I have an exercise about a 1D collision with a certain restitution coefficient, that is: $$e = \frac{|u_1-u_2|}{|v_1-v_2|}$$ One must calculate the velocities of the 2 colliding masses after the collision, with the mass and initial velocities given. They collide head-on, and thus the motion is all on the $x$-axis if you will. I found 2 solutions (obviously as you have to solve a quadratic equation), but they are both quite possible. One of the solutions has both masses moving in the same direction as they were before the collision but with a smaller magnitude and the other has them both traveling opposite the direction they originally came from. How do you determine which of the 2 solutions is more likely in such a scenario?
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$\begingroup$ Check your working as one of the solutions should be the initial conditions. $\endgroup$– FarcherMar 29, 2021 at 22:49
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$\begingroup$ Well normally one of them would be if you just solve it without the restriction of the restitution coefficient, but here that isn't the case. I get 2 different solutions and neither of them is the inital condition. $\endgroup$– Pim LaevenMar 29, 2021 at 23:09
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$\begingroup$ Moving in the same direction . . . . but with smaller magnitude implies that momentum has not been conserved. $\endgroup$– FarcherMar 30, 2021 at 6:19
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1$\begingroup$ I mean i guess that the second option is just if the particles pass through one another. $\endgroup$– Pim LaevenMar 30, 2021 at 10:08
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here in this question ,If the 2 bodies are moving in same direction, the velocity of the following body must be greater than the velocity of the first body in order to collide with it. other wise the relative separation between them exits always..Or if the bodies are moving in opposite direction, collision can be possible whatever be there velocities. So make sure your knowledge about their direction and magnitude both..
