Very simple question regarding work and energy transfer

[selftaught]

Not true; look at my post #34. The creation of new surface area (which occurs in fracture) stores energy because (electrostatic) atomic bonds have been broken.

Broken atomic bonds. (This applies to both additional surface area and crystal defects.)

You seem to be aggravated that it's taken a few pages of posts to figure out precisely what you're looking for. Your original question was "I can understand work in this situation in terms of W=Fd and Newton's law of action-reaction. I cannot understand work in terms of energy transfer in this situation as the object or ground possessed no energy to begin with." It was not "When someone falls and is motionless and injured, please delineate exactly how their original kinetic energy is now apportioned."

Again the multiquote didn't work. Too true, Mapes. You did refer to 'new surface area' in post 34. The first to suggest more than sound and noise energy. However, as explained in a previous post today, I'm not from your tribe and that phrase would not suggest a form of energy to anyone outside your tribe. My understanding of the forms of energy are as listed in a post by someone else reference Wikipedia, although my understanding came from more reliable sources.

Your right. I started out asking the question about the relationship between work and injury from a fall. I was then bombarded with a multitude of concepts other than work and energy so I introduced my second question which I advised I was saving for an additional post. This may have confused the issue, for which I apologise. I've got something to work with now concerning what form of energy the KE accumulated in a fall is converted to upon impact. It took a while, and is not easily sourced in any of the dozens of texts I've read on physics, mechanics, and biomechanics, but I've got more than most in explaining this issue. The influence of work on injury, with work being defined as, among other things, the means by which energy is transferred from one object or system to another is still unclear - particularly given Crowell's latest brief email to me on the subject.

Cheers

 

[Drakkith]

2. How does the concept of work explain the damage sustained when landing from a fall?

Lets do something simple first. If I drop a bowl on the ground and it shatters, how does work explain that?


Edit: Yes, I am asking you. This is a 2 way conversation and I don't know what you know compared to me. It is entirely possible you or I have the wrong idea about work and force and energy, and the only way to tell is to talk!

 

[selftaught]

For me pressing muti quote then quote, or pressing quote, are producing the same result. One long quote of the entire post rather than each paragraphe being a quote which i can then comment on. I'm obviously doing something wrong. Any suggestions?

 

[Drakkith]

Press the multi quote for each post you want to quote, then hit New Reply, not quote.

 

[Dale]

DaleSpam. Tried your advice but only got this one long quote. Ok for this reply but not for others.

Multi quote allows you to respond to several different posts at once. There is no automatic functionality for separately quoting individual paragraphs. What I do is I quote a post, then I copy the open-quote to the end so that I have a close quote followed by an open quote. Then I copy and paste that at each spot where I would like to insert my reply.

That restriction is based on the definition of injury as being exposure to energy

That is a bad definition. Mere exposure to energy does not cause injury, as I illustrated above.

There is a whole science developed around the concept that injury is caused by energy. All the safety features in your car have arisen from this science.

Not true. Many of the safety features in the car do not reduce the amount of energy transferred to the passengers. In fact, about the only one that I can think of which does is anti-lock brakes which reduce the speed of the vehicle prior to the collision. Safety belts, air bags, and crumple zones all reduce the force and acceleration sustained, but not the amount of energy transfered. Reducing the force, in turn, reduces the strain, which is the final cause of mechanical injury.

 

[Rap]

I think everything can be explained in terms of energy.

To simplify things, potential energy converts to kinetic energy, that's easy. When the object hits the earth, almost all of the kinetic energy ultimately gets converted to heat, because the object is no longer moving. That's easy too. The question of what are steps by which the kinetic energy gets converted to heat, that's the complicated part. Following where the energy goes from the time the object first touches the earth, until the collision is complete, is complicated.

Lets ignore all the small contributions:

1) Energy which deforms the Earth - If the Earth were elastic, but not rigid, it would absorb some of the energy and give it back to the object. If the Earth were elastic and perfectly rigid, it would absorb no energy, but it still would exert a force on the object.

