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PE Diagram

The potential...

Question

The potential energy of an object of mass $m$ moving in $x y$ plane in a conservative field is given by $u = a x + b y$ , where $x$ and $y$ are position coordinates of the object. Find magnitude of its acceleration.

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Solution

Given
$U = a x + b y$

$F_{x} = - \frac{d U}{d x} = - a$

$F_{y} = - \frac{d U}{d y} = - b$

$m a_{x} = - a$

$a_{x} = - \frac{a}{m}$

and
$m a_{y} = - b$
$a_{y} = - \frac{b}{m}$

Net acceleration , $a = \sqrt{a_{x}^{2} + a_{y}^{2}} = \sqrt{(- \frac{a}{m})^{2} + (- \frac{b}{m})^{2}}$

Hence $a = \frac{\sqrt{a^{2} + b^{2}}}{m}$

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