# Elasticity in collisions

## Homework Statement

a billiard ball of mass of 0.115kg moves with a velocity of 12.5m/s toward a stationary billiard ball of identical mass and strikes it in a head on collision. the first billiard ball comes to a complete stop. determine whether the collision was elastic.

## Homework Equations

Ek1 + Ek2 = Ek1' + Ek2'

p=mv

## The Attempt at a Solution

first i calculate the velocity of the steel ball after being struck by the billiard ball...
mv + mv = mv' + mv'
0.155kg(12.5m/s) = (0.155kg + 0.155kg)v
1.94 = 0.31v
v = 1.94/0.31
v = 6.26m/s

then i calculate the total kinetic energy before the collision (only the billiard ball because the steel ball was idle)

Ek = 1/2mv^2
Ek = 1/2(0.155)(12.5)^2
Ek = 12.1J

then i calculate the total kinetic energy after the collision

Ek + Ek = Ek' + Ek'
12.1 + 1/2(0.155)(0)^2 = 1/2(0.155)(0)^2 + 1/2(0.155)v^2
12.1 = .078v^2
v^2 = 12.1/0.078
v^2 = 155
v = 12.46m/s (but this doesnt make sense...)

so maybe this:
Ek = 1/2(0.155 + 0.155)(6.26)^2
Ek = 0.155(39.20)
Ek = 6.1J

- the answer in the back of my textbook is this:
v=6.32m/s[41.5' counterclockwise from the original direction of the first ball]; the collision is not elastic: Ek = 12.1J; Ek' = 10.2J

i got the first 2 correct but the third one i dont understand. as well.. i am not sure how to know whether something is considered an elastic collision or not)

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Excuse me,
assume system is isolated , no external forces, thus momentum conserved,
m*V+m*U=m*V'+m*U'
U=0 ,V'=0
we get that U'=V, 1 ball stops and the other one gets the speed of the other one.
thus Ek(initial)= mV^2/2 , Ek(final)=m*U'^2/2
because U'=V
Ek initial =Ek final...
Am I understanding Your question wrong??Do they scatter with an angle?? but it's head to head collision?

ok so are you agreeing with my answers?
and yes it was a head on collision, so there are no angles to worry about.

rock.freak667
Homework Helper
ok so are you agreeing with my answers?
and yes it was a head on collision, so there are no angles to worry about.
Well given what Dweirdo says, it does look like the final velocity of the other ball is 12.5m/s, which would imply that the collision is elastic.

0.155kg(12.5m/s) = (0.155kg + 0.155kg)v

you also used this to find v. This implies that you assumed the collision was completely inelastic.