1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equations of Motion w/ spring scale

  1. Feb 1, 2017 #1
    1. The problem statement, all variables and given/known data
    http://imgur.com/a/X7mWA
    QC78LeR.png
    2. Relevant equations
    1. ΣF = m a
    2. Στ = Iθ"

    3. The attempt at a solution
    First , assuming small motion, all movement of the scale can disregard x components (so the spring stretches only in vertical direction without an impact from the x directional movement). I summed torque around the pin, point O, which would be equal to the mass moment of inertia * theta double dot. so...

    mgL2 - kx1 = I0θ" (mass force positive since displacement is positive in the negative y direction)

    x1 is the spring movement upwards, however we want to relate that to the x displacement downwards with the mass, which we'll just call x. Now, using like triangles, x1=(L1/L2)x. Then I know x = rθ, differentiate with time twice to get x" = r θ" so then θ" = x"/r, where r = L2. Now we have ...

    (I0/L2)x" - k(L1/L2)x= mgL2 ===> (I0)x" + k(L1)x = mgL22

    This answer just doesn't feel right. I feel like I may not have correctly applied newtons 2nd law or maybe didn't correctly set up the kinematics. Any input would be helpful, thanks.
     
    Last edited: Feb 2, 2017
  2. jcsd
  3. Feb 2, 2017 #2
    You need not take into account the mass moment of Inertia of mass m, since it is a statics problem
     
  4. Feb 2, 2017 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    OK up to here.
    Check your math, this has at least 2 mistakes in it. One is a sign error.
    Also, what is I0? You need to express this in terms yuu were given.

    Also BTW not only is this not a static question but, contary to the problem statement iself, the scale swings forever back & forth since no damping mechanism was introduced.
     
    Last edited: Feb 2, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Equations of Motion w/ spring scale
  1. Equations of Motion (Replies: 1)

  2. Equations of Motion (Replies: 5)

Loading...