Elastic Collisions: Conserving Momentum, But Not K.E.?

AI Thread Summary
In the discussion on elastic collisions, it is noted that when five equal masses are involved, displacing the first ball results in momentum and kinetic energy being conserved as the energy transfers sequentially through the balls. However, when balls 2 through 5 are glued together and ball 1 is displaced with velocity 'u', the requirement to conserve momentum leads to a speed of 4/u for the glued masses, which creates a scenario where kinetic energy is not conserved. The conversation emphasizes that in this altered setup, ball 1 does not stop completely, and its interaction with the glued masses results in a recoil effect, complicating the conservation of kinetic energy. The discussion highlights the nuances of momentum conservation versus kinetic energy conservation in different collision scenarios. Ultimately, the complexities of elastic collisions are underscored, particularly when mass configurations change.
binbagsss
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assuming collisions are elastic...

right 5 equal masses, if you displace the first ball then you observe balls 2-4 stationary and 5 moves off with equal speed to the right, as all the momentum and energy is passed to ball 2, ball 1 stops, ball 2 then passes all its momentum and energy to ball 3 and then stops etc...

This conserves momentum and k.e.

However, if balls 2 and 5 are glued together, and you displace ball 1 with velocity 'u', then the other 4 must move of withspped 4/u to conseve momentum as mu = 4m*u/4, but then kinetic energy is not conserved...?

thankssss !
 
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binbagsss said:
However, if balls 2 and 5 are glued together,
I assume you mean that balls 2 through 5 are glued together?
and you displace ball 1 with velocity 'u', then the other 4 must move of withspped 4/u to conseve momentum as mu = 4m*u/4, but then kinetic energy is not conserved...?
Don't assume that ball 1 stops dead.
 
Doc Al is right
in case I, ball 1 stops as both ball 1.2 has same mass
but now its different case, ball 1 collides with mass 4m, so it will now recoil!with somewhat lesser velocity than u.
 

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