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Equations of Motion, help

  1. Mar 15, 2014 #1
    Equations of Motion, help....

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

    I'm attempting to draw a 'free body diagram' of 2 pulley's connected by a belt (open configuration), and hence derive the 'equations of motion'.
    The issue I'm having is in regard to, the 'tight' & 'slack' sides & wheather they should be modeled in exactly the same way? Will the difference enter the problem when I put the spring constants in (K)?


    2. Relevant equations

    Hooke's Law: F=-K.x
    Newton's 2nd Law: ∑F=m.a ∴ T=J.θ"
    F=Force
    m=mass, J= mass moment of inertia
    a=acceleration, θ"=angular acceleration,
    x=displacement, θ=angular displacement
    k=spring constant


    3. The attempt at a solution

    J1*θ"1+K1(θ1*r1-θ2*r2)=0
    J2*θ"2+K2(θ2*r2-θ1*r1)=0

    I've attached a drawing, it makes interpretation much easier, thanks...
    Pulley's & Springs_1.jpg

    Pulley's & Springs_2.jpg
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 15, 2014 #2
    Also, would this be the right equation to derive 'k', spring constant from 'E' Young's modulus, K=E*A/L (area/length)?
     
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