View Full Version : Re: Positive Work in Cyclic Motion

Peter Davidson, X 7455
09-05-1995, 09:49 PM
Dear Paolo de Leva & List

Thank you for your reply to my message on work done by
a tethered swimmer. I find this type of discussion interesting
and I have further points.

1) First, work is a form of energy but energy (or "effort") does not
necessary equate to work. There seems some confusion about this point.

2) For any question (for the definition of work to make sense) the system
in mind has to be defined clearly. The tether swimmer system consists
of the swimmer, the weight, the pool (including all the water affected by the
swimmer) and the weight apparatus. All these components play a role in
transmitting the forces of activity. Also, it has to be clearly stated the
initial and final states from which work is measured. Work is always a
comparison of energy between two states and not dependent on the path
taken between them. For cyclic motion, such as swimming, the common
convention is to define the first state as the start of a cycle and the
second state the end of a cycle (not necessarily the same cycle).

With these points in mind here are my comments after
Paolo de Leva statements ....

>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 other particles do matter because they play a crucial role in the
system. The system in mind cannot be arbitrary redefined without
justification to include and exclude components. In the above statement,
for example,where does this other "positive work" come from?
Why is it less important than the "water moved"?
For that matter, where does the boundary of "water moved" end ?

>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.

See point 1. Energy does not imply work

>...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!

This is interesting, if not the swimmer, then who does this "work"?
The wall is a part of the system because it transmits the swimming force.
A free body diagram around the pool and cutting though
the tether rope will show this.

>Not to talk of the fact that the water increases its total
>KINETIC ENERGY after every cycle,

After the first few cycles, the kinetic energy remains relatively
constant and is lost when the swimmer stops. During the cyclic
motion this kinetic energy is not available for work.

> 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.

Thus the work done on the object is zero. The person expended
a certain amount of energy, some of which was transfered to
the object in the form of kinetic energy and the rest was lost as heat.
The object's kinetic energy was also lost as heat in flight and coming to a rest.
If the final state was defined before the object came to a rest then
work would have been done.

>If what Peter wrote were true, we could say that a chairman who
>is bringing a suitcase upstairs 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.

Yes that is true. Note as in point 2, work is not dependent on
the path, just the initial and final states. All the stair climber
has done is used gravitational energy to destroy the suitcase
(I assume the suitcase is not a Samsomite and has not survived
the fall). Besides, work is a form of energy, so does it make sense to
say the damaged suitcase has more energy? Actually,
now it has less energy and greater disorder.

> 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!
>... you spent alot of your energy ...

See point 1. Besides, one of the conditions of the question is
that no work is done.

> 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.....

Again no work is done. At a constant velocity any resistance
along a level ground would be to overcome friction. (See Newton's Laws)
Overcoming friction is not a form of work just a form energy
lost to disorder.

I 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,

This implies that there is some form of internal energy gain
from each cycle. I think the biggest problem of exercise is energy
drain, not accumulation of energy.

>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.

It is common knowledge that the body moves its segments by forces
between body "parts".

>...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...

Work done is compared between one state relative to another.
The fact that you can refer the same relative angle as 30 degrees, 390 degrees
and 3630 degrees does not create more energy between these states.

>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?

To overcome friction and to create the resisting force.
See previous point on friction.

I have no further comments on Paolo de Leva's reply. I did not understand
the point of the spaceship examples and I cannot reply to the
"Nonsense, in my opinion" remark when no details were given.

------------Peter Davidson----------- *********
Doctorate Student, Biomechanics .:***********>*****
Health Sciences *:@*************>****
Universiy of Otago *** ******>****
PO Box 913, Dunedin ** *********
New Zealand * I I
peterd@gandalf.otago.ac.nz ~ ~

understanding entropy