2) Sound energy - A small amount of energy is lost in sound waves, which ultimately dissipate in the atmosphere as heat.

I think this about covers the energy lost by the object to other systems. That means most of the kinetic energy conversions to heat occur in the object as it collides with the Earth. Here are my ideas about the mechanisms by which the kinetic energy is converted to heat in order of importance, assuming the object is a human body. Please add to the list, I'm sure I am forgetting some.

1) Broken atomic bonds - tearing and breaking of things. Think of this as a spring that you stretch until it snaps. You add energy to it, it holds it as potential energy, the spring snaps, it vibrates but the vibration is damped, and all that potential energy goes to heat. During the collision, the energy added is due to the force of the Earth on the contact part of the object, then force transmitted to the part above it, etc.

2) Internal pressure waves or sound waves (compression and shear) which dissipate to heat.

3) Inelastic rearrangement of parts. This is what I was modeling as an inelastic spring, one that compresses, but does not bounce back. The permanent compression holds no potential energy - the energy that went into the compression was not used to bounce the spring back, but was rather dissipated as heat.

4) Permanent elastic deformation - Parts of the body may act as springs which are compressed, do not lose their stored potential energy as heat, but are prevented somehow from springing back. Like a bone that gets bent and lodged between two other bones or something. This is energy that is not converted to heat. I think this contribution is quite small.

 

[selftaught]

Lets do something simple first. If I drop a bowl on the ground and it shatters, how does work explain that?


Edit: Yes, I am asking you. This is a 2 way conversation and I don't know what you know compared to me. It is entirely possible you or I have the wrong idea about work and force and energy, and the only way to tell is to talk!

OK. Thanks. I see it can be explained two different ways which I cannot reconcile.

1. When work is described as the means by which energy is transferred from one object or system to another. And W=Fd. The bowl accumulates KE during its fall. The ground possesses no mechanical energy: KE+GPE+SE=0. Thus, the bowl has the capacity to do work on the ground but the ground does not have the capacity to do work on the bowl, unless, the work done by the bowl on the ground transfers its KE to the ground in the form of SE which is then transferred back to the bowl resulting in damage. (I'm still working on RAP's expanation). However, there is conflicting opinion as to whether or not the ground does work on bowl. Some suggest the work is internal to the bowl. Bottom line, I'm looking to understand the application of work in this context in terms of the transfer of energy only.

2. From a force perspective, easy peasy. W=Fd and Newton's third law. Bowl applies force to floor which applies reaction force in turn. Bowl deforms so work is done on bowl by floor. This is where it gets a bit tricky. The floor does not deform so no work is done on the floor. However, Crowell explained that if work is done on one object, work is also done on another. If no displacement of the floor ...? See above as regards to infintessimal deformation and transfer.

I keep on getting caught up with the transfer of energy, and this is the concept I am interested in.

Thanks

 

[selftaught]

Press the multi quote for each post you want to quote, then hit New Reply, not quote.

thanks

 

[selftaught]

Multi quote allows you to respond to several different posts at once. There is no automatic functionality for separately quoting individual paragraphs. What I do is I quote a post, then I copy the open-quote to the end so that I have a close quote followed by an open quote. Then I copy and paste that at each spot where I would like to insert my reply.

THanks. Giving it a try. Found I also had to copy the quote to the front of subsequent paragraphs.

That is a bad definition. Mere exposure to energy does not cause injury, as I illustrated above.

You'd be arguing against an entire scientific discipline. They refer to five forms of energy: mechanical, chemical, electrical, radiant, and thermal. There is also the absence of vital elements such as oxygen or heat but the main thrust is exposure to energy. The reference to 'exposure' proves problematic, as you can see, when explored.

