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2 masses attached with a spring falling

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data
    2 balls, each of mass M, are attached to each other by a spring with constant k.
    they hanged out by a rope, so they are in equilibrium, the rope was cut and they fall.
    do they Oscillate?

    2. Relevant equations
    effective g=g-a (vectors) when a=g, effective g=0.

    3. The attempt at a solution
    now my opinion is split here, from 1 point of view they both fall with acceleration g, so they shouldn't oscillate (that's based on logic) its like throwing a bottle with a hole in it, and no water will come out of the bottle , but on the other hand,the spring was stretched initially, and if m falls with acceleration g, the net force on it should be Fnet=mg, but in this case it's not, the spring is stretched so there is a force upwards(looking at the lower mass) and mg down , so what's the answer, will it?
  2. jcsd
  3. May 18, 2009 #2


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    When it is at rest and you displace it from equilibrium and release it what does it do?

    When it is hanging is there any displacement from equilibrium?

    When it is cut what displacement from the new equilibrium point are the weights from each other?
  4. May 18, 2009 #3
    At last a reply! :D
    thanks, ok so here is what i think:
    It oscillates.
    first, the equilibrium point will be when the spring is not stretched at all right?(when its cut i mean)
    so the displacement is the Xo which is mg/k imo, the initial stretch .
    but the displacement of each mass is different? :S so its mg/2k
    Am I right?
    I'll wait for your answers, If the above is true I think I can solve it using reduced mass :X

    well Thank You, waiting for reply.
    Last edited: May 18, 2009
  5. May 18, 2009 #4


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    Are you sure? There is displacement from the relaxed un weighted state of the spring.

    F = m*g = k*Δx

    Δx = m*g/k

    If there is displacement then there is potential energy = 1/2*k*x2
    Won't that energy cause something to happen?

    If g suddenly goes to 0, then won't Δx need to go to 0?

    In what way is that all that different from displacing a mass and releasing it?
  6. May 18, 2009 #5
    when both mass hang on a rope, they are in equilibrium :S no? so there is no displacement from equilibrium.
    or did you mean to ask if the spring stretched?
    so the equilibrium point changes, thus it's not in equilibrium anymore ,so it should oscillate ? no?
  7. May 18, 2009 #6


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    Yes it should oscillate.

    I expanded what I posted in the previous post a bit, which I guess you missed.
  8. May 18, 2009 #7
    Yes, missed the energy part :}
    so it will, ok thanks.
    and i treat it as 2 masses on an horizontal table?
  9. May 18, 2009 #8


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    As to the oscillation itself, yes it should behave the same I would think ... until it hits of course.
  10. May 18, 2009 #9
    Yes of course, I would suspect it would oscillate after hitting the ground XD
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