Pressure of a sphere on a regular surface

Click For Summary
SUMMARY

The pressure exerted by a sphere on a surface can be calculated by determining the contact area between the two, which is influenced by the materials involved and their properties. A practical method involves using colored dye to visualize the contact area, allowing for the calculation of pressure by dividing the weight of the sphere by the area of the dye transfer. Factors such as elasticity, density, gravitational acceleration, and temperature must be considered, as they affect the deformation of both the sphere and the surface. Empirical formulas or lookup tables may exist for specific material combinations, but variations are extensive.

PREREQUISITES
  • Understanding of basic physics concepts, including pressure and force.
  • Familiarity with material properties such as elasticity and density.
  • Knowledge of empirical methods for measuring contact area.
  • Basic experimental techniques for conducting physical demonstrations.
NEXT STEPS
  • Research the relationship between material elasticity and contact pressure.
  • Explore empirical formulas for calculating contact area for various materials.
  • Learn about pressure measurement techniques in experimental physics.
  • Investigate the effects of temperature on material deformation and pressure calculations.
USEFUL FOR

Students and professionals in physics, materials science, and engineering, particularly those interested in pressure calculations and material interactions.

umutbilgic
Messages
2
Reaction score
0
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!
 
Physics news on Phys.org
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.
 
anorlunda said:
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.
 
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.
 
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.
 

Similar threads

  • · Replies 69 ·
3
Replies
69
Views
5K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K