Not true. Many of the safety features in the car do not reduce the amount of energy transferred to the passengers. In fact, about the only one that I can think of which does is anti-lock brakes which reduce the speed of the vehicle prior to the collision. Safety belts, air bags, and crumple zones all reduce the force and acceleration sustained, but not the amount of energy transfered.

Again, you'd be arguing against an entire scientific field. They talk about amounts and at rates. And in this one paragraph you've uncovered my dilemma. 'Transferred' - explain that in terms of energy and landing from a fall. Force is involved in impact, and KE is pre-impact.

If you're interested in the application of mechanics to study injury and teh causes of injury, search for William Haddon, who is the so-called father of this field. Once he conceptualised injury in terms of 'energy exchange' he was appointed to a new office in the US government responsible for road safety.

Your last paragraph encaptulates my problem. KE is pre-impact, force is impact, in the three phases of an injury event. Given the definition of injury in terms of energy exposure, exchange, or transfer, I'm then attempting to reconcile any impact explanation with the initional pre-impact injury causeing energy.

 

[Rap]

OK. Thanks. I see it can be explained two different ways which I cannot reconcile.

1. When work is described as the means by which energy is transferred from one object or system to another. And W=Fd. The bowl accumulates KE during its fall. The ground possesses no mechanical energy: KE+GPE+SE=0. Thus, the bowl has the capacity to do work on the ground but the ground does not have the capacity to do work on the bowl, unless, the work done by the bowl on the ground transfers its KE to the ground in the form of SE which is then transferred back to the bowl resulting in damage. (I'm still working on RAP's expanation). However, there is conflicting opinion as to whether or not the ground does work on bowl. Some suggest the work is internal to the bowl. Bottom line, I'm looking to understand the application of work in this context in terms of the transfer of energy only.

I modified myself on that (see my post #40) - In the special case of an infinitely massive, perfectly rigid (hard) Earth, the Earth has the capacity to do work on the bowl without the Earth deforming. In this case, the Earth exerts a force on the bowl, but absorbs no energy. If the bowl emits no sound as it breaks, and after the collision, the bowl pieces are motionless, then you know, by conservation of energy, that the work done by the Earth on the bowl is equal to the kinetic energy of the bowl when it first touches the Earth, and all of that energy has been converted to heat, because there is no longer any kinetic energy. The work that was done is the result of the force by the Earth acting on the bowl.

Now comes the hard part - What are the processes by which the bowl's kinetic energy gets converted to heat? This is what we should concentrate on.

2. From a force perspective, easy peasy. W=Fd and Newton's third law. Bowl applies force to floor which applies reaction force in turn. Bowl deforms so work is done on bowl by floor. This is where it gets a bit tricky. The floor does not deform so no work is done on the floor. However, Crowell explained that if work is done on one object, work is also done on another. If no displacement of the floor ...? See above as regards to infintessimal deformation and transfer.
Thanks

This is correct, and equivalent to what I said above - it assumes an infinitely massive, perfectly rigid Earth. It is correct up to the point where you quote Crowell. Crowell says that if work is done on one object, it is done on the other. This means he is NOT assuming a perfectly rigid Earth. Since there is no such thing as a perfectly rigid body he is correct, but if there were, he would be incorrect. Nevertheless, we can make the approximation that the Earth is perfectly rigid. If it is close to rigid, we will get results that are close to the truth.

The confusion results from not knowing whether a perfectly rigid Earth is being assumed or not.

 

[Dale]

You'd be arguing against an entire scientific discipline.

It is more likely that I am arguing against your misunderstanding of an entire scientific discipline. But if you are correctly understanding the discipline then the discipline is in error. It will not be the first time.

The reference to 'exposure' proves problematic, as you can see, when explored.

Exactly, which is why you should try something else.

And in this one paragraph you've uncovered my dilemma. 'Transferred' - explain that in terms of energy and landing from a fall. Force is involved in impact, and KE is pre-impact.

