Relation Between Kinetic Energy And Momentum

Kinetic Energy

The kinetic energy of an object is the energy associated with the object which is under motion. It is defined as “the energy required by a body to accelerate from rest to stated velocity.” It is a vector quantity.

Kinetic Energy formula

Mathematically expressed as-

\(K.E=\frac{1}{2}mv^{2}\)

Where,

m is the mass of the object measured in kg.

v is the velocity of the object measured in m/s

Kinetic Energy unit

The SI Unit of Kinetic Energy is Joules.

Momentum

The momentum of an object is virtue of its mass. It os defined as the product of mass and velocity. It is a vector quantity.

Momentum formula

The momentum of a moving object can be mathematically expressed as –

\(p=mv\)

Where,

  • p is the momentum.
  • m is the mass of the object measure using kg.
  • v is the velocity of object measure using m/s.

Momentum unit

The SI Unit of Momentum is kg.m/s

Relation Between Momentum and Kinetic Energy

Kinetic energy and momentum of a moving body can be mathematically related as follow-

Consider the formula of kinetic energy-

\(K.E=\frac{1}{2}mv^{2}\)

Multiply and divide R.H.S by m

\(\Rightarrow K.E=\frac{1}{2}mv^{2}\times \frac{m}{m}\) \(=\frac{m^{2}v^{2}}{2m}\) \(=\frac{\left ( mv \right )^{2}}{2m}\)

We know that \(p=mv\). Substituting for mv in the above equation we get-

\(K.E=\frac{p^{2}}{2m}\)

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

If the Momentum(p) is constant

\(K.E\propto \frac{1}{m}\)

If Kinetic Energy(K.E) is constant

\(p\propto \sqrt{m}\)

If mass(m) is constant

\(p\propto \sqrt{K.E}\)

Hope you have understood the relation between Kinetic energy and momentum of a moving object.

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