# Energy in a rope

1. Jul 10, 2010

### Higgy

1. The problem statement, all variables and given/known data

A mass M hangs from a rope which is connected to a ceiling. The rope does not stretch. How much energy is stored in the mass-rope system?

2. Relevant equations

$$F_{g}=-mg=-Mg$$
$$W=Fd$$

3. The attempt at a solution

I'm confused. The mass will have potential energy equal to mgh, but we're not told the height. The rope doesn't stretch so there's no spring energy. So maybe the answer they want is zero?

EDIT: Forgot to include that they say the length of the rope is L.

Last edited: Jul 10, 2010
2. Jul 10, 2010

### rock.freak667

The center of mass of the rope will be at L/2, assuming the rope is uniform.

3. Jul 10, 2010

### Higgy

I'm guessing that we're supposed to think of the rope as massless, since they don't say anything about the mass of the rope.

Here's how I'm thinking about it. The mass feels a force downward of F=Mg. But it's in static equilibrium, since it's not moving. So it must be feeling a force upward of F=Mg, too. So the rope is pulling upward on the mass. The rope is attached to the ceiling, so it pulls on the ceiling with a force of F=Mg. The ceiling pulls back with a force of F=Mg. Nothing moves, nothing stretches.

There's a lot of "pulling" going on, so I imagine energy. But nothing moves, so maybe the system doesn't have energy? Can anyone confirm this or tell me where I'm going wrong?

Last edited: Jul 10, 2010
4. Jul 10, 2010

### rock.freak667

I now re-read the question, I thought you were finding the energy of the rope. The relative height of the mass would just be the length of the rope wouldn't it? (If you choose the point where the rope attaches to the ceiling as a 0 energy line)