Re: Energy, etc

[Brian McInnes <bmcinnes@PNC.COM.AU>]

Gordon Smith wrote
> The wall doesn't move, so no work
> The hand pushing against the wall doesn't move (on a realistic scale) so no
> work
> The wrist attached to the hand pivots, so some work
> The forearm attached to the wrist act as a lever, negligible work
> The elbow pivots, so some work
> The shoulder pivots, so some work
>
> Linking all these together, we find that the whole arm system changes it's
> effective horizontal length while pushing, so the reasonably constant force
> that is applied to the wall can be said to be applied through that change
> in distance.  Thus, as we push away from the wall, we are doing some work.
> It's a question of frame of reference.
>
> If you don't think this is so, place your hands attached to fully extended
> arms on the wall, and push.  You'll probably find that you don't go as fast.

Gordon, there are three external forces acting on the person.  I don't
think we have any troubles with two of these - the gravitational force
exerted by the earth on the person and the contact force exerted by
the floor.  The third force is the normal contact force exerted by the
wall on the person.  As long as the person is in contact with the wall
there is no relative movement between that force and its point of
application and so that force does no work on the person.
All the other movements are internal to the articulated person and do
not do work on the person, no more than do the various linkages in an
automobile do work on the automobile as it starts its journey.  The
changing in effective horizontal length of the arm during the push is
a necessary part of the mechanism that is resulting in changed motion
of the person.

To take the story a little further the change in the person's kinetic
energy is associated with a loss in chemical energy.

Jim Green notes "One does not have to go that far: There _is_ an
effective force on the CM.
The wall pushes on the finger bones; the finger bones push on the
wrist
bones; the wrist bones push on the ulna, the ulna pushes on the
humerus,
the ... "

All true, Jim, but irrelevant to the question of whether or not an
external force is doing work on the person and thereby causing a
change in kinetic energy.

To summerize.  There is a change in kinetic energy of the person.
There is a contact force exerted by the wall on the person.  That
contact force has a vital role to play in the mechanism of the changed
motion. That contact force does no work on the person.

Brian McInnes