Question

Establish the relationship between the kinetic energy and the momentum of the body.

Answer 1

Kinetic energy:

1. The energy possessed by an object by virtue of its motion is called kinetic energy.
2. A body of mass $m$ and moving with velocity $v$ having kinetic energy given by,

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

Momentum:

1. It is defined as the product of the mass and the velocity of the object.
2. A body of mass $m$ and moving with velocity $v$ having momentum given by,

$p=mv$

Relationship between the kinetic energy and the momentum:

$$\begin{gathered} K=\frac{1}{2}m{v}^2 \\ 2K=\frac{{\left(mv\right)}^2}{m} \\ 2Km=p^2 \\ p=\sqrt{2Km} \end{gathered}$$

Hence, relationship between the kinetic energy and the momentum is given by $p=\sqrt{2Km}$