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Prove that there is a loss of KE during one dimensional inelastic collision. |
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Answer» Solution :In a 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 enery before collision and `KE_(f)` be the total kinetic energy after collision. Total kinetic energy before collision, `KE_(i)=(1)/(2)m_(1)u_(1)^(2)+(1)/(2)m_(2)u_(2)^(2)""...(1)` Total kinetic energy after collision, `KE_(f)=(1)/(2)(m_(1)+m_(2))v^(2)""...(2)` Then the loss of kinetic energy is Loss of `KE, DeltaQ=KE_(f)-KE_(i)` `=(1)/(2)(m_(1)+m_(2))v^(2)-(1)/(2)m_(1)u_(1)^(2)-(1)/(2)m_(2)u_(2)^(2)""...(3)` SUBSTITUTING equation `v=(m_(1)u_(1)+m_(2)u_(2))/((m_(1)+m_(2)))` in equation (3), and on simplifying expand v by using the ALGEBRA `(a+B)^(2)=a^(2)+b^(2)+2ab`, we get Loss of KE, `DeltaQ=(1)/(2)((m_(1)m_(2))/(m_(1)+m_(2)))(u_(1)-u_(2))^(2)""...(4)` |
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