What is the Maximum Velocity of Two Blocks on a Spring?

[Cade]

Homework Statement

Two blocks are pushed down on a spring with 75J of elastic potential energy. The spring is released and the blocks are allowed to fly freely (not sure I translated this sentence correctly, maybe separately instead of freely). Block A has a mass of 2 kg, block B has a mass of 3 kg. What is the highest velocity reached by these two blocks?

Homework Equations

Energy conversion
Ei = Ef
75 = .5*m1*(v1)^2+.5*m2*(v2)^2

The Attempt at a Solution

I figured out only one equation, I need two because I have two unknowns.

75 = .5*2*(v1)^2+.5*3*(v2)^2

 

[Doc Al]

Two blocks are pushed down on a spring with 75J of elastic potential energy.

Do you mean that a block is at each end of the spring and the two blocks are pushed together, thus compressing the spring?

Hint: What else besides energy is conserved?

 

[Cade]

D'oh! I should have realized that they were on opposite sides, thanks!

Linear momentum is conserved (I think),
0 = m1v1 + m2v2 = 2v1 + 3v2

75 == .5*2*v1*v1 + .5*3*v2*v2
0 == 2 v1 + 3 v2
Gives v1 -> 6.71m/s, v2 -> 4.47m/s in opposite directions

 

[Doc Al]

You got it.

 

[Cade]

Thanks for the help.