Question

Can a body have mechanical energy even it's momentum is zero?

Answer 1

Hello mate,

$\huge{\red{\star}} {\blue{\underline{\huge{\mathfrak{Mechanical\:Energy}}}}} \huge{\red{\star}}$

Mechanical energy is nothing but the sum of the potential energy and kinetic energy that is possessed by the body.

$mehanical \: \: energy = \frac{1}{2} m {v}^{2} + mgh$

Let's say the momentum of the body is zero.

We know momentum is the product of mass and velocity, that is,

$p = mv \\ \\ mv = 0 \\ \\ m = 0 \: \: and \: \: v = 0$

But we know that mass cannot be equal to zero so let's take mass as a constant value and keep v = 0

Then mechanical energy becomes,

$\frac{1}{2} m {v}^{2} + mgh \\ \\ = \frac{1}{2} m(0) + mgh \\ \\ = mgh$

Hence we can say that mechanical energy cannot be zero if the momentum of a body is zero.

Hope it helps:)