A falling body's energy is maximum at the top of the fall, energy has been transferred to it by the elevator. During the fall there is little or no energy transfer at all. Assuming a rigid surface almost no energy is transferred to the ground and the injury is maximum. Assuming a very soft surface a large amount of energy will be transferred to the ground and the injury will be a minimum. In either case the ground does not transfer energy to nor do work on the body, the body transfers energy to and does work on the ground, resulting in a reduction of injury. The energy transfer theory is not very successful here.

Given the definition of injury in terms of energy exposure, exchange, or transfer, I'm then attempting to reconcile any impact explanation with the initional pre-impact injury causeing energy.

And you are having difficulty in that reconciliation because the definition is fundamentally bad.

 

[selftaught]

I modified myself on that - In the special case of an infinitely massive, perfectly rigid (hard) Earth, the Earth has the capacity to do work on the bowl without the Earth deforming. In this case, the Earth exerts a force on the bowl, but absorbs no energy. If the bowl emits no sound as it breaks, and after the collision, the bowl pieces are motionless, then you know, by conservation of energy, that the work done by the Earth on the bowl is equal to the kinetic energy of the bowl when it first touches the Earth, and all of that energy has been converted to heat, because there is no longer any kinetic energy. The work that was done is the result of the force by the Earth acting on the bowl.

Specific questions.

1. 'The Earth has the capacity to do work'. Energy is defined as the capacity to do work. What form of energy does the Earth have which then has the capacity to do work?

2. I understand the idea that the reaction force applied by the Earth causes displacement in terms of deformation of the bowl. The recently introduced idea that work done on one object is mirrored by work done on the other object causes me a problem. The bowl applies a force on the earth, but there is no displacement. No displacement, no work according to the most basic of texts. ... Or is that the answer. The displacement of the Earth as a result of the work done on it by the bowl is so infintessimal as to approximate zero displacement.

... bugger, if so, I still come back to, if the Earth does work on the bowl it transfers energy. What energy?

Crowell just threw a spanner in the works in emailing me now that 'work is done on the ground.'

Now comes the hard part - What are the processes by which the bowl's kinetic energy gets converted to heat? This is what we should concentrate on.

No, no, no. That's not what I'm interested in. It may be of generic interest but I'm focussed on energy and the transfer of energy to cause damage only .

 

[Rap]

A falling body's energy is maximum at the top of the fall, energy has been transferred to it by the elevator. During the fall there is little or no energy transfer at all. Assuming a rigid surface almost no energy is transferred to the ground and the injury is maximum. Assuming a very soft surface a large amount of energy will be transferred to the ground and the injury will be a minimum. In either case the ground does not transfer energy to nor do work on the body, the body transfers energy to and does work on the ground, resulting in a reduction of injury. The energy transfer theory is not very successful here.

"In either case..." - this is not correct. On a soft surface the object pushes into the soft surface which absorbs energy, then rebounds, transferring energy back to the object. In either case, the ground DOES do work on the object, or else its energy would not change. Finally, assuming a rigid surface, the body transfers no energy to the ground, and does no work on it. It exerts a force on the rigid surface, but since the rigid surface does not move, the dx in the equation W=F dx is zero and the work is zero. Looking at it another way, the rigid surface absorbs no energy, and so no work has been done on it.

 

[selftaught]

It is more likely that I am arguing against your misunderstanding of an entire scientific discipline. But if you are correctly understanding the discipline then the discipline is in error. It will not be the first time.

Not a lot of room to misunderstand. One of the fundamental breakthroughs of injury science was James Gibsons identification of energy as being the 'agent of injury' in 1961. William Haddon can to the same conclusion independently 3 months later and clarified some confusion surrounding Gibson's explanation by including a vehicle of vector that conveyed the agent of injury, energy.

Exactly, which is why you should try something else.

Can't. Given the definition of injury. If there was a definition that said injury was caused by the application of momentum or something else, all good, but to structure an argument I need support.

