How Much Energy Is Stored in a Non-Stretching Rope and Mass System?

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Homework Help Overview

The problem involves a mass hanging from a non-stretching rope connected to a ceiling, with a focus on determining the energy stored in the mass-rope system. The context includes gravitational potential energy and considerations regarding the rope's properties.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the potential energy of the mass and the implications of the rope's non-stretching nature. Questions arise about the height of the mass and whether the rope's mass should be considered. There is also contemplation on the forces acting on the mass and the system's energy state.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have offered insights into the forces at play and the concept of static equilibrium, while others are questioning the assumptions about the rope's mass and energy storage.

Contextual Notes

There is a lack of information regarding the mass of the rope and the specific height of the mass, which participants are considering in their reasoning. The problem's constraints and the definition of the energy reference point are also under discussion.

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Homework Statement



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?

Homework Equations



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

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:
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The center of mass of the rope will be at L/2, assuming the rope is uniform.
 
rock.freak667 said:
The center of mass of the rope will be at L/2, assuming the rope is uniform.

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:
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)
 

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