## Very simple question regarding work and energy transfer

Thanks for the concern Drakkith. Yes I have understood everything that has been said. To a large degree, the responses have reflected my research. No agreement and no definitive explanation.

When explaining conversion of energy (CoE) in a falling body, this principal is used to explain GPE converted to KE during the fall which is converted to heat, sound, and deformation/strain energy upon impact. If the surface does not deform then the body takes all the KE and deforms. But, if the body tissues do not have the ability to reform they do not possess strain energy. That is, they deform permenantly or rupture. Based on a purely CoE analysis/explanation and that energy cannot be created or destroyed but only change form, what form did the KE or strain energy convert into when the tissues ruptured? Nobody seems to be able to explain this, and different concepts are used once we cannot 'identify' what form the energy transformed into.

Some try to explain the permanent deformation in terms of inelastic energy or other terms to refer to energy that cannot be relesed. Energy is the capacity to do work, that is apply force over a distance, so if energy cannot be released surely it is not energy.

Many describe the deformation/damage of a body when impacting with the ground as being work done by the ground on the body. Many suggest since the ground is not discplced the fallen body does not work on the ground. But W=Fd and Newton's 3rd law; while the falling body may not being doing work on the ground, the reaction force of the ground is doing work on the body. But when work is defined as the transfer of energy, where is the energy that the ground is transferring to the body.

Some have suggested the earth actually possesses mechanical energy (ME) and that is what is transferred. Others that work is not being done by the ground upon the fallen body but internal forces are responsible for work on the body which results in deformation. Others suggest the minutest undetectable movements of the ground are strain energy from the transfer of KE from the fallen body which then rebounds to transfer the KE back to the fallen body. There appears to be no definitive explaination of how energy is 'transferred' to the fallen body on impact. The explanations are many, they conflict, appear flawed and sometimes appear like exercise in shoehorning. From a force perspective, I have no problem, from a transfer of energy perspective ... well.

And here I was thinking this was a simple question.

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I think you are misunderstanding Selftaught. The replies here are mostly in agreement with each other, some of us just can't explain it well or don't know it detailed enough to really explain it. =)

 But, if the body tissues do not have the ability to reform they do not possess strain energy.
I don't think this is true. The body can withstand stresses up to the point that they exceed a certain level, at which point you start getting permanent damage. I'm not familiar with "Strain Energy" but I think that is what you were asking.

 Based on a purely CoE analysis/explanation and that energy cannot be created or destroyed but only change form, what form did the KE or strain energy convert into when the tissues ruptured?
The kinetic energy was released as the rupturing or shattering or whatnot of the body. Specifically the energy is released by breaking connective tissues, blood vessels, and other things. Are you asking what is the exact name of this energy? It's still kinetic energy. Take the spring on a trampoline, materials can resist changing and absorb energy until they reach their breaking point. I can't give you the exact name of what it would convert into, as I dont know.

 But W=Fd and Newton's 3rd law; while the falling body may not being doing work on the ground, the reaction force of the ground is doing work on the body. But when work is defined as the transfer of energy, where is the energy that the ground is transferring to the body.
The ground is transferring the bodies own kinetic energy back at it. Honestly, if it helps, you might want to think of the ground as not transferring any energy, so instead the energy cant transfer anywhere else but the body, resulting in injury and such.

 Some have suggested the earth actually possesses mechanical energy (ME) and that is what is transferred. Others that work is not being done by the ground upon the fallen body but internal forces are responsible for work on the body which results in deformation. Others suggest the minutest undetectable movements of the ground are strain energy from the transfer of KE from the fallen body which then rebounds to transfer the KE back to the fallen body. There appears to be no definitive explaination of how energy is 'transferred' to the fallen body on impact. The explanations are many, they conflict, appear flawed and sometimes appear like exercise in shoehorning. From a force perspective, I have no problem, from a transfer of energy perspective ... well.
You don't always get the exact same answers from everyone here, but most are generally about the same thing, just explained in a different way. Not all of us are immersed in physics and science as much as others.

