Accelerating blocks connected by a spring

[XanziBar]

Homework Statement

Two 3.0 kg blocks on a level frictionless surface are connected by a spring with spring constant 1000 N/m. The left block is pushed by a horizonal force F to the right. At time t=0 seconds, both blocks are moving with velocity 3.2 m/s to the right. For the next second, the spring's compression is a constant 1.5 cm. What is the magnitude of F during that 1.0 s interval

Homework Equations

KE=.5*m*v^2
SPE=.5*k*(delta x)^2
F=(delta p)*(delta t)
change in energy = force * distance

The Attempt at a Solution

I tried to setup the following: Ei= .5*6kg*3.2^2
and Ef=Ei+F*d=.5*m*v1^2+.5*m*v2^2 +.5*k * (delta x)^2
Now I know everything about the spring potential energy at the end and the total energy (kinetic) at the beginning. But I guess the biggest problem I'm having is that I do not know the final velocities of either of the 2 blocks. I tried using conservation of momentum to relate them but got a much bigger mess with no obvious way to simplify. Would considering the center of mass of the 2 block system help? If I have the acceleration of the center of mass can I do something with that? Is this even the right approach at all? No matter what I do I get like 1 equation with 3 unknowns! Please help.

 

[XanziBar]

So... the change in momentum, F*(delta t)=m*v1f+m*v2f-2*m*v then that's a relationship between v1f and v2f in terms of the force (which is what I'm looking for). But with (1/2)*m*v1f^2+1/2*m*v2f^2+1/2*k*(delta x)^2=m*v^2+F*d that still leaves me with an unknown and no equation. Also, does the distance represent the distance that the center of mass travels?

Kind of struggling here, any ideas anyone?

 

[Jebus_Chris]

F=-kx ?

 

[XanziBar]

No, the force on the spring is not the same as on the block. X1=Vo+a1/2 X2=Vo+a2/2.

a1-a2=2*1.5 cm
F-kx=ma1
kx-ma2
F=m*(a1+a2)=3*(10.03)

==>> a2=5 m/s^2
a1=5.03 m/2^2.

Anyway, the forces are not the same but this problem should be do-able with conservation of energy/momentum.

 

[Jebus_Chris]

I just drew an fbd and solved and got 30n.