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Re: car acceleration



John Barrer wrote:

I'm uncomfortable with the "momentum transfer but no
energy transfer" model described in earlier posts.

I don't see why. It is a highly accurate description
of what is going on in that situation.

Consider a similar situation, the hypothetical
perfectly elastic collision between a fall ing ball
and the floor. Model the floor as an ideal spring.

OK.

During the first half of the interaction, as the
"floor spring" is being compressed, the floor does
"negative work" on the ball, thereby reducing both its
KE and momentum to zero (in the floor ref frame).
During the second half of the interaction, as the
"floor spring" is recovering it is doing "positive
work" on the ball, increasing both its KE and momentum

OK.

... to their original absolute values.

Or slightly less, if we take dissipation into account.

I think it's pretty
common (and also pretty clear to intro students) to
treat the force of the floor in this fashion, no?

Common? It doesn't matter whether it's common or
not. Since you have chosen to have the compliance
of the floor greatly exceed the compliance of the
ball, you have to treat it in this fashion. It is
what it is. It's your choice.

I consider such a floor to be so uncommon and atypical
that I would prefer to call it a trampoline, but
this is a minor point.

If you had chosen differently, such as a pogo-stick
on a concrete floor, every step of the analysis
would have been different.

Feynman said "the same equations have the same solutions".
But obviously, different questions may well have different
answers.

We
don't really care where the energy came from that
enables the "floor spring" to do its thing

It depends. Sometimes we don't care. Sometimes we do.

(but it was
from the gravitational interaction of the ball and the
Earth).

Not necessarily. You could have thrown the ball
at the floor (trampoline), at such a speed that the
gravitational contribution was negligible. Turn the
system 90 degrees so that the trampoline becomes
wall-like not floor-like if you want to get rid of
gravitational effects entirely. The physics of the
bounce is unchanged.

I haven't thought the accelerating car (or
accelerating person) situation completely through, but
so far it seems that the analogy is strong.

Au contraire, it's not strong at all.

Your foot
(or tire) is able to push back on the floor (or road)
b/c of friction, thereby deforming the surface. As the
surface recovers, it does work on you (or the tire)
thereby increasing both the KE and momentum (again in
the road or floor reference frame).

This effect is utterly negligible for real tires
on real roads. Tires are _rubber_ which is renowned
for its springiness. The road is something like
concrete, which is renowned for its non-springiness.

And in any case, even if we did have a springy road,
it would impart no more energy to the car than it
extracted a moment earlier. The idea of the road
imparting net energy to the road is preposterous.
(I'm assuming the road isn't made out of flubber.)

If we are content
to say the floor does work on the bouncing ball,

Huh? At one instant the trampoline does negative
work, and at the next instant it does positive work.
The total work is zero (or less than zero if we
count dissipation).

I
don't see why it is any less correct to say the road
does work on the tire.

1) Well, it is less correct, because of the
properties of real roads and real tires are not
well represented by the trampline model.

2) Even if the analogy were valid, the suggestion
that the road does work on the tire would be highly
misleading, because it seems to suggest net positive
work, which is untrue of the trampoline/ball system
and even more untrue of the road/tire system.

For the car, the source of the
energy that permits the surface deformation is the
chemical reaction in the engine, but doesn't that
energy provide the means to deform the surface so it
can push back on and accelerate the vehicle?

Deformation of the road is an irrelevant complication.
-- It contributes a tiny amount to the temporary
energy budget.
-- It contributes even less to the long-term energy
budget (net energy).
-- The net effect, whatever it is, contributes less
than zero to the acceleration of the car. It is
dissipative.

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

Human race-runners may benefit from running on a suitable
deformable surface. The deformation of the surface is
surely dissipative (it's not flubber, after all) but it
might be less dissipative than a human Achilles tendon.
This is important because of the huge non-steady forces
involved in the running stride.

This has no relevance to the car-acceleration problem,
because the car is stipulated to produce a steady force.
The car has nothing to gain from a deformable road.
It is recommended to treat the earth/road system as
a rigid body, and there is nothing to be gained by
making it more complicated.