Question 1198185
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Refer to this page
<a href = "https://openstax.org/books/physics/pages/8-3-elastic-and-inelastic-collisions">https://openstax.org/books/physics/pages/8-3-elastic-and-inelastic-collisions</a>
Quote: "In an elastic collision, the objects separate after impact and don’t lose any of their kinetic energy."
also
Quote: "An inelastic collision is one in which objects stick together after impact, and kinetic energy is not conserved."


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


m1 = mass of the first ball
vi1 = initial velocity of the first ball
vf1 = final velocity of the first ball


m2 = mass of the second ball
vi2 = initial velocity of the second ball
vf2 = final velocity of the second ball


Due to the elastic collision, we can use this conservation of momentum formula
m1*vi1 + m2*vi2 = m1*vf1 + m2*vf2
an example problem can be found here
<a href = "https://www.ck12.org/physics/Elastic-and-Inelastic-Collisions/lesson/Elastic-and-Inelastic-Collisions-PHYS/">https://www.ck12.org/physics/Elastic-and-Inelastic-Collisions/lesson/Elastic-and-Inelastic-Collisions-PHYS/</a>


We have these values
m1 = m2 = 0.16 kg
vi1 = 4 m/s
vf1 = 0 m/s (since the 1st ball comes to a stop)
vi2 = 0 m/s (the 2nd ball starts at rest)
vf2 = x = unknown


Let's determine x
m1*vi1 + m2*vi2 = m1*vf1 + m2*vf2
0.16*4 + 0.16*0 = 0.16*0 + 0.16*x
0.16*4 = 0.16*x
x = 4
It's not particularly interesting since each ball has the same mass, so we expect the amount of speed going in is the amount coming out (assuming no kinetic energy is lost to heat)
I suggest you try different mass values for each ball to see how the vf2 value will change.


Further reading
<a href = "https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions">https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions</a>


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Answers:
Velocity of the 2nd ball, after the collision, is 4 m/s
The collision is elastic.
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