How Does Lowering Half a Rope Affect Its Potential Energy?

In summary, during this maneuver, the potential energy of the 3.60-kg rope decreased by 102 J as the mountain climber lowered half of it, with a mass of 1.8 kg, to help their partner climb up the vertical cliff. This problem can be approached as a center of mass problem, where the object's mass can be considered to be concentrated at its center of mass when calculating gravitational potential energy.
  • #1
Shifty
10
0
A uniform 3.60- kg rope 23.0 m long lies on the ground at the top of a vertical cliff. A mountain climber at the top let's down half of it to help his partner climb up the cliff.

What was the change in potential energy of the rope during this maneuver?

-This in a moment of inertia assignment, so I'm guessing it uses it somewhere. Don't have a clue after that.

-Help would be appreciated :)
 
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  • #2
It may be a moment of inertia question, but this is a center of mass problem. I'll give you a hint: you can consider an object's mass to be concentrated at its center of mass when calculating gravitational potential energy.
 
  • #3
ideasrule said:
It may be a moment of inertia question, but this is a center of mass problem. I'll give you a hint: you can consider an object's mass to be concentrated at its center of mass when calculating gravitational potential energy.

Thanks for the reply :), but I already tried that and calculated the change to be -203 J, unfortunately it didn't yield a correct answer.

\Delta U=-mgy=203

y=23m/4

EDIT!: looking at this reply I realized the total mass would only be half since only half of the rope was lowered. That solved it, thanks :)!

m=3.6kg/2, implies \Delta U=102J
 
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FAQ: How Does Lowering Half a Rope Affect Its Potential Energy?

What is potential energy?

Potential energy is a type of energy that is stored in an object or system, based on its position or state. It has the potential to do work, and can be converted into other forms of energy.

How is a rope related to potential energy?

A rope can be used to transfer potential energy from one object to another. For example, a rope can be used to lift a heavy object, storing potential energy in the object as it gains height.

How does the length of a rope affect its potential energy?

The longer the rope, the greater its potential energy. This is because the weight or object being lifted has to travel a greater distance to reach a certain height, therefore storing more potential energy.

Can potential energy be converted into other forms of energy?

Yes, potential energy can be converted into other forms of energy, such as kinetic energy, thermal energy, or electrical energy. This conversion occurs when the object or system is allowed to move or change states.

What factors can affect the potential energy of a rope?

The potential energy of a rope can be affected by its length, the weight of the object being lifted, and the height it is lifted to. Other factors such as friction and air resistance can also affect the potential energy of a rope system.

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