2D Collision of 3 Billiard Balls

[Europa]

Homework Statement

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.

Homework Equations

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

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 = mv_1f +mv_2f
Y: mv₁ = mv_1f + mv_2f

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 I am a variable or something)

 

[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.

 

[PeroK]

Homework Statement

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.

Homework Equations

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

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 = mv_1f +mv_2f
Y: mv₁ = mv_1f + mv_2f

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 I am a variable or something)

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

 

[Europa]

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.

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.

 

[haruspex]

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.

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.

 

[BiGyElLoWhAt]

I would assume that there is no rolling, otherwise this problem would be impossible. Why don't you try using that p initial equals p final equation you posted was relevant. Whats p inital? What p final?

 

[BiGyElLoWhAt]

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

 

[haruspex]

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

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

 

[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 into find energy loss?

 

[BiGyElLoWhAt]

Yup

 

[Europa]

Thanks i got it :D

 

[BiGyElLoWhAt]

No problemo.