Same amount of force acting on a given surface produces different effect (result) depending upon the surface area of contact with with the force is applied. Consider following situation. Even if same force is applied by the person the bowling pin on the left hand side doesn't penetrate the wood but the nail on the right hand side very easily penetrates the wood. There are two factors that determines the penetration first is force and the second is the surface area.
So, in general
- Pressure is directly proportional to the force applied on the surface. i.e., P ∝ F --------- (1)
- The force that generates pressure is inversely proportional to the area that receives the force
P ∝ \(\frac1A\) ---------- (2)
From equation (1) and (2), we get
p ∝ \(\frac FA\)
∴ P = k \(\frac FA\)
This is to say, If 1 N of force is applied in 1 square meter area, then the pressure will be 1 N/m2 and thus k = 1