Question

How are kinetic energy and momentum related?
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Answer 1

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Kinetic Energy and Momentum Relationship

Kinetic energy is the energy that any substance has when it accelerates, whereas momentum is an object's mass in motion.

Explanation:

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Answer 2

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Relation Between Momentum and Kinetic Energy

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

Consider the formula of kinetic energy-

$k.e = \frac{1}{2} m {v}^{2}$

Multiply and divide R.H.S by m

$k.e = \frac{1}{2} m {v}^{2} \times \frac{m}{m} = \frac{ {m}^{2}{ {v}^{2} } }{2m} = \frac{m {v}^{2} }{2m}$

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

$ke = \frac{ {p}^{2} }{2m}$

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∝1÷m

If Kinetic Energy(K.E) is constant p∝√m

If mass(m) is constant p∝√K.E

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