How are force, area and pressure related to each other?

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Detailed Solution

Pressure (P) is the normal (perpendicular) force (F) acting on a surface per unit area (A). The fundamental relation is:

P = F / A

Rearrangements:F = P × A, A = F / P
SI units: Force in newton (N), Area in square metre (m²), Pressure in pascal (Pa = N·m⁻²)
Proportionality: For a fixed area, higher force ⇒ higher pressure; for a fixed force, larger area ⇒ lower pressure.
Thrust: The normal component of the force on a surface; pressure quantifies this thrust per unit area.

Quantity	Symbol	Definition / Relation	SI Unit
Force	F	Push or pull on a surface	N (newton)
Area	A	Surface on which the force acts	m²
Pressure	P	Force per unit area: `P = F/A`	Pa (N·m⁻²)

Find pressure: A 400 N force acts on an area of 0.02 m².
Solution:P = F/A = 400 / 0.02 = 20,000 Pa = 20 kPa
Find required area: To keep pressure ≤ 50 kPa with a 500 N force, what area is needed?
Solution:A = F/P = 500 / 50,000 = 0.01 m²

Wide shoes on snow reduce pressure (A ↑ ⇒ P ↓) and prevent sinking.
A sharp knife has a tiny contact area, so pressure is high for the same force (A ↓ ⇒ P ↑), making cutting easier.

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