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Work/Energy Theorem



Here are a couple of quick comments:
1. Most of the difficulties with W-E come from pushing the rigid body
approximation too far. NO REAL OBJECT IS COMPLETELY RIGID. If it were
then it would have no internal degrees of freedom and could not have
an internal energy (no heat transfer).

2. For a DEFORMABLE body, the internal 3rd law pairs of forces CAN DO WORK.
The internal work associated with those forces can cause the center of mass
to accelerate, IF there is an external constraint.

3. One way to look at the acceleration of a body due to a constraint force
at a fixed location is to think of the external force as cancelling one of a
PAIR of internal forces. I'll try to sketch:
{ <- ->}º<-
body F1a F1b F2
where F1 represents the pair of internal forces obeying Newton's 3rd law,
and F2 is the external force that keeps the boundary "º" stationary.
In this case magnitude(F2) = magnitude(F1b). The energy is supplied by
the changing F1a-F1b separation. F2 does no actual work, or transfer any
energy, BUT F2(dXcm) is equal to the Kinetic energy increase of the
center of mass. Part of the work done by the F1 pair may be internal,
and serve to increase the temperature of the body or contribute to
internal vibration or change of structure.

4. The above example emphasizes that the external force does NOT have
to be associated with the SOURCE of the energy. That energy may actually
come from the work done by inernal forces acting over the DEFORMATIONS
of the body.