Question

Can a body have potential energy without having momentum?

Answer 1

Definition of potential energy and momentum

The energy possessed by a body due to its position is known as potential energy. It is given as,

$PE=mgh$

where, $m$ is mass, $g$ is the acceleration due to gravity and $h$ is the height

Momentum can be defined as the product of mass and velocity. It is given as,

$p=mv$

where, $m$ is mass and $v$ is velocity.

Explaining if a body can have potential energy without having momentum

1. If a body is at rest, its velocity will be zero.
2. Since momentum is a product of mass and velocity, if velocity is zero, momentum will also be zero. $\left(p=mv=m\times 0=0\right)$
3. Therefore, a body at rest will have no momentum.
4. However, when a body is at rest, it can possess potential energy as potential energy does not depend upon velocity.
5. The potential energy of a body depends upon mass, acceleration due to gravity, and height. $\left(PE=mgh\right)$

Yes, a body can have potential energy without having momentum.