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Gravtiational PE

The potential...

Question

The potential energy function of a particle in a region of space is given as $U = (2 x^{2} + 3 y^{3} + 2 x) J$ . Here $x, y$ and $z$ are in meters. Find the force acting on the particle at point $P (1 m$ , $2 m$ , $3 m$ ).

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Solution

We know that force is given by-

$\to F = - \frac{\partial U}{\partial x} i - \frac{\partial U}{\partial y} j - \frac{\partial U}{\partial z} k$

$⟹ \to F = - (4 x + 2) i - 9 y^{2} j$
At $(1 m, 2 m, 3 m) -$

$\to F = (- 6 i - 36 j) N$

$⟹ \to F = - 6 (i + 6 j) N$

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