I am not an expert about the concepts of work and energy, and

luckily I have never needed to use these quantities in my work.

Anyway, I noticed that their application to the study of human motion

is so complex that deserves either:

a) a lot of study and a humble, doubtful attitude.

or

b) a lot of study, tons of effective thinking, and a good mind.

Only in this second case a proud, confident attitude with respect to

the results of your own mechanical analysis is safe. Otherwise, I am

convinced the opinion of a good physician should be asked before

drawing any conclusion.

In his recent message to BIOMCH-L, (Subject: "Tethered swimmer")

Peter Davidson wrote:

> ...Regarding your question on the amount of work done

> during tethered swimming, I believe the answer is zero.

I totally disgaree. It is true that the work done BY THE SWIMMER

ON THE WEIGHT is zero, because the weight does not move. However,

there's a lot of positive work done BY THE SWIMMER ON THE WATER.

Peter wrote:

> But the swimmer moves the water, so is not the swimmer doing work

> against the water? To determine this work, you would need to know

> the flow rate (volume (mass) and velocity)

>

> But that is only considering a system that incloses the hand

> and the whole water pushed. In the whole system, water must

> replace the water pushed back (assuming water is not compressed

> and there is no cavitation (vacuum)) and thus again the net

> work is zero. The water is just a medium that effectively

> allows the swimmer to push against the pool wall.

The truth is that the swimmer does positive work on some

particles of water. It does not matter at all that other systems at

the same time do work on other particles to refill the theoretical

gap left by the water moved by the swimmer (by the way, this is

positive work too). The important thing is that THE SWIMMER (actor)

does positive work on the particles of water that he touches and

pushes, and spends energy to do it. The work done LATER on these

particles BY THE WALL, for instance, or BY OTHER PARTICLES of water,

is not performed BY THE SWIMMER. Therefore, we are not interested in

it!

Again, I stress the importance of being extremely clear about:

(1) who or what is doing the work (THE SWIMMER, in our problem)

(2) the object(s) or particle(s) on which the considered work is done

(the weight, if the weight is moved, and every single particle of

water that is moved by the swimmer).

Who did the work to fill the theoretical gap? Was it the swimmer

or something else? Of course it was not the swimmer. I cannot discuss

exactly what happens to the infinite particles of water that are in

the pool. One thing I know for sure: the total work done by the

swimmer ON THE WATER is not zero!

Not to talk of the fact that the water increases its total

KINETIC ENERGY after every cycle, which means that the TOTAL work

done ON the water, BY swimmer, gravity, and walls is positive as

well.....

Consider also that the swimmer pushes a small amount of water

forward, e.g. when the arm splashes into the water after the arm

recovery. Somebody might think that this is negative work, and can be

subtracted from the (much larger) positive work done to push water

backward. This is of course wrong. The particles that are pushed

forward are not the same as those that are pushed backward....

Here I am stressing the importance of considering SEPARATELY

each of the particles on which the work is performed.

And let's not forget any particles! For instance, some water may

flow toward the swimmer's arm or body, hit the skin and receive

negative work FROM the swimmer, but this is negligible, compared to

the positive work done by the arm on many other particles of water

that are touching the arm at that time. Some negative work is also

done by the swimmer's legs on other particles of water.

I'll give three examples that I used to clarify the concept

in my mind before writing this message:

1) Somebody throws an object vertically upward, as high as he

can, starting from floor level. The object then falls down on the

floor and stops at its initial position. The net displacement during

the whole period of time was exactly zero.

In the time needed for the object to go from its initial to its

final position (initial=final=on the floor), what kind of work was

done BY the man ON that object (positive, negative, or zero)?

Nothwithstanding the fact that the net displacement was ZERO (!)

the work done by the man was large and positive! The TOTAL work was

zero (negative work was performed on the object BY SOMETHING ELSE,

NOT BY THE MAN), but we don't care. The man spent a lot of energy to

perform his LARGE POSITIVE work! Apparently, the work was zero.

However, the energy that was used to lift the object came from the

man's muscles, while the energy to bring the object back to its

initial position was spent by the gravitational field (potential

energy)! The work BY YOUR MUSCLES ON THE OBJECT was positive

(displacement and force have same direction). The work done BY THE

GRAVITATIONAL FORCE ON THE OBJECT was zero (first negative, then

positive, constant force). The work done BY THE FLOOR ON THE OBJECT

to stop its fall was negative! Total work ON THE OBJECT=ZERO.

