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The arrows in the figure represent the linear momentum of two balls before they collide. If the collision is perfectly inelastic, find the linear momentum after the collision. If the collision is perfectly elastic, find the linear momentum after the collision.

Figure

(Ignore whatever is written in pencil)

I've been trying to solve this problem, but I'm not sure what should I do, or where should I start. I asked my teacher if I had to take into account angles (which are not given), and she just said no. I honestly don't know what to do, can you help me out?

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It suffices to know that the total momentum in a closed system is always constant.

This means you can immediately write down some equations for the total momentum in this system. To do this, you start by writing down the x- and y-components of the momentum for each ball, and then sum each component to get the components of the final momentum.

In a perfectly inelastic collision, the two balls will stick together, since this results in the maximum loss of kinetic energy. In a perfectly elastic collision, kinetic energy is conserved.

However, note that in all cases, total momentum is conserved.

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  • $\begingroup$ For perfectly inelastic collision I got $8kg*m/s$ and for perfectly elastic collision I also got $8 kg*m/s$ Can that be possible? $\endgroup$
    – Nicholas J.
    Nov 13, 2012 at 18:00
  • $\begingroup$ Of course. Why not? Sometimes redundant information is included in the question to throw you off course. $\endgroup$
    – Jason Davies
    Nov 13, 2012 at 18:34
  • $\begingroup$ oh yeah, I was a bit confused but I was wrong about what was being asked, and yeah it was pretty easy considering what you stated "in all cases momentum is conserved" $\endgroup$
    – Nicholas J.
    Nov 13, 2012 at 18:50

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