Question

Difference between elastic and inelastic collisions. Show that there is always loss in kinetic energy in ordinary inelastic collision.

Answer 1

Answer:

Elastic and Inelastic Collisions. A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision.

Explanation:

Unlike elastic collisions, perfectly inelastic collisions don't conserve energy, but they do conserve momentum. While the total energy of a system is always conserved, the kinetic energy carried by the moving objects is not always conserved

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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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