Define the following.
Coefficient of restitution

Explanation

(a) The ratio of velocity of separation after collision to the velocity of approach before collision
i.e., `e=("velocity of separation"("after collision"))/("velocity of approach" ("before collision"))=((v_(2)-v_(1)))/((u_(1)-u_(2))`
(b) Power is defined as the rate of work done or energy delivered `P=("work done")/("Time taken")`
Its unit is watt
(c) The law of conservation of energy states that energy can neither be created nor destroyed It may be transformed from one form to another but the total energy of an isolated system remains constant
(d) In perfectly inelastic collision, the in kinetic energy during collision is transformed to another form of energy like sound, thermal, heat and light etc. Let KE, be the total kinetic energy before collision and `KE_(f)`, be the total kinetic energy after collision,
Total kinetic energy before collision,
`KE_(i)=1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)`
Total kinetic energy after collision,
`KE_(f)=1/2(m_(1)+m_(2))v^(2)`
Then the loss of kinetic energy is
`"Loss of KE",triangleQ=KE_(i)-KE_(f)=1/2 m_(1)+m_(2)v_(2)-1/2m_(1)u_(1)^(2)-1/2m_(2)u_(2)^(2)`
`"Substituting equcation" v=(m_(1)u_(1)+m_(2)u_(2))/(m_(1)+m_(2))` in equation(30, and on simplifying (expand v by using the algebra `(a+b)^(2)=a^(2)+b^(2)+2ab`, we get
`"Loss of KE",triangleQ=1/2((m_(1)m_(2))/(m_(1)+m_(2)))(u_(1)-u_(2))^(2)`