Potential energy of a massive string

[JCOM44]

How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it?
The string is uniform, so I know its center of mass is at L/2.

 

[phinds]

How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it?
The string is uniform, so I know its center of mass is at L/2.

How would you find the potential energy of just the string?

 

[JCOM44]

How would you find the potential energy of just the string?

I tried using the fact that the only force on the string is F=mg, then W=mg*y, and remembering that -∇U=W, I found that U=-½mgy^2, but I feel this is not right because it has no information about the length, am I doing something wrong?

 

[berkeman]

I tried using the fact that the only force on the string is F=mg, then W=mg*y, and remembering that -∇U=W, I found that U=-½mgy^2, but I feel this is not right because it has no information about the length, am I doing something wrong?

Potential energy is defined with respect to some reference height. You have the masses of the rope and the weight, so you have two centers of mass to sum for the total GPE. But each has to be some distance above the ground (if that's where you are taking GPE=0 to be), so when you do that sum, the length of the rope will come into play. Makes sense?

 

[CWatters]

How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it? The string is uniform, so I know its center of mass is at L/2.

More details required. Is the string hanging vertically? horizontally? Mass on the end? middle?

Is the string swinging back and forth like a pendulum?

Is the string acting like a spring?