Ideal Spring, Spring Constant, Equilibrium Length

[Spartan Erik]

Homework Statement

A 2.0 kg mass is attached to one end of an ideal spring with a spring constant of 500 N/m and a 4.0 kg mass is attached to the other end. The masses are placed on a horizontal frictionless surface and the spring is compressed 10 cm from its equilibrium length. The spring is then released with the masses at rest and the masses begin to move apart. When the spring has reached its equilibrium length, what is the speed of the 2.0 kg mass?

0.67, 1.0, 1.3, 2.1, none of these (all in m/s)

Homework Equations

Hooke's law: F = -kx
W(spring): 1/2kx(initial)^2 - 1/2kx(final)^2
W(applied): -W(spring) if stationary before/after displacement

The Attempt at a Solution

I don't know how I can utilize this data and relate it to velocity

 

[LowlyPion]

Homework Statement

A 2.0 kg mass is attached to one end of an ideal spring with a spring constant of 500 N/m and a 4.0 kg mass is attached to the other end. The masses are placed on a horizontal frictionless surface and the spring is compressed 10 cm from its equilibrium length. The spring is then released with the masses at rest and the masses begin to move apart. When the spring has reached its equilibrium length, what is the speed of the 2.0 kg mass?

0.67, 1.0, 1.3, 2.1, none of these (all in m/s)

Homework Equations

Hooke's law: F = -kx
W(spring): 1/2kx(initial)^2 - 1/2kx(final)^2
W(applied): -W(spring) if stationary before/after displacement

The Attempt at a Solution

I don't know how I can utilize this data and relate it to velocity

OK. You kind of have the right idea.

The work that the spring produces has gone into what? (Does it rhyme with Kinetic Energy by any chance?)

Also you have two masses that are being acted on by the same force, even if in opposite directions.
F = m₁a₁ = m₂a₂

Since you know that m₁ = 2 and m₂ = 4, then you know that m₂ = 2*m₁

What does that mean then for a₁ and a₂? If that is true for a₁ and a₂ then it must also be true for v₁ and v₂ at the moment that PE is converted wholly to KE.

That leads to Work = total KE = ... you should be able to get the rest.