First slide

Conservative force a negative gradient of potential energy

Question

The potential energy for a body of mass m that is acted on by a very massive body is given by $U = - m g x + k \frac{x^{3}}{3}$ . The corresponding force is

Moderate

A

$- m g + k x^{2}$
B

$m g - k x^{2}$
C

$m g - k x$
D

$- m g + k x$

Solution

$f o r c o n s e v a t i v e f o r c e F = - \frac{d U}{d x} = - (- m g + k x^{2}) = m g - k x^{2}$

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