 Quote by selftaught The ground has no mechanical energy. The object hits the ground. Given a hard surface that does not deform. There is no change in mechanical energy of the ground, therefore, no work is done on the ground and the KE accumulated during the fall has not been transferred to the ground.
As mentioned above, yes, the ground does deform, its just that it is very small. The Earth MUST apply a force to the object, and as you say, it cannot do this without some deformation. You could say that it does not deform, but then you have to say that the force of the Earth on the object is infinite for an infinitely small amount of time, so that the product F dx is finite.

 Quote by Drakkith I think you are misunderstanding Selftaught. The replies here are mostly in agreement with each other, some of us just can't explain it well or don't know it detailed enough to really explain it. =) I don't think this is true. The body can withstand stresses up to the point that they exceed a certain level, at which point you start getting permanent damage. I'm not familiar with "Strain Energy" but I think that is what you were asking. Strain energy is one of the three froms of mechanical energy along with gravitational potential energy and kinetic energy. Strain energy refers to the ability of an object to restore itself to its original shape once deformed. Your example of a trampoline is an example of strain energy when it is deformed. That is stored energy which is then converted into kinetic energy when reforming which is transferred to the trampolinist when they bounce upwards. There is no question associated with stresses and failure. The kinetic energy was released as the rupturing or shattering or whatnot of the body. Specifically the energy is released by breaking connective tissues, blood vessels, and other things. Are you asking what is the exact name of this energy? It's still kinetic energy. Take the spring on a trampoline, materials can resist changing and absorb energy until they reach their breaking point. I can't give you the exact name of what it would convert into, as I dont know. Exactly! What did the KE energy that caused the deformation that resulted in damage convert into? It has to convert into some form of energy according to the law of conservation of energy. The CoE doesn't allow for 'release' or 'absorption', it only allows for transformation from one form to another. Even if we look at the term 'released', what does that actually mean? It is released into what? The effect is damage to the body's tissues, no doubt, but 'released'? Released into another form of energy according to CoE. It is still kinetic energy unless you identify something that is moving. KE of a bat is applied to a bone which initially deforms. This slight deformation prior to failure is a transfer of KE to strain energy as the bone reforms. If the bone breaks, there is no strain energy in the bone as it does not have the ability to restore itself to its original shape. I can't see that the broken bone possesses kinetic energy. The ground is transferring the bodies own kinetic energy back at it. Honestly, if it helps, you might want to think of the ground as not transferring any energy, so instead the energy cant transfer anywhere else but the body, resulting in injury and such. Unfortunatly it doesn't help. I'm writing a book applying injury science to the tactics and techniques of combatives (no matter however they are described). I am also drawn like light to black hole to flawed arguments. Work is described as the transfer of energy and as Fd. With Newton's 3rd law that is the 'F' of the ground reaction force and the deformation of the falling body that is 'd', the ground appears to be doing work on the body when it impacts. Given the explanation of work as being the transfer of energy, back to this quandry, what energy is being transferred to the body given the body did not transfer any energy to the ground because the displacement of the ground was zero. You don't always get the exact same answers from everyone here, but most are generally about the same thing, just explained in a different way. Not all of us are immersed in physics and science as much as others.
I've written to a number of professors of biomechanics and have not received any responses as yet. The explanations provided here, while appreciated, appear to confirm what I have read to date in my research - that there is on definitive explanation concerning the issues I've raised.

Cheers :)

 Quote by Rap As mentioned above, yes, the ground does deform, its just that it is very small. The Earth MUST apply a force to the object, and as you say, it cannot do this without some deformation. You could say that it does not deform, but then you have to say that the force of the Earth on the object is infinite for an infinitely small amount of time, so that the product F dx is finite.
OK. Now that I can see, albeit, I have not come across in the multitude of books I've referred to on this subject. ... more research now to find an authoritative source for this explanation now. You see, I'm writing a book concerning injury science and as I'm no expert I'm supporting all my arguments with authoritative sources.