If what Peter wrote were true, we could say that a chairman who

is bringing a suitcase upstair at the third floor, then throws it out

through the window does the same work as another chairman who covers

the same horizontal distance on a completely horizontal path. I

disagree. The chairman problem is not so simple as it seems, though

(and this is what always happens when you deal with work and energy,

in my opinion). In fact, what if the suitcase were not thrown out of

the window, but simply brought back by the chairman himself

downstairs, to its initial position? Would the chairman do a

positive, negative or null work in the vertical direction? I leave

the answer to you.

Here are two other problems:

2) In the last three minutes you have been pushing a car . The

car has been running at constant velocity. There has been no change

in its kinetic energy. Therefore, NO WORK has been done on the car.

Did you do some work during these three minutes? YES, of course! The

TOTAL WOK was zero, but the "component" done by you was LARGE and

POSITIVE. Friction did negative work, but you don't care, you spent a

lot of your energy (some lost into heat, the rest used to perform

work), and this is what you are interested in.

3) Eracles is pushing two cars at the same time in two opposite

directions. The forces he is applying on the two cars have exactly

the same magnitude. At every given instant, the two cars move exactly

at the same speed, and their accelerations have exactly the same

magnitude. Hence during the considered period of time the two cars

covered exactly the same space (the magnitude of their displacements

was exactly the same).

How much was the total work done BY Eracles ON BOTH CARS

(positive, negative, or zero)? Consider that the center of mass of

the two cars together (car 1 + car 2) DID NOT MOVE! Its displacement

was ZERO! Even Eracles' center of mass did not move at all. Its

displacement was ZERO!.....

Peter also wrote:

> 4. The work done by the movement of the body

> segments is called internal work and over one cycle,

> is equal to zero. Swimming is just a series of movement

> cycles and thus the net internal work is zero.

I totally disagree. Internal work is not zero over one cycle,

EVEN THOUGH ANGULAR ACCELERATION IS ZERO, and final velocity+position

are the same as initial velocity+position! (Not to consider that,

when final velocity after one cycle is larger or smaller than initial

velocity, even the TOTAL work is not zero, but this is well known,

and my point is different).

By the way, internal work, in my opinion, should be defined as

work done BY parts of the body ON other body parts (muscles on bones,

bones on bones, etc.). Peter's definition is not clear, and I don't

know what exactly he meant. I just know that my own definition comes

directly from that of internal FORCES.

Peter, again, as others did before him, forgot to analyze the

different components, and isolate what we are talking about. In this

case we are dealing with what I would call the TOTAL "ANGULAR" WORK

performed ON the upper arm (actually, the work done in the tangential

direction on the rotating particles of the upper arm). In spite of

the fact that initial (linear) position = final (linear) position,

the angle is always increasing, and never goes back to zero. This

means that final ANGULAR position=initial ANGULAR position + 1 turn

(2*PI radians). (Of course I simplified the situation, by assuming

that the arm is moving on a plane instead of a 3D space; again, I

point out that the situation is extremely complex). Therefore, here

we are not going back and forth (as the chairman with the suitcase).

The arm keeps moving always in the same (angular) direction. It

follows that the work done by the muscles to keep the arm rotating at

constant speed is always POSITIVE, and becomes larger and larger, as

the arm rotates.

And why the swimmer needs to apply WITH HIS MUSCLES a torque

(tangential force=positive work) on the arm to keep the arm rotating

at constant angular velocity? Of course, because there is a QUITE

INTENSE, not negligible equal and opposite EXTERNAL torque applied on

the arm due to water resistance! And this external torque means that

there is an external NEGATIVE WORK done BY the water ON the arm.

Hence:

- TOTAL torque is zero,

- angular acceleration is zero (I am simplifying, of course),

- TOTAL work is also zero;

- however, INTERNAL WORK is large and positive.

The following examples can be used to better understand cyclic

motion. Consider for example the cyclic motion performed by the

forearm of a man who is shaking a coctail. Let's say the man performs

that action by cyclically flexing and extending the elbow, and let's

assume for the sake of simplicity that the force of gravity is zero

(the man is on a spaceship). Let's analyze one cycle (simplifying, of

course):

1) Flexion - first half: BICEPS (elbow flexor) does positive work ON

the forearm+shaker.

