Question

Can a body have momentum without having kinetic energy?

Answer 1

Definition of kinetic energy and momentum

Kinetic energy is the energy possessed by a body due to its motion. It is given as,

$KE=\frac{1}{2}m{v}^2$

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

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.

Explanation

1. A body that does not has kinetic energy is at rest.
2. When a body is at rest, its velocity is zero, therefore, kinetic energy will also be zero.

$$\begin{gathered} KE=\frac{1}{2}m{v}^2 \\ KE=\frac{1}{2}m{\left(0\right)}^2 \\ KE=0 \end{gathered}$$

3. If velocity is zero, momentum will also be zero.

$$\begin{gathered} p=mv \\ p=m\times 0 \\ p=0 \end{gathered}$$

Therefore, a body cannot have momentum without kinetic energy. This is because a body that does not has kinetic energy has zero velocity, and therefore, zero momentum.