Question

Loss of kinetic energy in inelastic collision formula

Answer 1

Answer:

Explanation:

An inelastic collision is a collision in which there is a loss of kinetic energy. While momentum of the system is conserved in an inelastic collision, kinetic energy is not. ... This type of collision is perfectly inelastic because the maximum possible kinetic energy has been lost.

Answer 2

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From conservation of momentum

${m}_{1 }{v }_{1}$

$= ({m}_{1} +{m }_{2} ){v}-{2}→{v}_{2}$

$= \frac{{m}_{1}}{{m}_{1} +{m}_{2}}×{ v }_{1}$

The ratio of kinetic energies before & after collision is

$\frac{{KE}_{f}}{{KE}_{i}}$

$= \frac{\frac{1}{2}×({m}_{1}+{m}_{2}) × (\frac{{m}_{1}}{{m}_{1} +{m}_{2}}×{ v }_{1})²}{\frac{1}{2}×{m}_{1}{v²}_{1}}$

$= \frac{{m}_{1}}{{m}_{1} +{m}_{2}}{×}{ v }_{1}$

The fraction of kinetic energy lost is

$\frac{{KE}_{i} – {KE}_{f}}{{KE}_{i}}$

$= \frac{1 –( \frac{{m}_{1}}{{m}_{1} +{m}_{2}})×{ v }_{1}}{{KE}_{i}} × {KE}_{i}$

$= \frac{{m}_{2}}{{m}_{1} +{m}_{2}}×{ v }_{1}$

Hence energy always loss in inelastic collision.

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