Re: BEFORE "Negotiating" a curve.

[brian whatcott <inet@INTELLISYS.NET>]

At 09:54 11/9/99 -0500, Ludwik wrote:
> Suppose a cylindrical wheel is set to roll on
> a flat horizontal surface in a
> good vacuum.... In the ideal world
> the CM would travel with a constant speed...
> But in the real world ... The kinetic energy
> of the CM was reduced .... the "net work
> done on the center of mass". In other words, F*d must be 3.2 J
> and F=(3.2)/5=0.64 N. Right or wrong?

Yes, if you want to think of this dissipation as work.

> My questions are:
> 1) Is there really a force F acting on the CM?

No.An upward force a little ahead of the floor beneath the center
of rotation can be demonstrated. And this can be resolved into
convenient unreal or imaginary components.

> 2) What is its nature? Why is it directed along -y?

The rolling energy is lost to less than perfect resilience of
the roller and of the floor. Along -y because you defined the
rolling direction as y. So the velocity decays with a component
 along -y because there is an upward force on the roller applied
 by the floor with a small component in the -y direction.

> 3) Where is it generated? How is it generated?

About the force which slows the roller...
 You may consider the roller to be compressing the floor, and
rolling up a slight incline. The recovering incline behind the
 roller is not perfectly resilient, so it does not apply as much
 force times distance as the frontal slope takes to compress.

> 4) How is it transferred to the center of mass?

 All of the mass of this solid  roller has to compress the floor
in front of the vertical line below the center of rotation.

> The same questions can be asked about a rolling marble ball or a bead.
>
> Ludwik Kowalski

They could be answered in much the same way.
 The deflection of surfaces is not fanciful. It can easily be measured.
 The less than perfect resilience of real world surfaces is not fanciful.

These two real world factors are sufficient to account for
a loss of rolling energy on a perfectly smooth surface in a vacuum.
 There is still a question where to locate the thermal effects.

But I suppose you care as little as I do, on this religious question.
(I see some thermodynamic discussions here as being strikingly
relevant to materials close to a change of state - as steam was -
when it was the prime mover supreme. But when far from freeze/boil
points as one usually is, it seems much less relevant...)


brian whatcott <inet@intellisys.net>
Altus OK