This nerdy thread is largely ignoring the dynamics of the human body.
The formulae and arguments I'm reading are mostly related to point
masses / rigid bodies, and the human body shouldn't be reduced to a
point mass in this case. Ferchrissakes, model the problem correctly!
Granted, kinetic and potential energies are involved, but to a human
being the quality that is most directly observed is "perceived work"
(i.e. energy expended) when engaged in an activity such as running /
riding, on or off a treadmill. Thinking about the center of mass is
only useful in determining quantities such as ground speed (which is
zero for one on a treadmill, quite boring!), net acceleration and drag
forces (again, zero).
If one is to attempt to calculate the actual quantity of work done, than
each segment of the human body (i.e. torso, thigh, calf, foot, etc.)
needs to be considered separately, as well, coupling equations
(involving driving and frictional forces) must be considered for the
intersegment connections (a.k.a joints & ligaments). This can get very
complicated, very quickly: the hip lifts the leg, the thigh extends the
calf and foot. Work must be done to overcome the inertia of the thigh,
calf and foot, the friction in the joints, as well as gravity / body
weight. Etc, etc, etc.
Some of the earliest posts in this thread had made similar points in
this regard.
Sure, more work will need to be done as the grade is increased or
decreased from the horizonal, but this isn't a surprise. No complicated
mathematics are required! ***If one thinks about this problem in the
frame of reference of the treadmill's belt, then the problem becomes
much easier*** An inclined treadmill = a hill, while a level
(horizontal) treadmill = flat ground. This is your first-order
approximation. 'Nuff said.
This talk of motors and friction doesn't relate to the rider on the
treadmill! The rider is merely overcoming gravitational forces (again,
think frame of reference), while the motor is doing the work to overcome
the load of the rider: to the motor, the load is created in the friction
between the belt and the belt support, which is increased by the weight
of the rider. You can put all the friction you want (or don't want)
between the belt and its support; the rider won't know the difference!
--
maestro8 - Mad Scientists for World Domination
Those are my principles. If you don't like those, I have others. --
Groucho Marx
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