Question

Potential energy of a particle is given by U = (2x2−8x) J, where x is in meter. The force on the particle will be zero at​

Answer 1

Given:

Potential energy of a particle is given by U = (2x²−8x) J.

To find:

Value of x when force on particle is zero?

Calculation:

Force can be calculated in general as follows:

$F = - \dfrac{dU}{dx}$

$\implies \: F = - \dfrac{d(2 {x}^{2} - 8x)}{dx}$

$\implies \: F = - \dfrac{d(2 {x}^{2}) }{dx} + \dfrac{d(8x)}{dx}$

$\implies \: F = - 4x + 8$

For F = 0 N, we can say:

$\implies \: 0 = - 4x + 8$

$\implies \: 4x = 8$

$\implies \: x = 2 \: metres$

So, force is zero when x is 2 metres.