A falling body's energy is maximum at the top of the fall, energy has been transferred to it by the elevator. During the fall there is little or no energy transfer at all. Assuming a rigid surface almost no energy is transferred to the ground and the injury is maximum. Assuming a very soft surface a large amount of energy will be transferred to the ground and the injury will be a minimum. In either case the ground does not transfer energy to nor do work on the body, the body transfers energy to and does work on the ground, resulting in a reduction of injury. The energy transfer theory is not very successful here.

Welcome to my world.

BTW, thanks for taking the time to help me with this problem.

 

[Rap]

1. 'The Earth has the capacity to do work'. Energy is defined as the capacity to do work. What form of energy does the Earth have which then has the capacity to do work?

The quick answer is that energy is NOT defined as the capacity to do work.

2. I understand the idea that the reaction force applied by the Earth causes displacement in terms of deformation of the bowl. The recently introduced idea that work done on one object is mirrored by work done on the other object causes me a problem. The bowl applies a force on the earth, but there is no displacement. No displacement, no work according to the most basic of texts. ... Or is that the answer. The displacement of the Earth as a result of the work done on it by the bowl is so infintessimal as to approximate zero displacement.

That is the answer. The recently introduced idea does not assume a rigid Earth (or floor). If the Earth is perfectly rigid, then no work is done on the Earth.

... bugger, if so, I still come back to, if the Earth does work on the bowl it transfers energy. What energy?

For a rigid Earth, it does not transfer energy, it exerts a force. This force acts on the body causing it to convert its kinetic energy to heat energy, but it does not transfer any energy. The rigid Earth absorbs no energy, and has no energy of its own, so there is none to transmit.

Crowell just threw a spanner in the works in emailing me now that 'work is done on the ground.'

No spanner, he is simply saying that the Earth is not perfectly rigid and he is right, it is not. There is no such thing as a perfectly rigid body. That does not mean that we cannot pretend it is rigid. If it is close to rigid, we will get results that are close to the truth. Send him your quote and this response, I believe he will agree.

 

[selftaught]

The quick answer is that energy is NOT defined as the capacity to do work.

Quite honestly, I don't know where to go from there. I can quote numerous texts which describe energy in exactly these terms. McGinnis, Biomechanics of Sport and Exercise, 'in mechanics,energy is defined as the capacity to do work' (p105). The same in Hall, Basic Biomechanics, p 408. Carr, Sport Mechanics for Coaches, p44. Whiting and Zernicke, Biomechanics of Musculoskeletal Injury, p56. I quote these because these are the texts open on my desk for the past week or two while I've tried to come to grips with this issue. Then there are the large number of other texts that I've referred to that define likewise.

The rigid Earth absorbs no energy, and has no energy of its own, so there is none to transmit.

That has been my position all along.

No spanner, he is simply saying that the Earth is not perfectly rigid and he is right, it is not. There is no such thing as a perfectly rigid body. That does not mean that we cannot pretend it is rigid. If it is close to rigid, we will get results that are close to the truth. Send him your quote and this response, I believe he will agree.

My apoligies. My cut and paste was shoddy. What Crowell said was 'No work is done on the ground' in the case of a body impacting with the ground. No work done on the ground by the body means, according to Crowell and agreed to here by I can't remember who, no work done on the body by the ground. Thus work does not get done.

In this case, what I think I'm left with is that upon impact no work is done, therefore no energy is transferred. The damage is explained in that the KE is not transferred but retained in teh body and converted into sound, heat, electrical, etc energy resulting in deformation, permanent deformation, and/or damage. A force has been applied by the body and the ground has applied a reaction force, and since there was no change in energy in the ground no work has been done.

Now, if this is correct, all I've got to find is support for this argument as there are a number of texts which refer to the damage to body and car from an impact with a solid object or Earth as being the cause of work done on it. Unless, ... I read one text which explained that 'scientists' used the terms transfer and transform to refer to the same thing. In this case, if transfer is used to refer to transfer from one form to another, the 'work done' is the transfer of KE to the other form of energy in the body. Of course I run into the problem of identifying the agents of force and reaction force in this case, given work is done on both agents.

