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Old May 21st 2017, 02:16 PM   #1
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About Conservation of Potential Energy

Hi Colleagues,

I copied a "thread" then extended it with a comment and questions. This is basic. I don't know the answers.

Problem:
A uniform 3.00 kg rope, 24.0 m long lies on the ground at the top of a vertical cliff. A mountain climber at the top lets down half of it to his partner to help him climb the cliff. What is the change in Potential energy of the rope during this maneuver ?

Solution:
Using a coordinate system where h = 0 at the base of the cliff,

U_1 = 0

U_2 = (-12/2 m) x (3/2 Kg) x (9.8 m/s^2) = -88.2 J

Note that the distance traveled by the center of mass of the portion of rope dropped over the side of the cliff is half the height of the cliff.

U_2 - U_1 = -88.2 J - 0 J = -88.2 J
###################

Comments and Further Questions:
It seems the rope is modeled as an "extended BODY" with its "shape" as a
characteristic (not property). Energy propoerties of an extended BODY are its kinetic energy and potential energy. The change of U (PE) is represented as a sum over rope discrete parts of changes of elevation-of-center-of-mass times "mg." With the lowering event, the PE change, (U2 - U1) , was calculated to be -88.2J.

i) what is this "lowering event." Is there work?
ii) about this -88.2J enregy change. Does the "-" sign imply energy transfer "across the rope boundary" or "out of" the rope?
iii) The energy of the rope decreased. In accord with Conservation of Energy (at this very basic level) did the energy of something else, or somewhere else increase. How does Conservation of Energy happen here?

Thanks JP

Last edited by THERMO Spoken Here; May 21st 2017 at 02:19 PM. Reason: syntax
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Old May 22nd 2017, 02:52 AM   #2
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Hi THERMO...

My attention is drawn to the wording of this question...
"What is the change in Potential energy of the rope during this maneuver ?"

I assume they mean "What is the change in Potential energy of the rope when the maneuver is complete"

Tell your teacher of the error in this question and you may get extra marks "during" implies the maneuver is still occurring... not complete... so how can you possibly give a definitive answer

I'll do this in my own way and see if it helps...

Half the rope remains at the top ...forget it

Half the rope is now hanging over the cliff ..center of mass 6 meters below where it started

Mass of this half of the rope is 1.5 kg

So change in potential energy is hmg = 6 x1.5 xg = 9g (g has not been given)

i) what is this "lowering event." Is there work?... the work is done by the rope as it's potential energy is lowered , it want's to fall over the cliff.

ii) about this -88.2J enregy change. Does the "-" sign imply energy transfer "across the rope boundary" or "out of" the rope? ... the energy is given up in friction , appearing as noise and heat , as someone/some thing slows the falling rope and brings it to rest .

iii) The energy of the rope decreased. In accord with Conservation of Energy (at this very basic level) did the energy of something else, or somewhere else increase. How does Conservation of Energy happen here? ...see answer to ii) above.

Last edited by oz93666; May 22nd 2017 at 03:13 AM.
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Old May 22nd 2017, 08:02 AM   #3
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Originally Posted by THERMO Spoken Here View Post
Hi Colleagues,

i) what is this "lowering event." Is there work?
Yes, work is done by the weight of the rope. The integral of the force of gravity acting over the distance h is work done by gravity, and that work produces heat due to friction in the hands of the mountain climber as he resists that force. If you think about the mechanics of lowering something and then stopping it, some sort of braking mechanism must be employed, and like the brakes on your car the basic mechanism is friction, which is a non-conservative force which creates heat which is removed from the rope &mountain climber system.

Originally Posted by THERMO Spoken Here View Post
ii) about this -88.2J enregy change. Does the "-" sign imply energy transfer "across the rope boundary" or "out of" the rope?
Not sure what you mean by "across the bondary." PE is a measure of an object's ability to do work. Given that the sign here is negative, it means that after the lowering the rope has less capability of doing work in the future than it had originally (i.e., it has less potential to do work). Where did that potential go? That potential is lost as heat.

Originally Posted by THERMO Spoken Here View Post
iii) The energy of the rope decreased. In accord with Conservation of Energy (at this very basic level) did the energy of something else, or somewhere else increase. How does Conservation of Energy happen here?
As above, the PE of the rope is converted to heat, which dissipates away from the system. This is similar to what happens in an inelastic collision: PE + KE is not conserved in an inelastic collision.
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