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Gravitational Potential of Hanging Cord

  1. Apr 27, 2015 #1
    1. The problem statement, all variables and given/known data
    A uniform cord of length .25 meters and mass .015 kg is initially stuck to a ceiling. Later, it hangs vertically from the ceiling with one end still stuck. What is the change in gravitational potential energy of the cord with this change in orientation?


    2. Relevant equations
    Ug = mgh



    3. The attempt at a solution
    The initial gravitational potential energy of the cord is mgh
    Considering a differential mass element of the cord $$\frac{m}{l}$$ the gravitational potential energy of the cord after the change in orientation is

    $$\int^{h}_{h_0} \frac{m}{l}gh = \frac {\frac{m}{l}gh^2}{2} - \frac{\frac{m}{l}g{h_0}^2}{2}$$

    Taking $$l = h$$ $$h_0 = 0$$ this simplifies to

    $$\frac{mgh}{2}$$

    Subtracting the final gravitational potential energy from the initial gravitational potential energy yields

    $$\frac{mgh}{2}$$

    Is this correct?
     
  2. jcsd
  3. Apr 27, 2015 #2
    Not sure as you didn't define what h is?
     
  4. Apr 27, 2015 #3

    rl.bhat

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    Homework Helper

    I
     
  5. Apr 27, 2015 #4

    rl.bhat

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    Homework Helper

    It is correct.
     
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