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Calculating the tesion in a string holding a 1 meter stick

  1. Sep 12, 2012 #1
    A meterstick (L = 1 m) has a mass of m = 0.13 kg. Initially it hangs from two short strings: one at the 25 cm mark and one at the 75 cm mark.



    What is the tension in the left string right after the right string is cut?



    Calculating the free body diagram where we put the acceleration of center of mass of the plank, mg and T.
     
  2. jcsd
  3. Sep 12, 2012 #2

    Doc Al

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    Staff: Mentor

    Hint: Consider torques about the point where the left string attaches to the stick.
     
  4. Sep 12, 2012 #3
    Yeah did that. I first calculated torque about the left string using integral calculas over a thin piece of stick at distance x. The total torque calculated was MGL/4. Then calculated Inertia. It came out to be 7ML^2/48. Then, I calculated angular acceleration as = 7g/12L.

    Finally, I calculated tension using free body diagram → T-mg+ ∫(dm * α * x) = 0
    →T-mg+∫(M/L*α*x.dx) = 0
    where x went from -0.25 to +0.75.

    T = mg-∫(ML*dm/L*x.dx)

    Is this the correct solution?
     
  5. Sep 13, 2012 #4

    Doc Al

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    Staff: Mentor

    Good.
    Redo that calculation.

    Not sure what you are doing here or what that last term represents.

    Just use: ƩF = ma
     
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