Hi,I have been struggling on this problem for a whole day,looking for someone to sort it out!
My question:(please see the attached diagram as well)
Consider 2 spheres A and B,having different masses (m and M) but equal in size.
A is moving to the right at a speed u, B is stationary(and at the right hand side of A).
The floor is smooth and the collision is elastic.
First,consider the KE of the system.Since KE is conserved,
0.5mu^2 = 0.5mv^2 + 0.5MV^2
mu^2 = mv^2 + MV^2
v = final speed of A
V = final speed of B
The max value of v = u (where A rebounds at it original speed),(i.e.velocity = -u)
in this case,
mu^2 = m(-u)^2 + MV^2
V = 0
B remains at rest and this makes sense.
The min value of v = 0,that is,
mu^2 = MV^2
V = √(mu^2/M)
On the other hand,the momentum of the system is conserved.
mu = mv + MV
If v = -u,
2mu = MV
And if M =m, V= 2u BUT NOT V = 0
If v = 0,
V = mu/M Which contradicts the above result again!
I know there must be something wrong leading to these inconsistent solutions.
Thx for everyone's help.
The Attempt at a Solution
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