... my head is hurting. I'm done for a while. Cheers. Thanks for the help.

Instead, the KE is converted to sound, heat, and electrical energy (ignoring for the moment such specialised concepts as crystals and large area or whatever) the results in deformation, permanent deformation, and damage in the fallen body.

 

[Dale]

Given the definition of injury.

The definition is clearly wrong.

I don't know James Gibson's background, but William Haddon was a MD, not a physicist. A MD's training is focused on medicine and not physics, and thus as a group their grasp of physics is loose at best. If you want to use that kind of loose interpretation of physics then don't expect to be able to do the kind of rigorous analysis that you seem to want, it simply won't work.

 

[Andy Resnick]

OK. A completely different response received from Ben Crowell (physics professor).

'In the example of the fracture, the energy is going into electrical potential energy to separate, e.g., one calcium atom from another.'

Just when I'm coming to grips with the conversion of KE to sound and heat energy when damage is inflicted on a body from a fall. ... Arghhhhhhhhh!

I mentioned fracture in Post 15.

 

[Rap]

Quite honestly, I don't know where to go from there. I can quote numerous texts which describe energy in exactly these terms. McGinnis, Biomechanics of Sport and Exercise, 'in mechanics,energy is defined as the capacity to do work' (p105). The same in Hall, Basic Biomechanics, p 408. Carr, Sport Mechanics for Coaches, p44. Whiting and Zernicke, Biomechanics of Musculoskeletal Injury, p56. I quote these because these are the texts open on my desk for the past week or two while I've tried to come to grips with this issue. Then there are the large number of other texts that I've referred to that define likewise.

Ah - it says "in mechanics, energy is defined as the capacity to do work". This is not generally true. In thermodynamics, energy cannot be totally converted into work, so this definition fails. And we are doing more than mechanics here, we are doing thermodynamics, because we are dealing with heat. Maybe it would be better to think of kinetic energy or potential energy as the capacity to do work, but not heat energy.

My apoligies. My cut and paste was shoddy. What Crowell said was 'No work is done on the ground' in the case of a body impacting with the ground. No work done on the ground by the body means, according to Crowell and agreed to here by I can't remember who, no work done on the body by the ground. Thus work does not get done.

Yes, that is true, but in the rigid Earth case, the body does work on itself. Please, let's consider a simple problem, where we know exactly what is going on, and watch what happens to the energy. If you don't understand this simple problem, then let me know, don't just skip over it or ignore it. Take a mass connected to a spring to its right, moving to the right, towards a rigid Earth. Let's say the spring can be compressed, but it will not expand, so that you can add energy of compression to it, but you cannot extract it. Some kind of racheting mechanism or something. When the spring touches the Earth, it exerts a force on the Earth, and the Earth exerts an equal force back. The spring compresses. The Earth is doing no work on the spring, because, on its end of the spring, there is no motion. The spring is not doing any work on the Earth, again, because there is no motion there. The amount of work done is dW=F dx and dx is zero. Work IS being done on the spring, by the moving mass however. It is exerting a force on the spring, equal and opposite to the force the spring exerts on it. Here, there is motion, dx is not zero, the kinetic energy of the mass is being transferred to the spring. When the spring reaches its maximum compression, the velocity of the mass is zero. But there is no rebound, because the spring cannot expand. So now the total original kinetic energy of the mass is bound up in the potential energy of compression of the spring, and nothing is moving. (Please note that I was wrong when I said the rigid Earth did work on the object)

Now you can extend this to the complicated case - For a rigid Earth, no work is done by the ground on the object, no work is done by the object on the ground, but different parts of the body perform work on different other parts, the net result of which is to convert almost all of the original kinetic energy of the body into heat.

