Re: [Phys-l] Another tire question

[John Denker <jsd@av8n.com>]

On 11/06/2007 12:28 PM, Rick Tarara wrote:

> How does a tire actually hold up a car?

Wow, what a nifty question.  Is there some way to cross-reference this
to the recent "practical physics" thread?
 
> At the Way Things Work site they talk about the footprint area of the tires 
> times the pressure equalling the weight of the car.  However, if I look at 
> the forces:  The road pushes up on the tires, but the tires must push up on 
> the wheels--with a force equal to the weight of the car (more or 
> less--depending on if you count the weight of the tires themselves).  

Yup.

>  The 
> two factors I see as possible are 1)  A pressure difference between the top 
> of the wheel and the bottom of the wheel--giving a net upwards force. 

Not a chance.  Pascal's principle.

>    The other--and I think this is the answer but need confirmation--is 
> that most (if not all) of the weight is supported by the sidewalls of the 
> tires which are stiffened by the air pressure.

That's most of it.

Actually it's not so much "stiffness" as /tension/.  Although
there is some stiffness, it's not crucial.  The tire would still 
work as a tire if it were made of thin fabric with infinite 
flexibility (zero stiffness).

The final ingredient is to notice that the sidewall changes
shape.  In the absence of stiffness, if it didn't change
shape, the force would be zero by symmetry.

Imagine looking at the tire from dead ahead, and taking
a cross section:
  http://www.av8n.com/physics/img48/tire.png

Think about the angle at which the sidewall meets the rim.