Predicting Momentum Change in Elastic Collisions

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In elastic collisions, the initial momentum of two particles can be used to approximate their velocities after the collision, even without directly observing them. It is noted that larger mass particles typically experience less change in velocity. The discussion emphasizes the importance of the center of mass (c.m.) coordinate system, where the total momentum remains zero before and after the collision. The outcome in lab coordinates is influenced by the scattering angle. The primary concern remains whether any energy is lost during the collision.
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If we know the initial momentum of particles a and b (mass a and b, initial velocity of a and b),
is it possible knowing the momentum after the collision without observing the velocity of two particles?
(well there is two variables therefore it seems impossible but we know that generally larger mass does not change its velocity much.)We assume the collision is perfectly elastic. Thanks.
 
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hmm I think it is possible to 'approximate' the velocity after collision. if we assume some conditions such as contact time during the collision.
 
In the center of mass coordinate system, the particle momenta add up to 0. The main question is whether there is any energy loss.

In the case of elastic collision, in the c.m. coordinates, each particle will have the same momentum before and after. In lab coordinates, it will depend on the angle of scattering.
 
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