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Homework Help: Accelerating blocks connected by a spring

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    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

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

    3. 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.
  2. jcsd
  3. Nov 23, 2009 #2
    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?
  4. Nov 23, 2009 #3
    F=-kx ?
  5. Nov 23, 2009 #4
    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

    ==>> 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.
  6. Nov 23, 2009 #5
    I just drew an fbd and solved and got 30n.
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