In this case, what I think I'm left with is that upon impact no work is done, therefore no energy is transferred. The damage is explained in that the KE is not transferred but retained in teh body and converted into sound, heat, electrical, etc energy resulting in deformation, permanent deformation, and/or damage. A force has been applied by the body and the ground has applied a reaction force, and since there was no change in energy in the ground no work has been done.

Yes.

Now, if this is correct, all I've got to find is support for this argument as there are a number of texts which refer to the damage to body and car from an impact with a solid object or Earth as being the cause of work done on it. Unless, ... I read one text which explained that 'scientists' used the terms transfer and transform to refer to the same thing. In this case, if transfer is used to refer to transfer from one form to another, the 'work done' is the transfer of KE to the other form of energy in the body. Of course I run into the problem of identifying the agents of force and reaction force in this case, given work is done on both agents.

I think that from looking at the above example, you can see that there are two systems, the mass and the spring, and the kinetic energy of the mass is transferred to the potential energy of the spring. This could also be thought of as a transformation of the mass-spring system.

 

[Drakkith]

Perhaps we are looking at this the wrong way. Think of the body, or any object really, as not 1 object, but LOTS. Think of it as it's composite particles. In this case it is easy to see how an arm can exert work on the bone causing it to fracture. If you look at each individual spot in the body, you can see where they are getting their energy from, what is doing work on them, and the result of that work. Add it all up into a macroscopic effect and you get injuries.

 

[Rayquesto]

potential energy plus the kinetic energy of a system is always the same, which can be accounted and assumed as zero. systems such as springs have a point in which the velocity is at its highest I think is called the eqaulibrium point. the points in which the spring reaches a maximum before stopping contains the highest potential energy and the highest force and highest acceleration. there's also the concept of work-kinetic energy theorem where work is transferred as kinetic energy is released, considering that velocity is constant. so, I hope you understand a little bit more. What are you confused about exactly?

 

[Rayquesto]

sorry not zero, but the kinetic energy plus the potential energy is constant.

 

[Dale]

One other problem with energy as the fundamental mechanism of injury is that energy is frame-variant and the extent of injury is not.

 

[Rap]

One other problem with energy as the fundamental mechanism of injury is that energy is frame-variant and the extent of injury is not.

I think this will not cause confusion. It will complicate the calculations, but not change the outcome. Just pick the simplest frame of reference (Earth stationary) and you can be certain that transformation to any other frame will modify the energy bookkeeping, but not the conclusions.

 

[Dale]

It will complicate the calculations, but not change the outcome.

That is just it. If energy were the sole cause of injury then because energy is frame-variant you would expect that injury would also be frame variant. But of course that is absurd, changing coordinate systems cannot possibly change the outcome, as you say. Therefore the inescapable conclusion is that injury is not merely due to energy.

Just pick the simplest frame of reference (Earth stationary)

Actually, I think that the best chance this idea has is to require that energy be defined in the body-stationary frame. In that frame the surface exerts a force on the body and as the body deforms it moves, so work is actually done on the body in this frame. Also, in the body-stationary frame the work done by a rigid surface is actually greater than the work done by a soft surface which corresponds with the greater injury. Of course, this frame is non-inertial.

 

[Rap]

That is just it. If energy were the sole cause of injury then because energy is frame-variant you would expect that injury would also be frame variant. But of course that is absurd, changing coordinate systems cannot possibly change the outcome, as you say. Therefore the inescapable conclusion is that injury is not merely due to energy.

Actually, I think that the best chance this idea has is to require that energy be defined in the body-stationary frame. In that frame the surface exerts a force on the body and as the body deforms it moves, so work is actually done on the body in this frame. Also, in the body-stationary frame the work done by a rigid surface is actually greater than the work done by a soft surface which corresponds with the greater injury. Of course, this frame is non-inertial.

I think that concluding that the injury is not due to energy is (practically) wrong. Its all a matter of bookeeping.

The bottom line is that, to do the problem very accurately, you have to use both conservation of energy and momentum. You have to assume that the Earth has finite mass.

