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Why momentum can be conserved and energy cannot in inelastic collisions


  • We know that momentum is a vector quantity and energy is a scalar quantity.
  • When there is inelastic collision KE is changed in some other form of energy such as heat sound etc.
  • But momentum being a vector does not get converted in other forms
  • By the definition  of momentum we can say rate of change of momentum is force. Thus if no external force is applied on the body ,change in momentum of the system is zero.

To give a more clear view on this suppose there are 2 conditions

1st Case
There are 2 balls moving in opposite direction with say about 2000m/s speed
There masses are m
Therefore their sum of momentum is 2000m-2000m=0(as they are moving in opposite direction)
While their sum of KE is 1/2m(2000*2000)+1/2m(2000*2000)

2nd Case
if the same ball is moving in opposite direction with 200m/s speed the momentum of the system would be same as above is  200m-200m=0
But their KE would be 1/2m(200*200)+1/2m(200*200)

Note
When there is friction or collision with wall then the external forces is applied and momentum is not conserved
But when 2 objects or ball collide then there is no change in momentum as forces are internal not external

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