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j_ung
Jun 3, 2010, 12:06 PM
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I think we've established over and over again that "absorbs force," is technically incorrect to describe what happens when rope stretches during a fall. So, what exactly is the correct terminology to denote what a dynamic rope does? Is it "dissipate energy?" "Eat force and poop energy?"
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rtwilli4
Jun 3, 2010, 1:11 PM
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I think what he means is... how do you explain what is happening?
I'd like to know also. When I am teaching and I am explaining how the force exerted on the climber and belayer can change depending on how much rope is out, I don't know how to say it properly.
I always say "the more rope is out, the more it will stretch and the less force will be exerted on you," but I know that technically this is not correct. What would a physics teacher say?
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jt512
Jun 3, 2010, 3:05 PM
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j_ung wrote: I think we've established over and over again that "absorbs force," is technically incorrect to describe what happens when rope stretches during a fall. So, what exactly is the correct terminology to denote what a dynamic rope does? Is it "dissipate energy?" "Eat force and poop energy?"
The rope stretches, converting the kinetic energy of the falling climber into strain energy in the rope. So, saying that the rope "absorbs" energy (as opposed to force) is not too far off the mark.
The reason that a dynamic rope reduces the impact force on the climber, relative to a static rope (or the ground), is that force F is proportional to acceleration a:
F = ma ,
where m is mass (of the climber).
The stretchier the rope, the smaller will be a; and the smaller a is, the smaller F will be. A dynamic rope is stretchier than a static one; therefore, by the above argument, the impact force will be lower for a dynamic rope than a static one, all else equal.
Jay
(This post was edited by jt512 on Jun 3, 2010, 3:43 PM)
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shockabuku
Jun 3, 2010, 3:11 PM
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I would say:
The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment.
Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided.
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clews
Jun 3, 2010, 3:24 PM
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shockabuku wrote: I would say: The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment. Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided.
Wrong
Although not entirely... it's still wrong
The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer
as Jay already said F=ma
F is the force on your body
m is your mass
a is your bodies acceleration
acceleration is the change in velocity (m/s) over time (s) which gives you m/s^2 ... (metric)
your change in velocity is constant... you're going from falling to stopped with any type of rope.
a dynamic rope will increase the time required to stop your fall...
when you divide m/s by a larger s you get a smaller F
get it??????
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clews
Jun 3, 2010, 3:26 PM
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clews wrote: shockabuku wrote: I would say: The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment. Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided. Wrong Although not entirely... it's still wrong The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer as Jay already said F=ma F is the force on your body m is your mass a is your bodies acceleration acceleration is the change in velocity (m/s) over time (s) which gives you m/s^2 ... (metric) your change in velocity is constant... you're going from falling to stopped with any type of rope. a dynamic rope will increase the time required to stop your fall... when you divide m/s by a larger s you get a smaller F get it??????
assuming hooks law applies to this situation...which it does
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jt512
Jun 3, 2010, 3:35 PM
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shockabuku wrote: Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment.
Really? When you stop bouncing has your rope returned to its unstretched length?
Saying that the rope "dissipates" the energy of the fall, by converting it to heat, is misleading. At the bottom of the fall, when the impact force is at its maximum, your kinetic energy is zero and the strain energy in the rope is at its maximum. So, kinetic energy has been converted to strain energy. Yes, some heat has been generated, but it is apparently small compared with the strain energy in the rope, as every model of impact force I've seen ignores the heat. Everything that happens afterward—heat generated by bouncing up and down—is largely irrelevant to understanding how ropes reduce impact force, because the maximum impact force has already occurred.
Good point about global warming, though.
Jay
(This post was edited by jt512 on Jun 3, 2010, 3:41 PM)
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ptlong
Jun 3, 2010, 4:17 PM
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jt512 wrote: At the bottom of the fall, when the impact force is at its maximum, your kinetic energy is zero and the strain energy in the rope is at its maximum. So, kinetic energy has been converted to strain energy. Yes, some heat has been generated, but it is apparently small compared with the strain energy in the rope, as every model of impact force I've seen ignores the heat.
Simple spring models for a rope do a very poor job of reconciling the two numbers that appear on the hangtag of every dynamic rope. The reason for this is that ropes are damped, close to critically so. And during a fall a significant amount of energy is converted to heat. If this were not so a Hooke's Law approach to ropes would be sufficient to explain their behavior. It is not.
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hafilax
Jun 3, 2010, 4:24 PM
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clews wrote: clews wrote: shockabuku wrote: I would say: The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment. Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided. Wrong Although not entirely... it's still wrong The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer as Jay already said F=ma F is the force on your body m is your mass a is your bodies acceleration acceleration is the change in velocity (m/s) over time (s) which gives you m/s^2 ... (metric) your change in velocity is constant... you're going from falling to stopped with any type of rope. a dynamic rope will increase the time required to stop your fall... when you divide m/s by a larger s you get a smaller F get it?????? assuming hooks law applies to this situation...which it does
I'm not sure that anyone has tried to come up with a microscopic model for how a rope dissipates the energy. How much goes into heat, rearrangement of molecules, breaking of bonds, friction between strands etc.? Rope manufacturers might know but for us the phenomenological model is fine.
