Question

Can a body have momentum without having kinetic energy?

Answer 1

Definition of momentum and kinetic energy

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.

Explaining if a body can have momentum without having kinetic energy

1. When a body is at rest, its velocity is zero.
2. When the velocity of a body is zero, its kinetic energy will also be zero. $\left[KE=\frac{1}{2}m{v}^2=\frac{1}{2}\times m\times 0^2=0\right]$
3. Conversely, it can be said that if a body does not has kinetic energy, its velocity is zero.
4. Since the momentum of a body is a product of its mass and velocity, if velocity is zero, momentum will also be zero. $\left[p=mv=m\times 0=0\right]$

No, a body cannot have momentum without having kinetic energy.