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Mechanics Problems, involving spring system and gravitation

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data
    A spring system is set up as follows: a platform with a weight of 10 N is on top of two springs, each with spring constant 75 N/m. On top of the platform is a third spring with spring constant 75 N/m. If a ball with a weight of 5.0 N is then fastened to the top of the third spring and then slowly lowered, by how much does the height of the spring system change?

    http://img856.imageshack.us/img856/4352/screenshot20130127at101.png [Broken]
    2. Relevant equations

    Ktotal parallel = K1 + K2 + ... Kn
    F = -kx

    3. The attempt at a solution
    Initially, I tried adding up all the springs in the system for an equivalent spring of 210 N/m, and then solving. That didn't work and the answer was incorrect. I feel like the 5 N ball will make the first spring push back some, and the 2nd and 3rd springs push back with a different amount of force. The trouble is, I'm lacking the conceptual understanding of how to go about calculating those values.


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

    Consider the two orbits around the sun shown below. Orbit P is circular with radius R, orbit Q is elliptical such that the farthest point b is between 2R and 3R, and the nearest point a is between R/3 and R/2. Consider the magnitudes of the velocity of the circular orbit vc, the velocity of the comet in the elliptical orbit at the farthest point vb, and the velocity of the comet in the elliptical orbit at the nearest point va. Which of the following rankings
    is correct?
    (A) vb > vc > 2va
    (B) 2vc > vb > va
    (C) 10vb > va > vc
    (D) vc > va > 4vb
    (E) 2va >vb√2 > vc


    http://img835.imageshack.us/img835/4352/screenshot20130127at101.png [Broken]
    2. Relevant equations
    vellipse = √GM ((2/R)-(1/a))



    3. The attempt at a solution
    I honestly have no idea how to solve this one. With this equation, I can calculate the velocity of an elliptical orbit, but the way they worded the problem, so that it's between two points—well, that honestly has me stumped. I thought about taking the minimum and maximum values and finding a range, but the thing is, I don't know for certain what the semi major axis is.
    All help on either of these is very much appreciated!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 28, 2013 #2

    haruspex

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    The behaviour of springs in series can be a bit surprising.
    If you had two springs in series, each 75 N/m, that would be just the same as one spring with a constant of 75 N/m - just longer. If they undergo a total extension of x, each extends x/2, generating a force 75x/2, and adding up to 75x.

    Btw, it's better to use separate threads for unrelated posts.
     
    Last edited: Jan 28, 2013
  4. Jan 28, 2013 #3
    But aren't all these in parallel? Which two springs are in series?
     
  5. Jan 28, 2013 #4

    haruspex

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    The two at the bottom are in parallel with each other, but as a pair they are in series with the one above.
     
  6. Jan 28, 2013 #5
    Why isn't it

    (1/kequivalent)=(1/75) + (1/75)
    kequivalent=75/2



    Isn't that the equation for springs in series?
    Also, why are those in series? I was under the impression that two springs on either side of an object would be considered in parallel...could you explain when a spring is in parallel vs series for me?
     
  7. Jan 28, 2013 #6

    haruspex

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    If you had a mass attached to two springs, one each side, and the other ends were fixed, then that would behave as parallel. But as far as the mass on top is concerned here, they're in series. Whether they're in series or in parallel wrt the platform is a bit hard to say because neither end of the top spring is fixed. So safest is to forget about trying to classify the system this way and just work from first principles.
    Create unknowns for the spring extensions and derive the force balance equations.
     
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