The reason why the impact force goes down as more rope is payed out is because the stiffness of the rope spring decreases with length. The same force will stretch a full 60m rope further than a 1m section of the rope. You can feel this while toproping. Near the bottom when you weight the rope you drop quite far but as you get higher this becomes less and less.
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clews
Jun 3, 2010, 4:42 PM
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hafilax wrote: So where's the damping? Just using Hooke's Law you end up with a harmonic oscillator. You need some dissipation mechanisms in there or the climber would end up wildly bounce up and down. Based on how little a climber bounces it seems to me that the rope-climber system behaves something like a critically damped to slightly over-damped simple harmonic oscillator (looking at rgold's paper he comes to the same conclusion).
I shouldn't have to explain damping in order to explain that the longer your rope stretches the softer your catch will be... as long as your rope follows something similar to what hookes law states... which it does... not entirely, but with the forces your body puts on your rope on a fall hookes law can be applied for basic understanding of the subject.
hafilax wrote: The same force will stretch a full 60m rope further than a 1m section of the rope. .
Thanks genius...
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ptlong
Jun 3, 2010, 4:51 PM
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clews wrote: I shouldn't have to explain damping in order to explain that the longer your rope stretches the softer your catch will be... as long as your rope follows something similar to what hookes law states... which it does... not entirely, but with the forces your body puts on your rope on a fall hookes law can be applied for basic understanding of the subject.
Yes, but that's not what the OP was asking. He wanted to know how to explain what was going on with regards to the energy.
You said:
clews wrote: The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer
This misrepresents what is going on. Damping (and the heat generated) is not insignificant.
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majid_sabet
Jun 3, 2010, 4:55 PM
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j_ung wrote: I think we've established over and over again that "absorbs force," is technically incorrect to describe what happens when rope stretches during a fall. So, what exactly is the correct terminology to denote what a dynamic rope does? Is it " dissipate energy?" "Eat force and poop energy?"
most of will become heat and goes to space
ohh *^^K, as soon jay512 is here we will have 32 pages of scientific data on what happens next
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shockabuku
Jun 3, 2010, 4:56 PM
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clews wrote: shockabuku wrote: I would say: The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment. Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided. Wrong Although not entirely... it's still wrong The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer as Jay already said F=ma F is the force on your body m is your mass a is your bodies acceleration acceleration is the change in velocity (m/s) over time (s) which gives you m/s^2 ... (metric) your change in velocity is constant... you're going from falling to stopped with any type of rope. a dynamic rope will increase the time required to stop your fall... when you divide m/s by a larger s you get a smaller F get it??????
No, it's not wrong, you're addressing a different issue.
What do you think happens to the energy generated during your fall?
Edit to add: And Jay is partially right, there is still a significant amount of energy stored in the rope but an appreciable fraction of the total fall energy is lost, else the climber would oscillate for a significant amount of time.
(This post was edited by shockabuku on Jun 3, 2010, 5:00 PM)
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clews
Jun 3, 2010, 5:06 PM
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ptlong wrote: clews wrote: I shouldn't have to explain damping in order to explain that the longer your rope stretches the softer your catch will be... as long as your rope follows something similar to what hookes law states... which it does... not entirely, but with the forces your body puts on your rope on a fall hookes law can be applied for basic understanding of the subject. Yes, but that's not what the OP was asking. He wanted to know how to explain what was going on with regards to the energy. You said: clews wrote: The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer This misrepresents what is going on. Damping (and the heat generated) is not insignificant.
fine
if we're talking about energy... not forces on the climber then the climber has potential energy that is converted into kinetic energy when they fall. The rope is critically damped to prevent oscillation, the belayer absorbes some of the kinetic energy when they fly up... that's a lot of the energy right there. The rest of the energy is lost due to friction with the rope against the draws and rock. That accounts for 99.99999% of your energy. If you want to talk about the energy transferred to the atmosphere due to the turbulence in the air and the sounds created and the small amount of heat given off by the rope stretching then go for it.
This is not specific to dynamic ropes. That is why although the same energy is "absorbed" and absorbed in the same manor that dynamic ropes do it in a way that minimizes force
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clews
Jun 3, 2010, 5:11 PM
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shockabuku wrote: clews wrote: shockabuku wrote: I would say: The rope dissipates energy, yes. It does so by transforming the falling climber's kinetic energy into heat energy which is lost to the environment. Work is done by the forces generated in the rope. Work transforms the kinetic energy of the falling climber into other forms of energy. Some of this transformed energy is stored in the rope as potential energy (like a spring). Some of the energy is transformed into heat by the friction between rope fibers as well as by the breaking of chemical bonds in the rope (this is why your rope gets stiff and wears out). Eventually the stored potential energy transforms into more heat energy (as you slowly bounce to a stop) and is dissipated into the environment. Ultimately, falling increases global warming and should be avoided. Wrong Although not entirely... it's still wrong The energy transferred to heat and noise and such will not make a large enough difference to make your fall noticeably softer as Jay already said F=ma F is the force on your body m is your mass a is your bodies acceleration acceleration is the change in velocity (m/s) over time (s) which gives you m/s^2 ... (metric) your change in velocity is constant... you're going from falling to stopped with any type of rope. a dynamic rope will increase the time required to stop your fall... when you divide m/s by a larger s you get a smaller F get it?????? No, it's not wrong, you're addressing a different issue. What do you think happens to the energy generated during your fall? Edit to add: And Jay is partially right, there is still a significant amount of energy stored in the rope but an appreciable fraction of the total fall energy is lost, else the climber would oscillate for a significant amount of time.
