Question

A potential energy function for a two dimensional force is of the form $U=9x^{3}y-12x$. Find conservative force at point (1, 2).

• A. $-42\hat{i}-9\hat{j}$
• B. $-36\hat{i}+18\hat{j}$
• C. $-18\hat{i}+9\hat{j}$
• D. None

Answer 1

The correct option is A $-42\hat{i}-9\hat{j}$

$F_x=-\frac{du}{dx}=-\frac{d}{dx}\left(9x^{3}y\right)+12\frac{d}{dx}\left(x\right)$
$=-27x^{2}y+12$
$F_y=-\frac{d}{dy}\left(u\right)=-\frac{d}{dy}(9x^{3}y-12x)$
$=-9x^3$
$F_x=-27\left(2\right)+12=-42$
$F_y=-9$