Elastic collision, frictionless surface

[synergix]

Homework Statement

Two air hocky pucks collide head-on elastically on a frictionless surface. The smaller puck has a mass of 0.050 kg and is moving to the right at 5.0 m/s while the larger puck has a mass of 0.10 kg and is moving to the left with a speed of 2.0 m/s. Find the velocity of each after the collision.

Homework Equations

M1V1+M2V2=M1V'1+M2V'2
.5M1V1^2+.5M2V2^2=.5M1V'1^2+.5M2V'2^2

The Attempt at a Solution

I am pretty sure I must derive an equation from conservation of momentum and conservation of energy.

 

[LowlyPion]

That would be the way to do it.

Select a positive X direction and be careful of signs.

Two equations, 2 unknowns.

 

[synergix]

Cant anyone help me?

 

[synergix]

ok, could you give me an idea of what first step I should take?

 

[synergix]

first I take the conservation of momentum:
M1V1+M2V2=M1V'1+M2V'2

Then I solved for V'1

V'1=(M1V1+M2V2-M2V'2)/M1
Then I substituted this for V'1 in the original equation:
M1V1+M2V2=M1[(M1V1+M2V2-M2V'2)/M1]+M2V'2

so now the only unknown variable is V'2. I have little expierence deriving equations so I am not confident this is correct. though it certainly seems to be. to me anyways.

 

[LowlyPion]

My first step would be to start plugging in the values and deriving the actual equations for this situation.

With the equations in hand then solve for the 2 velocities in the usual manner.