Question

Can a body have energy without having momentum?

Answer 1

Definition of momentum and potential energy

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

$p=mv$

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

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

$PE=mgh$

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

Explanation

1. Suppose that the body is at rest, therefore, $v=0$.
2. When velocity is zero, the body will have zero momentum, as $p=m\times 0=0$
3. However, even when a body has zero velocity, it can still possess potential energy because potential energy depends on mass, acceleration due to gravity, and height.

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