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Question

A potential energy function for a two-dimensional force is of the form $U = 3 x^{2} y - 7 x$ . Find the force that acts at the point (x,y).

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Solution

Potential energy $U = 3^{2} y - 7 x$

Force $F = - \frac{\partial U}{\partial x}^i - \frac{\partial U}{\partial y}^j$

So, $F = - (6 x y - 7)^i - (3 x^{2})^j$

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