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How to get the equation spring equation? Please help me understand!

  1. Nov 20, 2011 #1
    How do you use the equations

    m=Minital + deltaM
    and x=xinital + deltax
    and F=-mg

    to get x=(g/k)deltaM + ((Minital)(g)/k +xinital)

    (where m= mass. Minital is fixed inital mass and deltaM is additional weight added)
    (where x= displacement. xinital is when no downward force is applied and deltax is displacement from unstretched position)

    please explain how to get this equation

    Thank you
     
  2. jcsd
  3. Nov 20, 2011 #2

    atyy

    User Avatar
    Science Advisor

    It can't be done. You need one more equation: Force that the spring exerts on a mass = k * extension.
     
  4. Nov 20, 2011 #3
    so if I use F=-kdeltax than how can I now show the above equation?
     
  5. Nov 21, 2011 #4
    Perhaps I can help if I understand the problem better. What was the statement of the problem? The equations can come later.
     
  6. Nov 21, 2011 #5
    m = mi + Δm
    Fg = -mg
    so
    Fg = -g(mi + Δm)

    Fs = kΔx (positive since it is acting against gravity)

    We are looking for Δx when the forces cancel so
    0 = Fg + Fs
    -Fs = Fg
    -Fs = Fg = -g(mi + Δm) = -kΔx
    devide by -k

    Δx = g(mi + Δm)/k

    The using x = xi + Δx
    substitute Δx, multiply out and rearrange a bit and you get

    x=(g/k)Δm + (g/k)mi +xi
     
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