(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

One particle with massmis sitting at rest at the original of the rectangular coordinate system. Another particle, with massM, is moving along x axis and hit m at the original. Assume the collision is complete elastic so that M move along the direction making an angleAwith positive x-axis, whilemmove along other direction making angleBwith positive x-axis. We only know that after collision,M's momentum is1/kof original momentum (0 < 1/k < 1). Try to find out over what range ofm/Mis this possible.

2. The attempt at a solution

Assume the initial momentum of the system isP, since_{0}M's final momentum becomesP, so mass_{0}/kmwill attain momentum(k-1)P. Due to conservation of momentum, we have_{0}/k

[tex]P_0 = \frac{P_0}{k}\cos A + \frac{(k-1)P_0}{k}\cos B[/tex]

along the vertical direciton, momentum also conserved

[tex]\frac{P_0}{k}\sin A = \frac{(k-1)P_0}{k}\sin B[/tex]

These two equations are enough to solve for angle A and B so that we can find the relation between ratio of mass and ratio of velocity. But since we have a definite solution of A and B, why the question asking for a range of ration of mass make it possible? I have no idea how to do that.

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# Homework Help: Odd quetsion about elastical collision

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