Solving Elastic Collisions - Momentum & Final Velocity

[bjah]

Please clear up this problem...

Mass 1 = 8 kg, and v = 3 m/s to the right.
Mass 2 = 4 kg, and v = -3 m/s to the left.

Both objects are on the same x-plane. Totally elastic collision.
Momentum of mass 1 is 24, and momentum of mass 2 is -12.

How do I determine final momentum for each object, and therefore final velocity, after the collision?

Thank you.
Brad

 

[Nugatory]

Please clear up this problem...

Mass 1 = 8 kg, and v = 3 m/s to the right.
Mass 2 = 4 kg, and v = -3 m/s to the left.

Both objects are on the same x-plane. Totally elastic collision.
Momentum of mass 1 is 24, and momentum of mass 2 is -12.

How do I determine final momentum for each object, and therefore final velocity, after the collision?

Thank you.
Brad

You have two unknowns (the velocities of the two masses after the collision).
If you can find two equations in these two variables, just basic algebra will see you home.

Ask yourself what the definition of an "elastic" collision is, and that will give you one of your equations. Conservation of momentum will give you the other one.

 

[bjah]

And that's where I'm stuck!

(8 x 3) + (4 x -3) = (8 x Vfinal of mass 1) + (4 x Vfinal of mass 2)

But how do I combine the equations for conservation of momentum and kinetic energy?

 

[Nugatory]

And that's where I'm stuck!

(8 x 3) + (4 x -3) = (8 x Vfinal of mass 1) + (4 x Vfinal of mass 2)

But how do I combine the equations for conservation of momentum and kinetic energy?

What does the equation for conservation of energy say about the energy before and the collision?

 

[bjah]

KE initial must = KE final.

 

[haruspex]

KE initial must = KE final.

Right. So write out expressions for those two energies in this context.