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Peter Davidson, X 7455
09-27-1995, 03:06 AM
Dear Biomch-L,

There has been continued interest in the Tethered Swimming problem.
I have further comments on the matter and have been encouraged by
one of the list moderators to post them on Biomch-L.

The concepts introduced so far in the tethered swimming discussion
have been said to be taught in 1st and 2nd year Physics courses.
However, learning the definition of a concept and learning how to
apply a concept can be two completely different things. The same
concept applied different ways and on different levels can provide
information that may or not be useful to the original problem. With
this in mind, I have introduced a few more points.

1. The original problem is stated as: What is the work done during
tethered swimming?. This problem can be approached several ways.
Ideally it is best to choose the approach that gives the greatest
understanding of the concept of tethered swimming.

2. Tethered swimming is a system. Work done on or by a system is a
thermodynamic problem. Problems that occur in the biomechanical
field use concepts developed in other fields. Dismissing a problem
just because it requires concepts developed in another filed will not
bring you closer to understanding the original problem.

3. The system and the initial and final states of interest has to be
defined clearly. This is because work is a form of energy that is
transferred across the defined system's boundary between the two states.
Note that heat is also a form of energy that is transferred across
the system boundary between two states. This follows the first law
of thermodynamics:

dE = dW + dQ

where
dE is the change in energy of a system
dW is the work transferred across the system boundary
dQ is the heat transferred across the system boundary

4. The common equation W = F x is related to the above concepts.
This is best shown from a section in Fundamentals of Classical
Thermodynamics: SI Version 2e (1978) by G.J. Wylen and R.E. Sonntag
on page 61-62:

Quote...

"Work is usually defined as a force F acting through a displacement x,
the displacement being in the direction of the force. That is,

W=(integral from state 1 to 2)F dx

This is a very useful relationship because it enables us to find the
work require to raise a weight, to stretch a wire, or to move a charged
particle through a magnetic field.

However, when treating thermodynamics from a macroscopic point of view,
it is advantageous to tie in the definition of work with the concepts of
systems, properties, and processes. We therefore define work as follows:
work is done by a system if the sole effect on the surroundings
(everything external to the system) could be the raising of a weight.
Notice that the raising of a weight is in effect a force acting through a
distance. Notice, also, that our definition does not state that a weight
was actually raised, or that a force actually acted through a given
distance but that the sole effect external to the system could be the
raising of the weight. Work done by a system is considered positive
work done on a system is considered negative. The symbol W designates
the work done on a system.

In general, we will speak of work as a form of energy. No attempt will
be made to give a rigorous definition of energy. Rather, since the concept
is familiar, the term energy will be used as appropriate, and various
forms of energy will be identified, Work is a form of energy that fulfils
the definition above."

End of Quote.

5. In the tethered swimming problem, the system of interest can be
stated as being the swimmer. In this case the boundary would be the
surface of the swimmer. Over each cycle, assuming the body temperature
remains relatively constant, the change in energy of the system, dE,
would be negative and would equal to the energy loss in chemical bonds
(respiration). The energy lost would equal the heat loss, dQ, to the water
and air and the work done, dW, on the water. The work done would be the
force applied to the water over the distance applied. From the force
analysis point of view, the net force and direction on the water would
be equal in magnitude and opposite in sense to the tension on the tether.

The water is not included in this system and thus the effect on the water,
such as change in kinetic energy, cannot be calculated at this point.

6. The system of interest can also be redefined to include the pool water
and possibly the pool wall and weight apparatus. The energy change of
the system would have to include any internal thermal energy increases
(reflected by temperature rise) of the water etc as well as the change in
the swimmer's chemical energy (assuming the kinetic and potential energy
remains relatively constant). The heat loss would include any heat lost
to the environment, which my be considerable because water can be
an excellent conductor. And finally, any work done would be any work
done on the environment or could be done to the environment.

Note, since in this case the environment does not move, work is not
being done on the environment. However, this does not eliminate the
possibility that work can be done on the environment. In other words,
"that the sole effect external to the system could be the raising of the
weight" (excerpt from the above quote).

7. I believe the approach used in point 6 gains a greater understanding
of the tethered swimming problem. The approach in point 5 just calculates
the effort to "push" something over a distance. Everybody knows that
a person who pushes something over a distance has the potential to do
work. A greater understanding of the problem would only be achieved if
the effect was considered on relevant components in the environment.
For example, I believe there is a significant difference between the
case of a weight lifter lifting up and dropping the same weight repeatedly
and the case of a weight lifter raising a series of identical weights
to a given height. The approach in point 5 would not distinguish
between the two cases. From the point of view of the weight lifter,
the same work is being done.

However, considering the effect on the weights, there is a
distinguishable (and measurable) difference between the to cases.
In the first case, the only effect on the environment is the release of
heat energy. In the second case, the lifted weights can lift other weights
(using a lever apparatus) in the environment and return to their initial
position. Thus "the sole effect external to the system could be the raising
of the weight". This shows that in the second case work has been done.

In the problem of the tethered swimmer, the approach in point 5 would
not distinguish between a swimmer held in place or a swimmer moving
forward at a constant velocity (and possibly lifting a tethered weight).
All that is learned is that the person can fight a resistance by pushing
back.

8. Point 6 gains a greater understanding of the problem because it
includes the pool water, a relevant component of the swimmer's
environment. The energy flow within the system can be studied
including the swimmer and the interacting water. The analysis can be
done as follows: The swimmer's hand creates a pressure gradient in
the water. This pressure gradient causes the water to move back and
gain momentum. The water eventually slows down loses its energy
as heat and imparts its momentum on the water or directly on the wall
as a impulse wave. The question "What is the work done during
tethered swimming?" can be looking at the possibility of doing work
with the water momentum before it is lost as heat. Rephrased another
way: can useful energy (work) be transferred out of the tethered swimming
system without affecting the swimmer? I think that this is a more
rewarding approach to the tethered swimming question.

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