Define perfectly inelastic collision. Show that kinetic energy for perfectly inelastic collision is not conserved.

Asked by Sayoni Maiti | 8th Oct, 2014, 05:28: PM

Expert Answer:

 
begin mathsize 14px style The space collision space in space which space maximum space amount space of space kinetic space energy space has space been space lost space during space collision space is space called space perfectly space inelastic space collision. Let space straight m subscript 1 space be space the space mass space of space the space body space with space velocity space straight u subscript 1 space projected space towards space straight a space bdoy space of space mass space straight m subscript 2 space which space is space at space rest space left parenthesis straight u subscript 2 equals 0 right parenthesis After space the space collision comma space two space bodies space will space stick space together space and space with space moving space velocity space straight v. space As space the space total space linear space momentum space of space the space system space remain space constant comma therefore Pi equals straight P subscript straight f space space space space space space left parenthesis Pi equals Initial space momentum space and space straight P equals space Final space momentum right parenthesis rightwards double arrow straight m subscript 1 straight u subscript 1 plus straight m subscript 2 straight u subscript 2 equals left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis straight v rightwards double arrow straight m subscript 1 straight u subscript 1 equals equals left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis straight v space space space left parenthesis straight u subscript 2 equals 0 right parenthesis rightwards double arrow straight v equals fraction numerator straight m subscript 1 straight u subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction To space calculate space loss space of space straight K. straight E. space in space this space collision Totla space straight K. straight E. space before space collision equals straight E subscript 1 equals 1 half straight m subscript 1 straight u subscript 1 squared Totla space straight K. straight E. space after space collision equals space straight E subscript 2 equals 1 half left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis straight v squared equals 1 half left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis open parentheses fraction numerator straight m subscript 1 straight u subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close parentheses squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator straight m subscript 1 squared straight u subscript 1 squared over denominator 2 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction Loss space of space straight K. straight E. equals space straight E subscript 1 minus space space straight E subscript 2 equals space 1 half straight m subscript 1 straight u subscript 1 squared minus fraction numerator straight m subscript 1 squared straight u subscript 1 squared over denominator 2 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction equals fraction numerator straight m subscript 1 squared straight u subscript 1 squared plus straight m subscript 1 straight m subscript 2 straight u subscript 1 squared minus straight m subscript 1 squared straight u subscript 1 squared over denominator 2 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction space equals fraction numerator straight m subscript 1 straight m subscript 2 straight u subscript 1 squared over denominator 2 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction We space can space say space that space loss space of space straight K. straight E. space is space positive. space Hence space Kinetic space energy space for space perfectly space inelastic space collision space is space not space conserved. space space space space space space space space space space space space space space space space space end style

Answered by Priyanka Kumbhar | 9th Oct, 2014, 10:28: AM

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