Question

How are Kinetic energy and momentum related?

Answer 1

Step 1: Kinetic Energy and Momentum

1. Kinetic energy is the energy possessed by an object due to its motion. It is a scalar quantity. Its SI unit is Joule.
2. Mathematically, $K.E=\frac{1}{2}m{v}^2$ , where, $m$ is the mass of the object measured in kg and, $v$ is the velocity of the object measured in m/s.
3. The momentum of an object is defined as the product of mass and velocity. It is a vector quantity. The SI Unit of Momentum is kg.m/s.
4. Mathematically, $p=mv$, where, $m$ is the mass of the object measured in kg and, $v$ is the velocity of the object measured in m/s.

Step 2: Relation between Kinetic energy and momentum:

Kinetic energy and momentum of a body can be related as follows:

We know that formula of Kinetic energy, $K.E=\frac{1}{2}m{v}^2$

Now, multiply and divide R.H.S. by $m$.

$$\begin{gathered} K.E=\frac{1}{2}m{v}^2\times \frac{m}{m} \\ K.E=\frac{{\displaystyle m^2{v}^2}}{{\displaystyle 2m}} \end{gathered}$$

We know that, $p=mv$

$\therefore K.E=\frac{m^2{v}^2}{2m}=\frac{p^2}{2m}$

The above equation gives the relation between Kinetic energy and the momentum of the object under motion.