Question

Derive an expression for final velocity V1 and V2 if the objects of mass M1 and M2 moving with velocity V1 and V2 in case of inelastic collision.​

Answer 1

Answer:

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Explanation:

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Answer 2

$v= \frac{m_{1}v_{1 } + m_{2}v_{2 }}{m_{1}+ m_{2}}$

In a collision, the total initial kinetic energy of the bodies (before collision) is not equal to the total final kinetic energy of the bodies (after collision) then, it is called as inelastic collision.

In perfectly inelastic collision, the loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, heat, light etc.

Let $KE_{i}$ be the total kinetic energy before collision and$KE_{f}$be the total kinetic energy after collision. Total kinetic energy before collision,

$KE_{i}=\frac{1}{2}m_{1}v_{1 }^{2} + \frac{1}{2}m_{2}v_{2 }^{2}$------>   (1)

Total kinetic energy after collision,

$KE_{f}= \frac{1}{2} (m_{1}+m_{2})v^{2}$------->   (2)

Then the loss of kinetic energy is

Loss of KE, $\Delta Q = KE_{i} - KE_{f}$

$=\frac{1}{2}m_{1}v_{1 }^{2} + \frac{1}{2}m_{2}v_{2 }^{2}-\frac{1}{2} (m_{1}+m_{2})v^{2}$------>(3)

Substituting equation

$v= \frac{m_{1}v_{1 } + m_{2}v_{2 }}{m_{1}+ m_{2}}$

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