So, today I learnt that P=F/A. For something with a flat surface, it is easy to grab. Then came to my mind, how about the pressure exerted by a curved surface? How do you calculate the pressure? To make it easier I'll make 2 example questions.
a)Calculate the pressure exerted by a 10kg cylinder with a radius of 5m and a height of 10m on a flat surface.(g=10ms^-1)
b)Calculate the pressure exerted by a 10kg sphere with a radius of 5m on a flat surface. (g=10ms^-1)
For the cylinder, if you place in on its face, the pressure is the weight of the cylinder over its base area. If you are placing it on its curved side; then there would be three answers to your question-
Mathematician: Purely theoretical situation, perfect sphere and perfect plane would be perfectly smooth at all levels of magnification, thus there will be a single point of contact, resulting in zero area and undefined pressure.
Physicist: Slightly more realistic, there are atoms, so the sphere and plane would not be perfectly smooth, but would be composed of hard spherical atoms, so the sphere would rest on three atoms to obtain a stable equilibrium. For all intents and purposes, contact area is infinitely small, so pressure is infinitely large.
Engineer: Even if you could make a perfectly smooth sphere and plane, they would deform upon contact, thus making the contact area small but finite, and the pressure large but finite.
Realist: Perfectly smooth spheres and planes don't exist.
See what suits you!!
