Pressure of a sphere on a regular surface

[umutbilgic]

Since the pressure a sphere exerts on a surface tends to infinity, how do you actually calculate it? My guess would be trying to see how many atoms of the surface (a straight line) and of the sphere collide. But this is very dependent on the materials and exterior factors.

I have searched online for this too but maybe someone here know how. Thanks!

 

[anorlunda]

If you want to calculate a real world finite answer, then you must assume some nonzero finite area of the sphere flattened and in contact with the surface.

 

[umutbilgic]

If you want to calculate a real world finite answer, then you must assume some nonzero finite area of the sphere flattened and in contact with the surface.

Yes but my question is, how do you know how much is in contact. A formula would have to have parameters such as the elasticity of the surface and the sphere, density of both maybe even gravitational acceleration and temperature.

 

[anorlunda]

there may be formulas or lookup tables determined empiracally for specific materials, but every material is different.

Your question could cover a sphere made of diamond, steel, wood, foam rubber, water, an inflatable ball, an orange, silly putty, a meatball ...
The flat surface it touches could also be made of any material, and that too will deform. So you must consider all combinations of sphere and flat surfaces.

Do you see the problem with such a general question?

How about a kitchen experiment? Choose a sphere and a flat surface. Put some colored dye on one of them, then place the sphere on the flat. Lift it off again and look at the spot of color transferred. The weight of the sphere divided by the area of that spot is the pressure.

 

[CWatters]

Perhaps of interest..

http://www.boeing.com/assets/pdf/commercial/airports/faqs/calctirecontactarea.pdf

The tire contact area for any aircraft tire is calculated by dividing the single wheel load by the tire inflation pressure. If the load is expressed in pounds, and the tire pressure in pounds per square inch, then the area is in inches squared.

The same method should work for other inflated objects but might not always be very accurate.