2) Flexion - second half: TRICEPS (elbow extensor) does negative work

ON the forearm+shaker

3) Extension - first half: TRICEPS does positive work ON the

forearm+shaker.

4) Extension - second half: BICEPS does negative work ON the

forearm+shaker.

Conclusion:

Total work BY BICEPS=zero.

Total work BY TRICEPS=zero.

Total work (BICEPS+TRICEPS)=zero.

Now let's consider a very similar motion: hammering a nail into

the spaceship wall. Can you see that in this case the work done by

BICEPS over one cycle is not zero anymore? Some of the negative work

is performed by the wall+nail on the forearm+hammer system.

Conclusion:

TRICEPS work is zero

Total work is zero

BICEPS work is positive!

TRICEPS+BICEPS work is positive!.

This is Peter's conclusion:

>In summary, the tethered swimmer is a system that isn't

>designed to produce work, so one shouldn't expect to

>be able to measure any work done. The system is 100

>percent inefficient.

Nonsense, in my opinion.

By the way, it should be also noticed that the energy spent by

the swimmer is much more than the positive work done by the swimmer

on external bodies! Efficiency is low, but not zero.

P.S. I admit I did a terrific misktake while I was writing the draft

of this text. Luckily, I asked an opinion to my friend Jesus Dapena,

who spotted my mistake immediately. Thanks a lot to Jesus. Now, I

believe that everything is correct, but who knows? I am not one of

those who can be called an expert of work and energy.

__________ _________ ___________~___ ________ _________________~___

/ ~ ~ ~ ~ \

/______________~______~__________ _______~_____~______________~_____~_____\

| Paolo de Leva ~ \ Tel.+ FAX: (39-6) 575.40.81 |

| Istituto Superiore di Educazione Fisica > other FAX: (39-6) 361.30.65 |

| Biomechanics Lab / |

| Via di Villa Pepoli, 4 < INTERNET e-mail address: |

| 00153 ROME - ITALY \ deLEVA@RISCcics.Ing.UniRoma1.IT |

|_____________________~________~__________________ __________________ _____|

challenging entropy :-)

luckily I have never needed to use these quantities in my work.

Anyway, I noticed that their application to the study of human motion

is so complex that deserves either:

a) a lot of study and a humble, doubtful attitude.

or

b) a lot of study, tons of effective thinking, and a good mind.

Only in this second case a proud, confident attitude with respect to

the results of your own mechanical analysis is safe. Otherwise, I am

convinced the opinion of a good physician should be asked before

drawing any conclusion.

In his recent message to BIOMCH-L, (Subject: "Tethered swimmer")

Peter Davidson wrote:

> ...Regarding your question on the amount of work done

> during tethered swimming, I believe the answer is zero.

I totally disgaree. It is true that the work done BY THE SWIMMER

ON THE WEIGHT is zero, because the weight does not move. However,

there's a lot of positive work done BY THE SWIMMER ON THE WATER.

Peter wrote:

> But the swimmer moves the water, so is not the swimmer doing work

> against the water? To determine this work, you would need to know

> the flow rate (volume (mass) and velocity)

>

> But that is only considering a system that incloses the hand

> and the whole water pushed. In the whole system, water must

> replace the water pushed back (assuming water is not compressed

> and there is no cavitation (vacuum)) and thus again the net

> work is zero. The water is just a medium that effectively

> allows the swimmer to push against the pool wall.

The truth is that the swimmer does positive work on some

particles of water. It does not matter at all that other systems at

the same time do work on other particles to refill the theoretical

gap left by the water moved by the swimmer (by the way, this is

positive work too). The important thing is that THE SWIMMER (actor)

does positive work on the particles of water that he touches and

pushes, and spends energy to do it. The work done LATER on these

particles BY THE WALL, for instance, or BY OTHER PARTICLES of water,

is not performed BY THE SWIMMER. Therefore, we are not interested in

it!

Again, I stress the importance of being extremely clear about:

(1) who or what is doing the work (THE SWIMMER, in our problem)

(2) the object(s) or particle(s) on which the considered work is done

(the weight, if the weight is moved, and every single particle of

water that is moved by the swimmer).

