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POSITIVE work in cyclic motion

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  • POSITIVE work in cyclic motion

    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.
    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
    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

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

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