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Re: bouncing ball or car acceleration



John Barrer wrote:
...
a system with internal structure changes the
anlaysis

Bingo. You got it.

(W-E theorem no longer applies).

It no longer applies simply or directly.
(But it may be applied with difficulty to
the separate subcomponents of the system.)

... breaking the skater into
arm+torso makes sense. But for the arm to push on the
torso, the wall must push on the hand/arm b/c the arm
can't accelerate the torso by pushing against the air.
And then how does the wall "know" to push on the arm
if the wall doesn't deform?

The wall does deform. It must deform. It just
doesn't deform much. And there is no universal ratio
between the force that the deformed wall generates
(in accordance with Hooke's law) and the energy stored
in the deformation. Work it out:
F = k x (Hooke's law) [1]
E = .5 k x^2 (integral thereof) [2]
hence E = .5 F^2 / k [3]

so if we are given any known force F, the
energy of deformation is inversely proportional
to k. Brick walls are proverbial for their
large k values. This implies negligible energy
transfer.

=================

BTW note the correspondence in the form of equations
[2] and [3] to the energy of a capacitor at constant
charge and constant voltage, respectively.