the force on the object at the following (x,y) coordinates:

vector F(+6 m,+1 m) = ___N i hat + ___N j hat

vector F(+6 m,-1 m) = ___N i hat + ___N j hat

vector F(-6 m,+1 m) = ___N i hat + ___N j hat

vector F(-6 m,-1 m) = ___N i hat + ___N j hat

 

[Matterwave]

Use the equation $F=-\nabla U$. Maybe show us your work so we can see what's going wrong?