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Re: [Phys-l] Another tire question



Here is a way of visualizing the interaction of the bead with the rim.
Put a short length of rubber hose (such as that attached to the heater
core in your car) on a fixed horizontal rod of diameter matching the
inner diameter of the hose. Put a hose clamp such as the one depicted
at
<http://www.amazon.com/Stainless-Steel-Hose-Clamps-3304-5903180/dp/B0000
AZ3YW/ref=sr_1_10?ie=UTF8&s=sporting-goods&qid=1194959502&sr=8-10>
on the end of the hose and clamp it down so that the hose walls inside
the clamp are about 70% of their unloaded thickness. The (rod plus
hose) plays the role of the rim, the hose clamp plays the role of the
bead. Now pull upward on the top of the hose clamp. This simulates the
upward force of the upper part of the sidewall on the bead. If you pull
hard enough you will notice that the part of the hose wall inside the
lower part of the hose clamp becomes more compressed and the part of the
hose wall inside the upper part of the hose clamp becomes less
compressed. This represents visual evidence that the pressure of the
hose clamp on the bottom of the hose is increased and the pressure of
the hose clamp on the top of the hose is decreased.

A similar thing happens when you lower a car to the pavement. Prior to
lowering, the bead is exerting roughly the same pressure all the way
around the rim, where it is in contact with the rim. When the car is on
the pavement, the sidewalls pull up on the upper part of the bead harder
than they pull down on the lower part of the bead. The pressure being
exerted on the bottom of the rim by the bead is greater than it was
before lowering the car to the pavement and the pressure being exerted
on the top of the rim by the bead is less than it was.

Note that if you consider the object whose equilibrium is under study to
be the (rim plus bead), then the object is supported by the upper
sidewall pulling upward harder on the upper part of the (rim plus bead)
than the lower sidewall is pulling downward on the lower part of the
(rim plus bead).

But if you consider the object whose equilibrium is under study to be
the rim, then the object is supported by the bead pressing upward on the
bottom of the rim harder than the bead is pressing downward on the top
of the rim.

The last time I put a car tire on a rim was in 1972. (The car was a red
1964 Mustang with a 289 cubic inch engine.) My recollection is that the
substance I put on the inner portions of the tire was a lubricant rather
than a glue. The correctness of this recollection is supported by the
ad for "rim ease tire mounting lubricant" at:
<http://www.pitposse.com/rimeatimolu.html>
That is not meant to imply that nobody uses tire glue; see
http://www.duratrax.com/caraccys/dtxr2000.html ,
but rather, that glue is not essential.