Question

How are K.E and momentum related ?

Answer 1

Let us get some idea about the Kinematics. Kinematics is the study of how a group of bodies’ moves without taking into account the forces or potential fields that influence the motion. In other words, kinematics investigates how momentum and energy are exchanged among interacting bodies. As a result, no momentum component exists outside of the interaction plane.

Complete step by step answer:
Let us understand about kinetic energy. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When work is performed on an object by applying a net force, the object accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle that is determined by its mass as well as its motion.
$K.E = \dfrac{1}{2}m{v^2}$
Here, $m$ = mass and $v$ = velocity

Now let us talk about momentum. Momentum is a physics concept that refers to the amount of motion possessed by an entity. The momentum belongs to a sports team that is on the rise. The term "momentum" refers to "mass in motion." Since all objects have mass, if they are moving, they have momentum - their mass is moving.
$p = mv$
By squaring both the sides we will get,
${p^2} = {(mv)^2}$
On dividing by $2m$ both the sides we will get,
$\dfrac{{{p^2}}}{{2m}} = \dfrac{1}{2}m{v^2}$
As we saw above that the kinetic energy is $K.E = \dfrac{1}{2}m{v^2}$ So we can use this in the above equation:
\dfrac{{{p^2}}}{{2m}} = K.E \\\ \Rightarrow {p^2} = 2m \times (K.E) \\\
Taking square root both the sides we will get,
$\therefore p = \sqrt {2m(K.E)}$
Now, let us come to the question and understand the relation between them. Since they are both related to an object's velocity (or speed) and mass, momentum is a vector quantity that defines how much mass is moving. Kinetic energy is a scalar representation of an object's energy from motion.

Note: The Kinetic Energy of an object has a direct relationship with its mass, meaning that as the mass of an object increases, so does its Kinetic Energy. The same can be said for velocity. However, mass and velocity are related in a roundabout way.