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Grade: 12th pass


a particle A moving with momentum p suffers a one dimensional collision with a particle B of the same mass but at rest.During the collision B imparts an impulse I to A.The coefficient of restitution is?please explain it`s answer

6 years ago

Answers : (1)

8 Points
							It is given in the question, initial momentum of the particle-A is `p`.
Also, the momentum of particle -B will be zero due to its initial position at rest.
Now, after the collision, assuming p1 and p2 be the linear momentum of the particles A and B.
Now, Impulse imparted, I = change in momentum, `delta p`.
Impulse for particle-B  = I         .....(i)
Impulse for particle-A = p - p2    or  p2 = p - I  ..........(ii)     
  (Final momentum - initial momentum for particle -A).
Coefficient of restitution,

            Difference of final velocities after collision      v2 - v1      mv1 - mv2       p1 - p2
   e =   --------------------------------------------------------   =  ---------  =  -------------  =   ---------- .....(iii)
            Difference of initial velocities                                u                 mu                p        
  (where, m is the mass of the each particle and `u` is the velocity of particle-A before collision and v1 and v2 be the velocities after collision of particle A` and `B`).
From eqns. (i), (ii) and (iii), we get to know,

             p1  - p + I         I -  p + I        2 I     
    e =   .................  =   ...............  =   .....  - 1
                  p                      p               p
6 years ago
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