Thanks RAP.
 Drakkith. Sorry about my posting. I'm new here and didn't know how to do the quoting thing. I've come here after exhausting all other resources. Cheers

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 Quote by selftaught The explanations provided here, while appreciated, appear to confirm what I have read to date in my research - that there is on definitive explanation concerning the issues I've raised.
To me it seems like you got some good definitive explanations. Which specific issue still lacks a definitive explanation?
 DaleSpam ... my exploration of these issues is really crystalising them in my mind, so thank you for the opportunity for presenting them in hopefully a more succinct form. 1. Conservation of Energy (CoE) - energy is neither created nor destroyed, it can only change form. 2. Principle of CoE is often explained using a falling object as an example. 3. Gravitational potential energy (GPE) is transformed to kinetic energy (KE) during the descent. 4. Upon impact GPE = 0, KE = 0 of the object after KE was maximum just before impact. 5. If the impact surface does not deform and neither does the object then 100% of the KE has been transformed into sound and heat energy. 6. If the impact surface does not deform and the object does, some of the KE was transformed into deformation. 7. If that deformation returns to its original shape, the KE was transformed into strain energy (SE; also referred to as deformation energy or elastic energy). 8. If the deformation goes beyond its tolerance limits, damage results which means the object/body cannot return to its original shape, which means the SE has been transformed into another form of energy. 'Absorbed', 'dissipated', 'lost', are all used to explain the effect, but, it does not explain it in terms of the law of CoE which states that energy can only be transfromed from one form to another. 9. What form of energy does this SE take when tolerance limits are exceeded and the material/tissues cannot restore themselves to their original shape, ie. when damage results? The work issue is hopefully resolved based on a recent posting, however, subject to finding authoritative support. With regards to this issue, you can see I'm not alone in being confused as to the energy mechanism in the injury process. The World Health Organisation refers to 'transfer of energy or prohibits the transfer of energy'. Whiting and Zernicke refer to two principles in the injury process: conservation of energy and transfer of energy. They appear to be both trying to explain injuries occuring when energy is transferred and where it appears not to be transferred. This situation involves the concept of work. 1. W=Fd 2. McGinnis: work is 'the means by which energy is transferred from one object or system to another'. 3. W = change in KE + GPE + SE 4. Someone hitting another person resulting in deformation beyond tolerance levels is the transfer of KE. No problems (apart from above). Work is being done by the person hitting on the person being hit. 5. Many suggest the injury resulting from a fall is because of the work done on the person's body by the impact surface. 6. The ground has no ME: KE + GPE + SE = 0. 7. Was any energy transferred from the falling body on impact? 9. Many suggest (with the exception of a recent post) that no deformation occurs on a hard surface therefore there is no change in ME, therefore no work is done by the body on the ground, therefore the ME of the ground remains 0. 10. No ME means nothing to transfer therefore the ground cannot do work on the person's body. We need another principle to explain the injuries; maybe CoE. 11. Unfortunatley Newton's 3rd law and W=Fd suggests work is done on the faller's body. The reaction force is applied to the body which deforms it. 12. But where did the energy come from to be transferred when work is conceptualised in terms of the transfer of energy? 13. Some suggest 'retransmission'. This relies on energy being first transferred to the impact surface, ie. work being done by the body on the impact surface, and then the impact surface transferring the energy to the body, ie. the impact surface doing work on the body. 14. If the impact surface SE = 0 upon impact, this retransmission argument would appear to fail, even though the W = Fd argument still holds, albeit we cannot identify where the energy came from to transfer to the person's body resulting in deformation and injury. I'm now on the hunt for an authoritative source that will support the infintesimal increase in SE upon impact resulting in a transfer of KE from the faller's body to the ground which then rebounds transforming SE into KE and transferring it to the faller's body by doing work on it. If anyone can point me in the direction of a book that would provide this support, very much appreciated :).
 Mentor Surely you do not think that ALL of these 23 points lack definitive explanation. For instance, the first number 1, conservation of energy, is clearly as definitive as anything can possibly be. Energy is conserved. So I ask again. Which issues are the ones that lack definitive explanation?

 Quote by DaleSpam Surely you do not think that ALL of these 23 points lack definitive explanation. For instance, the first number 1, conservation of energy, is clearly as definitive as anything can possibly be. Energy is conserved. So I ask again. Which issues are the ones that lack definitive explanation?
DaleSpam. Thanks for your post. Regarding the specific issue that you raised. If you think the conservation of energy (CoE) is clearly as definitive as anything can possible be, please explain what form of energy the kinetic energy (KE) accumulated during a fall is transformed into when an injury or damage occurs when a body or an object impacts with the ground and the ground does not deform. The CoE states that energy cannot be created or destroyed, it can only be transformed into another FORM of energy. The CoE does not refer to the release, dissipation, or deformation of energy. It states one form of energy transformed or converted into another.