nope... still wrong
the heat created by the rope when it stretches does nothing to stop your fall
the OP asked what happens in the dynamic rope...
nothing noteworthy happens in a dynamic rope that doesn't happen in a static rope except for stretch
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ptlong
Jun 3, 2010, 5:22 PM
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clews wrote: The rope is critically damped
clews wrote: the heat created by the rope when it stretches does nothing to stop your fall
These two statements are contradictory.
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clews
Jun 3, 2010, 5:33 PM
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ptlong wrote: clews wrote: The rope is critically damped clews wrote: the heat created by the rope when it stretches does nothing to stop your fall These two statements are contradictory.
Must I point out that after you fall and the rope catches you you start swing? Only after you stop yourself against the rock do you stop moving... there we go, the source of this magical critical damping
Sure there is some damping in the rope but most of it comes from friction between rope, quickdraws, and you hitting the rock
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clews
Jun 3, 2010, 5:34 PM
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clews wrote: ptlong wrote: clews wrote: The rope is critically damped clews wrote: the heat created by the rope when it stretches does nothing to stop your fall These two statements are contradictory. Must I point out that after you fall and the rope catches you you start swing? Only after you stop yourself against the rock do you stop moving... there we go, the source of this magical critical damping Sure there is some damping in the rope but most of it comes from friction between rope, quickdraws, and you hitting the rock
sure i said rope... typo... should have said system
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summerprophet
Jun 3, 2010, 5:38 PM
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Well I am not sure of the teaching you are doing, but due to your lack of knowledge, I will assume it is guiding, or climbing instruction (rather than physics or sciences).
If elongation models, plasticity, and Hooks law are more than you care to explain to your clients, here is how I dumb it down for them:
The rope stretch uses time to elongate the fall over a longer period. If you were to hit the ground, time is essentailly instant, and bad things generally happen.
By distributing this interaction between go and stop over a longer period of time, the force is distributed to the climber without reaching the values where bad things happen.
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ptlong
Jun 3, 2010, 5:53 PM
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clews wrote: Sure there is some damping in the rope but most of it comes from friction between rope, quickdraws, and you hitting the rock
clews wrote: sure i said rope... typo... should have said system
Ropes are damped, almost critically. This is an observed fact.
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JimTitt
Jun 3, 2010, 5:57 PM
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Climbing ropes convert force into energy, absorb that energy and convert it into heat which is then slowly dissipated.
The laws of conservation of energy tell us that all the potential energy gained by the climber before he fall must be converted into heat when he falls, whether it is in friction in the belay device, through the runners or just in breaking of his bones as he hits the ground.
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d0nk3yk0n9
Jun 3, 2010, 6:08 PM
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Here's another way to look at why a rope that stretches more results in less force on the falling object (in this case the climber):
Impulse is defined as the product of a force and the time for which it is applied(for a changing force, it's the integral of force over time, but we'll use the simple version):
I = F x t
This also happens to be equal to the change in momentum. Momentum (p) is defined as mass times velocity.
p = mv
I = (delta)p
F x t = (delta)p
For a constant mass, (delta)p = m x (delta)v.
F x t = m x (delta)v
So the force felt is F= m x (delta)v / t
What this means is that when you fall on a rope, you feel more force the more abruptly (quickly) the rope stops you once it begins to apply force to you. So a static rope applies more force because it stops you much more quickly instead of stretching, while a dynamic rope applies less force to you because it applies it over a longer time as it stretches.
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j_ung
Jun 3, 2010, 6:09 PM
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jt512 wrote: j_ung wrote: I think we've established over and over again that "absorbs force," is technically incorrect to describe what happens when rope stretches during a fall. So, what exactly is the correct terminology to denote what a dynamic rope does? Is it "dissipate energy?" "Eat force and poop energy?" The rope stretches, converting the kinetic energy of the falling climber into strain energy in the rope. So, saying that the rope "absorbs" energy (as opposed to force) is not too far off the mark. The reason that a dynamic rope reduces the impact force on the climber, relative to a static rope (or the ground), is that force F is proportional to acceleration a: F = ma , where m is mass (of the climber). The stretchier the rope, the smaller will be a; and the smaller a is, the smaller F will be. A dynamic rope is stretchier than a static one; therefore, by the above argument, the impact force will be lower for a dynamic rope than a static one, all else equal. Jay
That's pretty much what I was looking for. Thanks, Jay.
J
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