If you use a frame where the Earth is initially at rest, then the only energies are the objects initial KE due to its velocity V, its final heat energy Q, its final KE (very small) and the Earth's final KE (very small). All the very small parts are not what we are interested in, so we can discard them. The momenta we have to deal with is the objects initial momentum, its final momentum (very small) and the Earth's final momentum. So that's easy, the initial momentum of the object gets transferred to the Earth and forget about the small stuff.

If you use an inertial frame where the object is initially at rest and the Earth is moving towards it at velocity V, then the energies are the initial KE of the object (zero), and the initial energy of the Earth (very large). The final energies are the KE of the object, the heat energy Q, and the KE of the Earth (very large). The final energies are the KE and Q of the object, and the KE of the Earth (very large). The initial momentum is just the momentum of the Earth (very large). The final momenta are the momentum of the object and the final momentum of the Earth (very large). Now we have a bunch of very large quantities that we are not interested in mixed in with the quantities that we are interested in.

This complicates things because now we have to watch the very large quantites closely, we cannot ignore them. We cannot assume the mass of the Earth is infinite, we cannot assume its initial and final velocities are the same. It complicates the bookkeeping and is not a good idea.

We definitely don't want to go to an accelerated frame of reference. Not only will we have all the problems listed above, but we will have to come up with a virtual force field to explain why inertial objects seem to accelerate.

 

[Dale]

Right, but in the Earth's frame energy transfer does not explain the injury since no energy is transferred (rigid surface). So despite the extra complications, you simply cannot use the "usual" frame if you want to equate energy transfer to injury.

Also, in biomechanics a body's rest frame, or even the rest frame of a single bone, is often used. So many people involved on the technical side of this field are familiar with non-inertial frames.

 

[Rap]

Right, but in the Earth's frame energy transfer does not explain the injury since no energy is transferred (rigid surface). So despite the extra complications, you simply cannot use the "usual" frame if you want to equate energy transfer to injury.

Also, in biomechanics a body's rest frame, or even the rest frame of a single bone, is often used. So many people involved on the technical side of this field are familiar with non-inertial frames.

Right, no energy is transferred from the Earth. It is the kinetic energy of the object which is transformed into heat as a result of the force applied by the Earth.

I think in this case we do not want to use huge numbers such as the mass of the Earth. If we stay in the body frame, we have to invent a force field which explains why the Earth decelerates from V to zero during the time of the collision. I don't think we want to do that either.

 

[Dale]

Right, no energy is transferred from the Earth.

This is the key point. There is an injury, there is no transfer of energy. Therefore, in the Earth's frame the transfer of energy is not the cause of the injury as asserted by the OP.

 

[Rap]

This is the key point. There is an injury, there is no transfer of energy. Therefore, in the Earth's frame the transfer of energy is not the cause of the injury as asserted by the OP.

Ah, I see what you are saying, and that is interesting. In the Earth inertial frame, there is no transfer of energy from the Earth, while in, let's say, the inertial frame of the object when it first touches the Earth, energy is transferred from the Earth to the object.

That means that the question of whether energy is transferred from the Earth is frame-dependent. I think that to do it properly, in any frame, the conservation of momentum must be included, so in that sense you are right, its not a matter of energy alone, its a matter of energy and momentum. Let me rephrase to say that the bookkeeping math for energy and momentum are simplest in the Earth inertial frame, where it happens that (practically) no energy is transferred from the Earth, and (practically) all of the object's initial momentum IS transferred to the Earth. Does that sound right to you?

 

[Dale]

That means that the question of whether energy is transferred from the Earth is frame-dependent.

Yes, exactly.

Let me rephrase to say that the bookkeeping math for energy and momentum are simplest in the Earth inertial frame, where it happens that (practically) no energy is transferred from the Earth, and (practically) all of the object's initial momentum IS transferred to the Earth.

Agreed.