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Homework Help: Spring question

  1. Jan 22, 2007 #1

    dnt

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    1. The problem statement, all variables and given/known data

    A 6 kg mass and 3 kg mass are at rest on a frictionless table. A massless spring is compressed between them and they are held together with a string. When released (string is cut) the 6 kg mass moves to the left at 4 m/s - what is the velocity of the 3 kg mass as it moves to the right?

    2. Relevant equations

    a little unsure - i beleive i need to use the F=kx (force of a spring) and assume that k is constant throughout since its the same spring for both.

    3. The attempt at a solution

    what i did was assume that the force on each mass was the same since each was compressed the same and had the same spring constant, k.

    what i then did was assume that if that force moved the 6 kg mass 4 m/s to the left, that it would have an equal reaction to the 2nd mass which was only 3 kg. thinking in terms of momentum (is that correct?) i said the 2nd mass would move to the right at 8 m/s:

    (6 kg)(4 m/s) = (3 kg)(x m/s)
    x = 8 m/s

    is this correct? does my logic work?

    thanks.
     
  2. jcsd
  3. Jan 22, 2007 #2
    Conservation of momentum.
     
  4. Jan 22, 2007 #3

    dnt

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    so then my answer is correct.

    m1v1 + m2v2 = m1v1 + m2v2

    the first two are 0 because v1=v2=0

    then you have:

    0 = (6)(4) + (3)(x)

    x = -8 (8 m/s in the other direction)

    right?

    so basically this spring is considered a "collision"?
     
  5. Jan 22, 2007 #4

    PhanthomJay

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    Gold Member

    I'd say it was more of an explosion than a collision, but in either case, in the absence of external forces, momentum is always conserved, and your answer is correct, good job.
     
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