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Thursday 17 October 2013

Are conservation laws correct!

case - In an isolated system, a 5 kg ball 'A'  with 10 m/s velocity is made to hit a 10 kg ball 'B' at rest. After collision the balls move together in the same direction .The plane and the balls are friction less and there is vacuum in the system( zero drag).

According to conservation of energy:
 Total energy after collision = Total energy of the system initially 
                                         =  energy of ball A + energy of ball B 
                                         = 1/2 mv*v  + 1/2 mv*v
                                         = (1/2 x 5kg x 10m/s x 10m/s) + (1/2 x 10kg x 0m/s x 0m/s)
                                        =  250 J  --------------( 1)

According to conservation of momentum:
     Total momentum of 2 balls before collision = Total momentum of balls after collision
=> mu(A) + mu(B)                       =   v[m(A) +m(B)]       { u = initial velocity ; v = final velocity of the balls}
=> 5kg x 10m/s + 10kg x 0m/s     =   v[5kg + 10kg]
=> 50kg m/s                                 =   v[15kg]                   
=> v                                             =   10/3 m/s

Now , Total energy after collision  = 1/2  * m(A+B)  * v * v
                                                    = 1/2  * (5kg +10kg)  *10/3 m/s  *10/3 m/s
                                                    = 83.33 J  --------------------(2)
(1) and (2) contradicts each other .

Hence either of the laws is wrong !

  

2 comments:

  1. Now , Total energy after collision = 1/2 * m(A+B) * v * v
    Statement is wrong as initially you have taken both the energies of A and B separately with masses separately. So how can you take final energy and combined mass?
    Also after collision, ball A will not start from rest so correct formula for it's energy will be 1/2*m(v^2-u^2).

    ReplyDelete

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