I've just read a book on Conservation Laws by Benjamin Crowell. He refers to an example of a comet impacting Jupiter and 100% of the KE being transformed into heat and sound energy. It is a very simplistic example and of course ignores deformation of the surface of the planet. ... and in this case, if the deformation is not deformation/strain/elastic energy, that is, if the deformation does not reform to its previous shape, than that KE that caused the deformation has been transformed into another form of energy. What form of energy has that KE been transformed into? THAT question has not been answered here, nor is it answered in any of the multiple texts I've referred to, nor has it been answered tonight by the profession engineer who resides in the same apartment block as I do.

That is one issue that lacks an explanation, let alone a definitive explanation.

The issue of reconciling work, the transfer of energy, and injury or damage resulting from impact from a fall has only one potential explanation in the posts to date. Unfortunately, Crowell tends to cast doubt on it. Again, no definitive support from an authoritative source can be found to explain what energy, or where it came from, is being transferred to the impacting body to cause deformation, let alone damage. The common response is, as my engineer source tonight immediately suggested and which was evidenced in the posts, can't you answer the question from a force perspective. You CAN. No question. BUT, from an energy perspective, there are problems. The ground has no mechanical energy, and given, as Crowell suggests, no work is done/energy transfered by the impacting body with the ground, the ground has NO mechanical energy to transfer to the body causing deformation of any description.

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 Quote by selftaught If you think the conservation of energy (CoE) is clearly as definitive as anything can possible be, please explain what form of energy the kinetic energy (KE) accumulated during a fall is transformed into when an injury or damage occurs when a body or an object impacts with the ground and the ground does not deform.
In the end, heat and strain. There is a transient change of some of the energy into mechanical waves, but in relatively short order those go to heat. Which is the next point that lacks a definitive explanation?

Btw, you really need to learn to be more concise.

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 Quote by selftaught Energy is the capacity to do work. How can it be energy if it cannot be used to do work? Seems, to this novice, a bit of 'shoehorning' is going on.
Hang on- not all energy can be used to perform work. Energy takes on many different forms, and can be interconverted between forms. The process is not 100% efficient (from the laws of thermodynamics), and so some energy is permanently 'lost', in the sense that it cannot be used to perform work.

 Quote by DaleSpam In the end, heat and strain. There is a transient change of some of the energy into mechanical waves, but in relatively short order those go to heat. Which is the next point that lacks a definitive explanation? Btw, you really need to learn to be more concise.
Most refer to heat and sound energy. Strain energy refers to the ability of an object/body to restore itself to back to its original shape after being deformed. If the deformation goes beyond the limits of its ability to restore itself back to its original shape, eg. it is damaged, by definition it does not possess strain energy. Hence, the KE was not transformed into strain energy. You're only left with heat and sound energy then. Based on that logic, you'd be arguing that in a fall which results in damage and no deformation of the impact surface the kinetic energy accumulated during the fall is converted into heat and sound energy only. Therefore, injuries are caused by KE being converted into heat and sound energy. If that is your argument, then you're probably the first to articulate that argument. And I could not argue against you as I've not found anything that argues (or supports) that proposition.

Re concise - I wonder what explanations would have been provided if I simply (as I have) asked, what form of energy is the KE transformed into when a body/object impacts a nondeforming surface? As has been seen by the responses, that probably would not have helped.

But thanks for your post. It's all helping in building an appreciation that this issue is not well considered nor understood.

 Quote by Andy Resnick Hang on- not all energy can be used to perform work. Energy takes on many different forms, and can be interconverted between forms. The process is not 100% efficient (from the laws of thermodynamics), and so some energy is permanently 'lost', in the sense that it cannot be used to perform work.
I am focussed on mechanical energy primarily. In mechanics, the definition of energy is the capacity to do work. Given the conservation of energy, energy cannot be created nor destroyed. I would have thought 'permanetly lost' would equate to being destroyed. I understand the not 100% efficient idea, but the energy that is 'lost' transforms into another form of energy that then may be used to do work. If I'm incorrect I'd appreciate being corrected, but with a reconciliation with the idea that energy cannot be created nor destoryed and its definition as the capacity to do work.