Who did the work to fill the theoretical gap? Was it the swimmer

or something else? Of course it was not the swimmer. I cannot discuss

exactly what happens to the infinite particles of water that are in

the pool. One thing I know for sure: the total work done by the

swimmer ON THE WATER is not zero!

Not to talk of the fact that the water increases its total

KINETIC ENERGY after every cycle, which means that the TOTAL work

done ON the water, BY swimmer, gravity, and walls is positive as

well.....

Consider also that the swimmer pushes a small amount of water

forward, e.g. when the arm splashes into the water after the arm

recovery. Somebody might think that this is negative work, and can be

subtracted from the (much larger) positive work done to push water

backward. This is of course wrong. The particles that are pushed

forward are not the same as those that are pushed backward....

Here I am stressing the importance of considering SEPARATELY

each of the particles on which the work is performed.

And let's not forget any particles! For instance, some water may

flow toward the swimmer's arm or body, hit the skin and receive

negative work FROM the swimmer, but this is negligible, compared to

the positive work done by the arm on many other particles of water

that are touching the arm at that time. Some negative work is also

done by the swimmer's legs on other particles of water.

I'll give three examples that I used to clarify the concept

in my mind before writing this message:

1) Somebody throws an object vertically upward, as high as he

can, starting from floor level. The object then falls down on the

floor and stops at its initial position. The net displacement during

the whole period of time was exactly zero.

In the time needed for the object to go from its initial to its

final position (initial=final=on the floor), what kind of work was

done BY the man ON that object (positive, negative, or zero)?

Nothwithstanding the fact that the net displacement was ZERO (!)

the work done by the man was large and positive! The TOTAL work was

zero (negative work was performed on the object BY SOMETHING ELSE,

NOT BY THE MAN), but we don't care. The man spent a lot of energy to

perform his LARGE POSITIVE work! Apparently, the work was zero.

However, the energy that was used to lift the object came from the

man's muscles, while the energy to bring the object back to its

initial position was spent by the gravitational field (potential

energy)! The work BY YOUR MUSCLES ON THE OBJECT was positive

(displacement and force have same direction). The work done BY THE

GRAVITATIONAL FORCE ON THE OBJECT was zero (first negative, then

positive, constant force). The work done BY THE FLOOR ON THE OBJECT

to stop its fall was negative! Total work ON THE OBJECT=ZERO.

If what Peter wrote were true, we could say that a chairman who

is bringing a suitcase upstair at the third floor, then throws it out

through the window does the same work as another chairman who covers

the same horizontal distance on a completely horizontal path. I

disagree. The chairman problem is not so simple as it seems, though

(and this is what always happens when you deal with work and energy,

in my opinion). In fact, what if the suitcase were not thrown out of

the window, but simply brought back by the chairman himself

downstairs, to its initial position? Would the chairman do a

positive, negative or null work in the vertical direction? I leave

the answer to you.

Here are two other problems:

2) In the last three minutes you have been pushing a car . The

car has been running at constant velocity. There has been no change

in its kinetic energy. Therefore, NO WORK has been done on the car.

Did you do some work during these three minutes? YES, of course! The

TOTAL WOK was zero, but the "component" done by you was LARGE and

POSITIVE. Friction did negative work, but you don't care, you spent a

lot of your energy (some lost into heat, the rest used to perform

work), and this is what you are interested in.

3) Eracles is pushing two cars at the same time in two opposite

directions. The forces he is applying on the two cars have exactly

the same magnitude. At every given instant, the two cars move exactly

at the same speed, and their accelerations have exactly the same

magnitude. Hence during the considered period of time the two cars

covered exactly the same space (the magnitude of their displacements

was exactly the same).

How much was the total work done BY Eracles ON BOTH CARS

(positive, negative, or zero)? Consider that the center of mass of

the two cars together (car 1 + car 2) DID NOT MOVE! Its displacement

was ZERO! Even Eracles' center of mass did not move at all. Its

displacement was ZERO!.....

Peter also wrote:

> 4. The work done by the movement of the body

> segments is called internal work and over one cycle,

> is equal to zero. Swimming is just a series of movement

> cycles and thus the net internal work is zero.

I totally disagree. Internal work is not zero over one cycle,

EVEN THOUGH ANGULAR ACCELERATION IS ZERO, and final velocity+position

are the same as initial velocity+position! (Not to consider that,

when final velocity after one cycle is larger or smaller than initial

velocity, even the TOTAL work is not zero, but this is well known,

and my point is different).

