Question

if v(x) =1/2 kx²is a potential energy function of a conservative force, then the conservative force is​

Answer 1

Answer:

If v(x) =1/2 kx²is a potential energy function of a conservative force, then the conservative force is​ given by

Explanation:

Answer 2

SOLUTION

GIVEN

The potential energy function of a conservative force is given by

$\displaystyle \sf{ v(x) = \frac{1}{2}k {x}^{2} }$

TO DETERMINE

The conservative force

CONCEPT TO BE IMPLEMENTED

If v(x) is the potential energy function of a conservative force then the conservative force F is given by

$\displaystyle \sf{ F = - \frac{dv}{dx} }$

EVALUATION

Here it is given that v(x) is a potential energy function of a conservative force given by

$\displaystyle \sf{ v(x) = \frac{1}{2}k {x}^{2} }$

Then the conservative force is

$\displaystyle \sf{ = - \frac{dv}{dx} }$

$\displaystyle \sf{ = - \frac{d}{dx} \bigg( \frac{1}{2}k {x}^{2} \bigg) }$

$\displaystyle \sf{ = - \frac{1}{2} k \frac{d}{dx} \bigg( {x}^{2} \bigg) }$

$\displaystyle \sf{ = - \frac{1}{2} k .2x }$

$\displaystyle \sf{ = -kx }$

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