# Gravitational Potential of Hanging Cord

1. Apr 27, 2015

### NotZakalwe

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. Apr 27, 2015

### paisiello2

Not sure as you didn't define what h is?

3. Apr 27, 2015

### rl.bhat

I

4. Apr 27, 2015

### rl.bhat

It is correct.