Gravitational Potential of Hanging Cord

[NotZakalwe]

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

U_g = 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?

 

[paisiello2]

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

 

[rl.bhat]

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

U_g = 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?

I

 

[rl.bhat]

It is correct.