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NotZakalwe
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Homework Statement
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?
Homework Equations
Ug = mgh
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?