By the way, internal work, in my opinion, should be defined as

work done BY parts of the body ON other body parts (muscles on bones,

bones on bones, etc.). Peter's definition is not clear, and I don't

know what exactly he meant. I just know that my own definition comes

directly from that of internal FORCES.

Peter, again, as others did before him, forgot to analyze the

different components, and isolate what we are talking about. In this

case we are dealing with what I would call the TOTAL "ANGULAR" WORK

performed ON the upper arm (actually, the work done in the tangential

direction on the rotating particles of the upper arm). In spite of

the fact that initial (linear) position = final (linear) position,

the angle is always increasing, and never goes back to zero. This

means that final ANGULAR position=initial ANGULAR position + 1 turn

(2*PI radians). (Of course I simplified the situation, by assuming

that the arm is moving on a plane instead of a 3D space; again, I

point out that the situation is extremely complex). Therefore, here

we are not going back and forth (as the chairman with the suitcase).

The arm keeps moving always in the same (angular) direction. It

follows that the work done by the muscles to keep the arm rotating at

constant speed is always POSITIVE, and becomes larger and larger, as

the arm rotates.

And why the swimmer needs to apply WITH HIS MUSCLES a torque

(tangential force=positive work) on the arm to keep the arm rotating

at constant angular velocity? Of course, because there is a QUITE

INTENSE, not negligible equal and opposite EXTERNAL torque applied on

the arm due to water resistance! And this external torque means that

there is an external NEGATIVE WORK done BY the water ON the arm.

Hence:

- TOTAL torque is zero,

- angular acceleration is zero (I am simplifying, of course),

- TOTAL work is also zero;

- however, INTERNAL WORK is large and positive.

The following examples can be used to better understand cyclic

motion. Consider for example the cyclic motion performed by the

forearm of a man who is shaking a coctail. Let's say the man performs

that action by cyclically flexing and extending the elbow, and let's

assume for the sake of simplicity that the force of gravity is zero

(the man is on a spaceship). Let's analyze one cycle (simplifying, of

course):

1) Flexion - first half: BICEPS (elbow flexor) does positive work ON

the forearm+shaker.

2) Flexion - second half: TRICEPS (elbow extensor) does negative work

ON the forearm+shaker

3) Extension - first half: TRICEPS does positive work ON the

forearm+shaker.

4) Extension - second half: BICEPS does negative work ON the

forearm+shaker.

Conclusion:

Total work BY BICEPS=zero.

Total work BY TRICEPS=zero.

Total work (BICEPS+TRICEPS)=zero.

Now let's consider a very similar motion: hammering a nail into

the spaceship wall. Can you see that in this case the work done by

BICEPS over one cycle is not zero anymore? Some of the negative work

is performed by the wall+nail on the forearm+hammer system.

Conclusion:

TRICEPS work is zero

Total work is zero

BICEPS work is positive!

TRICEPS+BICEPS work is positive!.

This is Peter's conclusion:

>In summary, the tethered swimmer is a system that isn't

>designed to produce work, so one shouldn't expect to

>be able to measure any work done. The system is 100

>percent inefficient.

Nonsense, in my opinion.

By the way, it should be also noticed that the energy spent by

the swimmer is much more than the positive work done by the swimmer

on external bodies! Efficiency is low, but not zero.

P.S. I admit I did a terrific misktake while I was writing the draft

of this text. Luckily, I asked an opinion to my friend Jesus Dapena,

who spotted my mistake immediately. Thanks a lot to Jesus. Now, I

believe that everything is correct, but who knows? I am not one of

those who can be called an expert of work and energy.

__________ _________ ___________~___ ________ _________________~___

/ ~ ~ ~ ~ \

/______________~______~__________ _______~_____~______________~_____~_____\

| Paolo de Leva ~ \ Tel.+ FAX: (39-6) 575.40.81 |

| Istituto Superiore di Educazione Fisica > other FAX: (39-6) 361.30.65 |

| Biomechanics Lab / |

| Via di Villa Pepoli, 4 < INTERNET e-mail address: |

| 00153 ROME - ITALY \ deLEVA@RISCcics.Ing.UniRoma1.IT |

|_____________________~________~__________________ __________________ _____|

challenging entropy :-)