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Define the following. loss of kinetic energy in inelastic collision. |
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Answer» Solution :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)=(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, `Delta Q=KE_(i)-KE_(f)` `=(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, `Delta Q=(1)/(2)((m_(1)m_(2))/(m_(1)+m_(2)))(u_(1)-u_(2))^(2)`. |
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