# Homework Help: 2D Collision of 3 Billiard Balls

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1. Mar 11, 2015

### Europa

1. The problem statement, all variables and given/known data
A 500 g billiard ball is going at 10 m/s [E] when it impacts 2 other identical billiard balls. Afterwards, you observe 2 of the balls moving at 2 m/s [30 W of S] and 3 m/s[45 N of E] respectively. Calculate the Energy lost in the collision.

2. Relevant equations
KE = 1/2mv^2
p = mv
p(initial) = p(final)
Energy lost = final energy - initial energy

3. The attempt at a solution
Since there is some energy lost, this is only a near elastic collision.
Using,p(initial) = p(final), break the initial and final into components.
X: mv1 = mv1f +mv2f
Y: mv1 = mv1f + mv2f

Since the masses are all the same we can cancel them out.

X: 10 = 3cos45 - 2sin30
Y: 0 = 3sin45 - 2cos30

I don't even know what i am solving for, don't i already know every variable in the conservation of momentum equation? (Pretty sure im a variable or something)

2. Mar 11, 2015

### BiGyElLoWhAt

You're supposed to take the initial energy of the system and compare it with the final energy of the system using conservation of momentum as the link between.

3. Mar 11, 2015

### PeroK

I think you might have forgotten the momentum of the first ball after the collision!

4. Mar 11, 2015

### Europa

Can you explain how to link them?
Otherwise,
E1 = 1/2mv2, which is just 25 J, since only 1 ball is moving.
Do i not know E2 as well since i have their masses and their final velocities? where does momentum come in? I know it is not this simple.

5. Mar 12, 2015

### haruspex

As PeroK posted, there are three balls, and all have a velocity after the collision. How can you find the velocity of the third ball?
For the energy, the incoming ball is rolling, not sliding, I would have thought. However, it is not stated whether the observed velocities after collision are immediately afterwards or after rolling has been attained, so it's quite unclear whether you are supposed to allow for rolling.

6. Mar 12, 2015

### BiGyElLoWhAt

I would assume that there is no rolling, otherwise this problem would be impossible. Why dont you try using that p initial equals p final equation you posted was relevant. Whats p inital? What p final?

7. Mar 12, 2015

### BiGyElLoWhAt

Actually i semi retract that statement, the rolling is irrelevant.

8. Mar 12, 2015

### haruspex

It's irrelevant if you take all post collision velocities and energies as being immediately after collision.

9. Mar 12, 2015

### Europa

Oh ok i see, i thought the 3rd ball just stopped. so finding the velocity of the third ball through momentum, and then plug in to find energy loss?

10. Mar 12, 2015

### BiGyElLoWhAt

Yup

11. Mar 12, 2015

### Europa

Thanks i got it :D

12. Mar 12, 2015

### BiGyElLoWhAt

No problemo.

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