Conservation momentum for y- axis

[inky]

Homework Statement

A ball P of mass m kg is dropped from a point A, which is 2 m vertically above a point B on a horizontal floor. After P hits the floor at B, it rebounds and hits another ball Q, of the same mass, which has also been dropped from A. The impact between the two balls is direct and takes place at the mid-point of AB. The coefficient of restitution in each impact is 5/7 . Neglecting air resistance, find the speed of P
(i) immediately after it hits the floor,
(ii) immediately after it collides with Q.

Ans: (i)4.52 m/s (ii) 3.74 m/s

Homework Equations

e=(velocities after collision)/(velocities before collision)

Law of conservation of momentum

The Attempt at a Solution

Please see attachment.

I tried to calculate this problem but some of them said my calculation is wrong because they mentioned that I can't use law of conservation of momentum for last part because of gravity. So how to calculate to get correct answer?Thanks a lot.

 

[Delphi51]

There is an implied assumption that the duration of the collision is zero. So the impulse applied to the masses F*Δt is zero during the collision and so the change in momentum m*Δv on each mass is zero.

If the time duration of the collision was nonzero, the collision force would have to be specified as a function of time. If it was a nice constant force you could work out the motion during the collision beginning with an F = ma formula for each mass. Looks complicated. The answer would not be 3.74 unless the duration was very short.

 

[inky]

If the time duration of the collision was nonzero, the collision force would have to be specified as a function of time. If it was a nice constant force you could work out the motion during the collision beginning with an F = ma formula for each mass. Looks complicated. The answer would not be 3.74 unless the duration was very short.[/QUOTE]

ma_P=ma_Q
(-v_P^'-0.583)/t={-v_Q^'-(-4.47)}/t
v_Q^'-v_P^'=5.053

But from coefficient of restitution formula
v_P^'-v_Q^'=3.61

So I can't find the velocity. I think acceleration is incorrect.We need to consider gravity or not.
Actually this is CIE exam 2002W Question. Please see examiner report.Pls. see attachment.

If I consider v=u-gt for each ball then add , I can get one equation and another from e formula. So I got 0.423 ms^-1. This answer is not the examiner' answer.

 

[inky]

Please see examiner report.Pls. see attachment.

 

[Delphi51]

Sorry, I don't understand your last post. You did get the 3.74 answer given in the latest attachment using the method described in the attachment. Done!

 

[inky]

Sorry, I don't understand your last post. You did get the 3.74 answer given in the latest attachment using the method described in the attachment. Done!

No. We could not use Law of conservation of momentum for falling objects because of the external force acting on it. I don't want the answer. I want correct method.

 

[Delphi51]

My take on it is that, yes, you can use the law of conservation of momentum during the collision - if you assume the duration of the collision is very short. If it is not very short, then you do not have sufficient information to do the problem and it's answer would depend on the collision force function of time.