Finding the potential energy function( I don't know how the answer came to be)

  • Thread starter Raziel2701
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Homework Statement


The give force is conservative [tex]F=A(y,x,0)[/tex] where A is a constant.


The Attempt at a Solution


To find the potential function we integrate the negative of the force. Setting the potential U to be zero at the origin, we can integrate over an easy path, so I think going over to the x direction once, and then up in the y direction could work right?

So here are the two integrals(the z-direction force is zero so it's integral would be zero as well.

[tex]-A\int_0 ^x y' dx' +-A\int_0 ^y x' dy'[/tex]

If I do those integrals I get -2Axy, yet the answer is supposed to be -Axy, I'm wondering if maybe the path I'm using is wrong?
 

Answers and Replies

  • #2
tiny-tim
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Hi Raziel2701! :smile:

The first integral (over x) has to be at y = 0, so it's zero. :wink:

(the second integral (over y) is at x = x)

(btw, isn't it obvious that (y,x,0) = grad(xy) ? :smile:)
 

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