Cheers :)

 Quote by selftaught Thanks for the concern Drakkith. Yes I have understood everything that has been said. To a large degree, the responses have reflected my research. No agreement and no definitive explanation.
Ok, if you want to get serious, lets get serious. The best way to understand what is going on is to start with simple examples and build up to more complicated ones. A semi-elastic collision between two bodies is the most complicated, so that comes last.

First, you consider an elastic collision. Think of a small mass with a small spring to the right of it, moving with velocity V to the right. That's "the object". Then, to the right of it is a large mass with a large spring to the left of it. That's the Earth, its not moving. When the object and the Earth first touch, both springs start to compress. The Earth exerts a force on the object, compressing its spring and slowing it down, the object exerts an equal force on the Earth, compressing its spring and making the Earth move to the right. The Earth is so massive, that we can say it hardly moves at all. After a while, the object comes to rest because of the force of the Earth spring pushing back on it. Now both springs are in their maximum deflection. Some of the original kinetic energy is in the object spring, some of it in the Earth spring, the total of both is the original kinetic energy of the object when it first touched the Earth. The Earth and the object keep pushing on each other, and the object starts to move to the left, away from the Earth. Both springs start to decompress. When the object gets to the position where it first touched the Earth, both springs are back to their original unstressed length, and all of the energy that was contained in the springs has now been transferred to the kinetic energy of the object as it moves to the left, away from the Earth. To summarize, before the object touched the Earth, all the energy was its kinetic energy. During the collision, that kinetic energy was converted to the potential energy of the springs. Part of the kinetic energy went to potential energy of the Earth spring, part went to the kinetic energy of the object spring. Then, when the object started to move away from the Earth, the potential energy of both springs was transferred to the object, until it had regained all of the original energy which is now its kinetic energy, except it is moving to the left, not the right. As far as work is concerned, the total distance either object moved while the forces were in effect is zero, while the force at any point was the same going in as when going out. The work done on the object is zero - its energy is unchanged. The work done on the Earth is zero - it is still motionless.

Now lets do an inelastic collision. In this case, the entire kinetic energy of the colliding object gets converted to heat, and it sticks to the Earth, not by gravity, but because the collision is inelastic. We can think of an inelastic body ("object" or "Earth" or both) as a very damped spring, it gets compressed, but the energy that was formerly held by the compression of the spring is now converted into heat energy, and the spring stays compressed. The object has been deformed (or "injured"). Also, there is a partially elastic body, where its spring gets compressed and bounces back, but does not bounce back to its normal position. Part of the energy going into it is converted to heat, part is stored as potential energy of compression. There are many ways to have an inelastic collision. You can have the object be inelastic while the Earth is elastic or partially elastic, the object can be elastic or partially elastic, while the Earth is inelastic, or you can have both be inelastic. If both are partially elastic, the object will bounce off the Earth, but not as energetically as if the collision were elastic.

Lets say the object is inelastic, the Earth is elastic. Then, just as before, the object spring and the Earth spring get compressed until the object stops. The energy that would have been kept in the object spring as potential energy is now converted to heat, and the object spring stays compressed. The Earth spring expands, compressing the object spring even more, all of which gets converted to heat in the object. When the Earth spring has expanded to its normal position, the object and the Earth are motionless, and all of the original energy has been converted to heat contained in the object. The object spring is compressed (injured), and contains no potential energy. As far as work is concerned, the force on the object as it moves in is not the same as the force on the object as it moves out. Although the total distance moved while the force is in effect is zero, the forces are not the same at a particular point going in as going out. This means the integral of F dx is not zero, the work done on the object is not zero, but is equal to the original kinetic energy, all of which has been converted to heat.

Now lets say the object is elastic, the Earth is inelastic. The same thing happens, but in reverse. The object and Earth wind up motionless, but now all the kinetic energy of the object has been converted into heat that is contained in the Earth, and the Earth spring is permanently compressed, with no deformation or "injury" to the object. Work has been done on the Earth, not the object, and its energy has increased. All of the original kinetic energy of the object is now contained in the Earth as heat, and the Earth is deformed.

