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Re: car acceleration



Rick Tarara wrote:
...
During the push
there MUST be some deformation of the wall.

Some deformation? Yes.
Significant deformation? No, not for realistic
walls and realistic hands.

That deformation may be very small,

yes.

but then the forces are very large.

No, the force is specified in the statement
of the problem. The amount of deformation is
given by the specified force divided by the
stiffness of the wall, and the divisor is
usually very large.

Energy is stored in the deformed
wall BUT came from the person.

Is there the slightest evidence that this
energy is significant? I haven't seen any.

As the wall rebounds there is a force

yes.

(perhaps quite large)

no.

that acts through a displacement (perhaps quite small)

small indeed.

that will account for the change in KE of the person.

no.

In the end analysis,
the energy does come from the person, but was temporarily stored in the
wall.

no.

There is no evidence that the required amount
of energy was stored in the wall. And beaucoup
evidence to the contrary. Do the calculation.
Put in some numbers. Assume an ordinary brick
wall, not a trampoline.

There will also be dissipative losses, but we can imagine those being
minimized.

OK.

...
I'm having trouble with
the mechanism by which the energy stored as chemical PE ultimately becomes
KE of the CM through only internal conversions.

Thank you for saying so. It's a lot easier on
me if I know which bits of the explanation need
clarification or amplification.

Try this, see if it helps: Consider the skater's
arm as an independent agent. The _arm_ pushes
the skater. The arm does work, plain old F dot dx
work, because the skater's torso moves a distance
dx while the arm is exerting a force F on it.

It is this work that imparts KE to the torso in
accordance with the work-KE theorem. After the
motion is established, the skater grabs the arm
and brings it along for the ride.

This work is internal to the skater. No work or
other energy flows across the wall/skater boundary.

This follows the advice I've given at
http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-work-KE
and elsewhere:

-- The work-KE theorem only applies to objects with
no internal structure.
-- If you have a complex object, if you want to
apply the work-KE theorem, you must decompose the
object into pointlike components and apply the
theorem to each component separately.