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Horizontal Spring, Find Unstretched length

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data

    A spring of stiffness 1500 N m-1 is stretched between two points 2 m apart. If the tension in the spring is 200 N, what was the unstretched length of the spring? And what is the energy stored in the spring when it is stretched between the two points?

    2. Relevant equations

    F=-K*x

    U = 0.5 K*(x2)


    3. The attempt at a solution

    I don't even know where to begin from !!!

    X0 is the position of equilibrium of the spring , so this is our reference point , meaning that if X0 is our first point and X1 is our second point , then A= 2 m , right ? So F=-kA but this isn't true ?! what can i do ? I thought we always measured everything relevant to X0 , so how can we find the unstretched part ?!
     
  2. jcsd
  3. Apr 29, 2012 #2

    Doc Al

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    Staff: Mentor

    In Hooke's law (your first equation), x stands for the amount of stretch (beyond the unstretched length). You're given the tension, so you can figure out x.
     
  4. Apr 29, 2012 #3
    But we know x , it is 2m ( A=2m ) But 200 = 1500*2 isn't true .
     
  5. Apr 29, 2012 #4

    Doc Al

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    Staff: Mentor

    Nope. 2m is the total length of the stretched spring, not the amount of stretch. Use Hooke's law to find the amount of stretch.
     
  6. Apr 29, 2012 #5
    So it should be F= k ( streched length - natural length ) = k( X1 - X0 )

    Xo = X1 - 2/15 = 1.866666 m Therefore A=0.13333333333333 m .

    so U=13.3 J . Thank you :)
     
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