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A ball of mass m=50g strikes with velociy v=4m/s with a lift floor which is moving with velocity v=2m/s. If e=1/2 the speed of the ball just after collision? Ans=5

A ball of mass m=50g strikes with velociy v=4m/s with a lift floor which is moving with velocity v=2m/s. If e=1/2 the speed of the ball just after collision?
Ans=5

Grade:11

2 Answers

Kaustubh Nayyar
27 Points
6 years ago
coefficient of restitution = ½ = (velocity of seperation) / (velocity of approach)
     = (v – 2) / 6      v be the speed of the after collission
this gives v = 5
Ajaykrishnan Jayagopal
11 Points
6 years ago
In the given question, the direction of motion of the lift has not been mentioned.
We shall consider a frame of axis such that the velocity in the upward direction is taken as positive
Hence, we shall find the answer for two cases:
Case 1 ( Lift is moving downwards and ball is also moving downwards):
 u = initial velocity of lift = – 2 m/s
 uB = initial velocity of ball = – 4 m/s
 vL = final velocity of lift = – 2 m/s (because the lift is a massive object whose velocity is on negligibly affected by the momentum of the ball)
 vB = final velocity of ball
 
Now,
          e =  (relative velocity of separation)/(relative velocity of approach)
             =  ( vL – v)/( uB – u)
         Therefore,
            ( – 2 –  vB ) / ( – 4 – ( – 2 )) = ½
            vB = -1 m/s
 Therefore, after collision, the ball moves down with velocity 1 m/s.
 
Case 2 ( Lift is moving upwards and the ball is moving downwards):
 u = initial velocity of lift = + 2 m/s
 uB = initial velocity of ball = – 4 m/s
 vL = final velocity of lift = + 2 m/s (because the lift is a massive object whose velocity is on negligibly affected by the momentum of the ball)
 vB = final velocity of ball
 
Now,
          e =  (relative velocity of separation)/(relative velocity of approach)
             =  ( vL – v)/( uB – u)
         Therefore,
            ( 2 –  vB ) / ( – 4 –  2 ) = ½
            vB = 5 m/s
 Therefore, after collision, the ball moves up with velocity 5 m/s.
 
The answer to the second case matches the answer provided in your question.
 

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