Re: [Phys-l] Another tire question

[Rick Tarara <rtarara@saintmarys.edu>]

----- Original Message ----- 
From: "Carl Mungan" <mungan@usna.edu>
> (2) ground exerts an upward force of 600 lbs - calculated as weight
> of car divided by 4 (crudely assuming equal support by each of the 4
> tires); I don't understand Rick's concern here, as the ground is
> *only* in physical contact with lower half of tire
If the tire is sitting on the ground--no wheel involved--we would not split 
it in two.  We would say that the ground pushes up on the tire.  When I 
stand on the floor, the floor pushes up only on my feet, but we say that the 
floor pushes up on me.  We resort to tension/stiffness/compression and the 
like to explain how these contact forces are 'distributed' over all parts of 
the object.  I guess my concern here was--why consider the tire in halves 
and not thirds, 10ths, or whatever.  Why are we isolating the effect of the 
ground to the lower half and not distributing it to the whole tire as we do 
with the ground on my feet distributed to my whole body.  Again, with a 
really rigid object (not that I'm a rigid object ;-) I think you would and 
the force distribution mechanism would be different than what we are talking 
about for the tire.

> Second, Shurcliff's article also has baffling features in it.
> Shurcliff claims the different slope of the lower portion of the tire
> sidewall has a small *but nonzero* effect on the problem. But he then
> uses numbers that contradict this fact: including the slopes, he
> calculates the "downward force exerted by the lower half of tire"
> (I'm not keen on this choice of wording) to be 1900 - 500 = 1400 lbs.
> But if I were to exclude the slopes, presumably I would instead
> calculate 2000 - 600 = 1400 lbs, exactly the same answer! That is,
> using his numbers the slopes have a *zero* effect. What's the deal -
> is it a zero effect or not?

I puzzled over this as well.  Your analysis would indicate that the tire 
would work the same without any bulging on the lower half, but for that to 
happen, the tire would have to be more rigid--bringing in other 
possibilities for the forces.  So, assuming the tire HAS to bulge some when 
the car's weight is added, then Shurcliff seems to be saying that this 
changes the direction of the bead force and therefore the vertical component 
of that force (1900 versus 2000 lbs in his example), but then he claims the 
road force component is also less (500 rather than 600lbs).  I assume this 
is the road force as transmitted to the bead through a change in the tension 
in the sidewalls.  The two effects basically cancel out so that the net 
difference between bead force pulling up on the top is less than the bead 
force pulling down on the bottom of the wheel remains the same for any 
amount of 'bulge'.

****************

Michael just answered and IF I understand him, the tire WON'T work without 
the bulge.  In Shurcliff's analysis it would be the bulge that transmits the 
road force and reduces the vertical tension force on the bottom half of the 
bead.  That seems to me then that the 'slope' is entirely responsible for 
the top/bottom force difference--hence Shurcliff would not be correct in his 
two piece analysis--road/slope.

I think I'm getting confused again--or maybe was never 'un-confused'.

Rick