Question 1198185
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Two billiard balls collide. Ball 1 moves with a velocity of 4 m/s, and ball 2 is at rest. 
After the collision, ball 1 comes to a complete stop. What is the velocity of ball 2 after the collision? 
Is this collision elastic or inelastic? The mass of each ball is 0.16 kg.
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The logic and explanations in the post by @math_tutor2020 are not perfectly correct,
so I came to explain everything in a right way.


In particular, tutor @math_tutor2020 writes quoting


<pre>
    "An inelastic collision is one in which objects stick together after impact, 
     and kinetic energy is not conserved."
</pre>

And then @math_tutor2020 makes a conclusion


<pre>
    We can see that since the billiard balls don't stick together, 
    and instead separate, this means the collision is elastic.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is NOT CORRECT. By the definition, a collision of two bodies is called inelastic collision 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if two bodies remain separate, but kinetic energy is not conserved.



The "sticking together" condition determines OTHER type of collision, called 
"plastic collision", or, in other terminology, "perfectly plastic collision"


But "inelastic collision" means loosing of kinetic energy, only: it is transformed 
into other types of energy (heat energy or interior energy).



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution to the given problem is as follows:


<pre>
Two bals have the same mass of 0.16 kg.
Before collision, ball 1 moves with a velocity of 4 m/s; ball 2 is at rest.
After collision, ball 1 comes to a complete stop.


To determine the speed of the second ball, use the momentum conservation law,
which is held at any collision (elastic, inelastic, plastic).


it says  "momentum before the collision = momentum after the collision",  or,  for given conditions, 


    {{{m[1]*v[1]}}} = {{{m[2]*v[2]}}},  or   {{{0.16*4}}} = {{{0.16*v[2]}}},  which implies  {{{v[2]}}} = 4 m/s.


So, the balls "exchanged" their velocities after the collision.

It makes it obvious that the kinetic energy is conserved;  so, the collision is ELASTIC.
</pre>

Solved, with complete explanations.


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This topic on collisions requires full and completely clear understanding, if a person claims to be an expert.