Question

The potential energy of mass m is U=ax+by.the magnitude of acceleration of body is

Answer 1

Given:

The potential energy of mass m is U=ax+by.

To find:

Acceleration of the object ?

Calculation:

• First of all, we will perform PARTIAL DERIVATIVE to get force function.

$U = ax + by$

$\implies \: F = - \bigg(\dfrac{ \partial U}{ \partial x} + \dfrac{ \partial U}{ \partial y} \bigg)$

$\implies \: F = - \bigg \{\dfrac{ \partial (ax + by)}{ \partial x} + \dfrac{ \partial (ax + by)}{ \partial y} \bigg \}$

$\implies \: F = - (a + b)$

• So, acceleration of the object :

$\implies a = \dfrac{ F }{m}$

$\implies a = \dfrac{ - (a + b)}{m}$

So, acceleration of the object is -(a+b)/m.