Question

Derive the relationship between kinetic energy and momentum.

(Need good/well explained answers)
(All the best)

Answer 1

Answer :-

Let a body of mass m moving with a velocity v. Then its

kinetic energy K = 1/2 mv² -- (1)

and momentum p = mv -- (2)

Where:-

• m = mass
• v = velocity

Substituting the value of v = p/m from eqn. (2) in eqn. (1), we get,

⟹ K = 1/2 m(p/m)²

⟹ K = p²/2m

⟹ p² = 2mK

Thus, kinetic energy K and momentum p are related as:

⟹ p = √2mK or K = p²/2m

Answer 2

QUESTION:-

Derive the relationship between kinetic energy and momentum.

EXPLANATION:-

We know that:-

$\bf\;K.E=\frac{1}{2}mv^2---- (eq-1)$

and ,

P=mv---------(eq-2)

[m=mass v=velocity]

From eq-2 we have,

P=mv

v=p/m

Substitute v=p/m in eq-1 we get:-

$\bf\;K.E=\frac{1}{2}mv^2\\\\K.E=\frac{1}{2}m(\frac{p}{m})^2\\\\K.E=\frac{p^2}{2m}\\\\P^2=2mk\\\\\boxed{\bf\;\underline\ P=\sqrt{2mk}\;or\;K.E=\frac{p^2}{2m}}$