Double Ball Drop: Solve Elastic Collision Velocity Problem

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AI Thread Summary
The discussion revolves around calculating the velocities of two balls of different masses after an elastic collision with the ground. The user initially sets up the conservation of momentum equation but struggles with the correct assumptions for the velocities post-collision. Participants emphasize that both linear momentum and kinetic energy are conserved in elastic collisions, suggesting the user should derive two equations to solve for the unknown velocities. The user expresses concern about the complexity of the resulting quadratic equation, questioning whether it's necessary for this seemingly simple problem. The conversation highlights the importance of correctly applying conservation laws in solving collision problems.
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Homework Statement



Hi everyone. Hope I'm not breaking any forum rules, because I've alread wrote this one in another thread by mistake. Here is where it should be.

Two balls of different mass are dropped one in top of the other, with the light one on top. After they collide with the floor (elastic collision), what is the velocity of both balls?

m is the mass of the small ball
M is the mass of the heavier one
v is the velocity of both balls before the collision with the ground
v1 and v2 are the velocities of the lighter and heavier ball respectively.

Homework Equations



pi=pf

The Attempt at a Solution



(m + M)v = mv1 + Mv2

What do i assume now?

I first assumed that mv1 = -(m+M)v + Mv2
but it doesn't look right to me because v1 turns out 2v2.

What am i doing wrong?

Thanks in advance.
 
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tiny-tim said:
Hi Gibanga! Welcome to PF! :smile:


Hint: https://www.physicsforums.com/library.php?do=view_item&itemid=38" means that energy is conserved. :wink:

Thank you very much.

Linear momentum is also conserved.

So i get two equations and two unknowns and a very ugly quadratic equation jumps out of there. Should i solve it or am i wasting my time? This looks like a very simple problem and I'm just making it more complex...
 
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