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Spring Rotational Problem

  1. Nov 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Four masses M in deep space are connected by four identical light springs with spring constant k and equilibrium length L. The four mass, four spring assembly is square and lies in a plane; all four masses are rotating with ω =√(k/M), in uniform circular motion about an axis perpendicular to the plane and equidistant from all four masses. What is the kinetic energy of this system?

    2. Relevant equations
    mac2r
    F=kx
    KE=1/2*ITotalω2
    3. The attempt at a solution
    ITotal=4MR2 where R is the distance to mass when the masses are rotating. R should be large that L because the springs will stretch when the system is in motion.
    R=(√2)/2(l+Δl)
    ITotal=2*M*(l+Δl)2
    KE=2*(l+Δl)2*k
    I feel like this is incomplete especially with respect to Δl. Is there any other way to put it. I was thinking of maybe finding what Δl maybe using Hooke's Law but I don't know how to go about that. I was thinking of equating it to the centripetal force. Please let me know and thank you in advance
     
  2. jcsd
  3. Nov 12, 2013 #2

    Doc Al

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    Staff: Mentor

    You're on the right track.

    Combine Newton's 2nd law with Hooke's law. Draw a diagram of the forces acting on each mass.
     
  4. Nov 12, 2013 #3

    gneill

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    Staff: Mentor

    Yes, use the centripetal force. The springs meet at each corner of the square and their tensions add vector-wise to make up the centripetal force. You can find an expression for the radial distance of the masses that way.
     
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