I have one problem about prefectly inelastic condition. When I read the reference book, it mentioned that when one object moving with an initial speed u1, and another object is in rest, after collision, if both object moved together as one object with a final speed v, this is perfectly inelastic condition.

My question is, what is the reason this cannot be an elastic collision? ie the total kinetic energy of system before =the total kinetic energy of the system after?

siddharth
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I have one problem about prefectly inelastic condition. When I read the reference book, it mentioned that when one object moving with an initial speed u1, and another object is in rest, after collision, if both object moved together as one object with a final speed v, this is perfectly inelastic condition.

My question is, what is the reason this cannot be an elastic collision? ie the total kinetic energy of system before =the total kinetic energy of the system after?

Because, if the objects stick together and move with the same velocity after collision, energy is not conserved.

For a simple example, lets say you have an object of mass m1 and velocity v1 colliding with another object of mass m2 which is at rest. The conservation of momentum will give you,

$$m_1 v_1 = (m_1 + m_2)v_f$$

where, $v_f$ is the final velocity of the combined objects which are now stuck together.

If you take the ratio of the KE before and after collision, you have

$$\frac{KE_{initial}}{KE_{final}} = \frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} (m1+m2) v_f^2}$$

Substituting for the value of $v_f$ from the conservation of momentum, you get

$$\frac{KE_{initial}}{KE_{final}} = \frac{m1+m2}{m1}$$

This shows that the intial KE is always greater than the final KE and so energy is not conserved.

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