Notice that deformation is associated with conversion to heat. An elastic body does not deform and does not acquire heat in a collision.

Now we have to consider the real case. If the collision is not completely inelastic, the object will bounce off the Earth after the collision. In the real case, there is a little bounce, but lets say we can ignore that. Now we can say the collision is inelastic. But is the object inelastic while the Earth is elastic or partially elastic? Maybe the object is elastic or partially elastic while the Earth is inelastic? Maybe both are inelastic. All of these possibilities will yield an inelastic collision.

So now we have a more complicated set of possibilities. I think we can assume that the object is inelastic, since it gets very deformed. I'm not sure, but I think we might say that the Earth is inelastic as well. In this case, part of the initial kinetic energy goes into heating the object, part goes into heating the Earth. How much goes where depends on the strength of the object spring and the Earth spring. Since the Earth is much "harder" than the object, I think we can say that most of the kinetic energy is converted to heat in the object and the Earth ultimately absorbs only a small fraction of the energy. I might be wrong on this.

The process of the kinetic energy being absorbed by a real object is complicated. The simple idea of a spring does not cover it all. There are pieces sliding past each other, creating friction heat, there are damped springs being compressed, there is viscous effects of fluids being mechanically stirred which converts to heat. There is "flattening" of the object, but that probably doesn't account for a lot of the energy. There are sound waves generated in the object, which are eventually dissipated into heat. Also, there is a third object here - the atmosphere. Some of the energy gets converted to atmospheric sound which radiates away, but that probably doesn't account for a lot of the energy. The bottom line is that a good portion of the object's kinetic energy is passed to the Earth, which is then passed back to the object. Most of the kinetic energy winds up in the object as the form of heat, with the object being quite deformed.

If you go over the 23 points, I think that the above argument shows that:

5 is wrong, heat is generally associated with deformation, except for viscous stirring of fluids.

6 is wrong, there is no "energy of (permanent) deformation". Permanent deformation occurs because energy has been converted to heat.

7 is right, but incomplete - the strain energy is then released, to either impart kinetic energy, or converted to heat.

8 is correct but not covered by the above argument - This is a case where you could say the spring breaks. When this happens, pieces of the object are suddenly moved around, colliding elastically and semi-elastically with each other, creating heat and internal sound waves, all of which finally wind up as heat, with the resulting deformation being evidence of that process.

9+6 is incorrect. Again, and again, and again, the ground acquires energy from the object upon impact. You have to understand that this is true. Just because it seems hard does not mean it acquires no energy. If you have a very strong spring, it need hardly move at all in order to absorb a lot of energy.

9+7 - YES

9+9 wrong
9+10 wrong
9+12 Again, from the impacting object
9+13 Again, correct
9+14 Again, SE of the Earth is not zero, it acquires energy from the impacting object.

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 Quote by selftaught Most refer to heat and sound energy.
That is fine. I mentioned mechanical waves (sound) as a transient form of energy that quickly decays into heat. I prefer the term mechanical waves as it includes compression waves that are outside of the audio frequency as well as shear waves which are not generally associated with sound and probably cause the majority of the soft tissue damage in a fall. But as long as everyone understands that we are talking about a generalized "sound energy" then that is OK.

 Quote by selftaught Strain energy refers to the ability of an object/body to restore itself to back to its original shape after being deformed. If the deformation goes beyond the limits of its ability to restore itself back to its original shape, eg. it is damaged, by definition it does not possess strain energy. Hence, the KE was not transformed into strain energy.
Some of the body's KE does remain as elastic strain energy even after severe plastic deformations. Consider an undamaged body simply at rest on the ground compared to one in free fall. The falling body is unstrained and the body on the ground is elastically strained. Similarly for a damaged body at rest on the ground.

 Quote by selftaught It's all helping in building an appreciation that this issue is not well considered nor understood.
If by not well understood you mean by you, then I agree. If you mean by the field in general, then you are simply wrong. The equations of motion have been around for about 3 centuries and are well known and validated. Additionally modern computational techniques make realistic modeling of viscoelastic materials quite feasible.

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