Deriving the Inelastic 3-Body Equation for Colliding Balls with Different Masses

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To derive the inelastic 3-body equation for colliding balls of different masses, the conservation of momentum principle is essential, where momentum before the collision equals momentum after. The discussion emphasizes the need to consider the center of mass for calculations, although this approach is typically limited to two-body collisions. The problem involves analyzing two scenarios: varying the mass of the top ball and then varying the mass of the larger base ball, both falling from a fixed height. The focus is on incorporating the collision with the ground into the general inelastic equation. Understanding these dynamics is crucial for accurately modeling the behavior of the system.
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What equation should I use to represent a 3 body inelastic equation .. two ball of different masses falling together and colliding with the stationary ground.

And any hints on deriving the two body equation shown below
 

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momentum before equals momentum after.

or you could calculate the centre of mass. but that would only work for a two body collision (i think).
 
Why don't you describe the exact problem you are trying to solve?
 
Im writing a research essay on balls of different mass falling from a fixed height onto the floor. Divided into two parts, I first vary the mass of the top ball and then for the next part I vary the mass of the bigger base ball. No I am using the general inelastic equation.. attached above and I need to go about first deriving it and then incoporating a collision with the floor. So a 3 body collision?
 

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