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Re: [Phys-l] Another tire question

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Brian Whatcott
Sent: Saturday, November 10, 2007 7:33 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Another tire question

At 03:26 PM 11/10/2007, Rick T., you wrote:
Brian,

To me, what is still in question is just how is the force that acts
upwards
ON THE WHEEL applied by the tire bead--which is the only part of the
tire
in
contact. I hope all agree that there is no force contribution ON THE
WHEEL
from the air pressure.

...Supposing I am the Brian being addressed, I would concur that the
tire
bead exerts considerable radially inwards and sideways (outwards)
force on the rim when properly inflated, and it may be considered
strongly attached by frictional force to the rim of the usual
automobile
wheel.

If the tire in question is of the type that can hold its pressurized
structure without a rim, this is the kind that bears upwards on the
rim
in the lower half, where the upper half can almost show daylight under
if underinflated.

I am not disposed to think of the sidewall and bead as structural
entities.
The entity in question is an inflated tire which has distinct
structural
properties when inflated. If you take one of Jiminy the Clown's long
slender rubber balloons, from the material of which toy giraffes
are built, you will easily see that it can pass a compressive force
from one end t'other
When you press on a wall with the end of such a balloon, the wall is
exerting a force toward you on the end cap of the balloon. In
equilibrium, that end cap is not accelerating toward you because of the
air pressure inside the balloon pushing the end cap away from you. It's
lack of acceleration is not because of longitudinal compression in the
sidewalls. The sidewalls are in fact in tension. They are pulling the
end cap of the balloon toward you. (You can tell this is true because
if you let air out of the other end of the balloon, while holding that
other end of the balloon in a fixed position, the end cap that was in
contact with the wall, will accelerate toward you.) The air in the
balloon has to counteract both the force of tension exerted by the
sidewalls on the end cap, and the force exerted on the end cap by the
wall to keep the end cap in equilibrium. You can also tell that the
sidewalls are in tension because the balloon is longer when it is
inflated than when it is not inflated. You reduce that longitudinal
tension in the sidewalls of the balloon when you press on the wall with
the end of the balloon, but you don't turn it into compression. A big
difference between this case and the case of the tire is that the "high"
pressure air inside the balloon is not also pushing the endcap toward
you in a manner analogous to the high pressure air inside a tire not
only pushing up on the bottom of the hub but also pushing down on the
top.
without changing shape, angles etc., etc.
Inflatable airplanes, of which there have been several prototypes
built also needed to handle both compressive and tensile forces via
inflated fabric. Why should the inflated tire wall cause such
consternation?


Brian Whatcott Altus OK Eureka!

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