How are force, area, and pressure related?

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Detailed Solution

Pressure (P) is the normal force per unit area acting on a surface.

Core Formula

P = F / A

P = pressure
F = perpendicular (normal) force on the surface
A = area of contact

Rearrangements

F = P × A (force needed for a given pressure and area)
A = F / P (area required to keep pressure within a limit)

SI Units

Quantity	Symbol	SI Unit
Force	F	newton (N)
Area	A	square metre (m²)
Pressure	P	pascal (Pa) = N m⁻²

What the formula means

For the same area, greater force → greater pressure.
For the same force, larger area → smaller pressure (e.g., snowshoes vs. high heels).
Only the perpendicular component of force contributes to pressure.

Numericals

Example 1: Find pressure

A 600 N crate rests on the floor over an area of 0.50 m².
P = F / A = 600 / 0.50 = 1200 Pa

Example 2: Find required area

A 700 N person wants floor pressure not to exceed 2000 Pa.
A = F / P = 700 / 2000 = 0.35 m² (total area in contact)

Pressure increases with force and decreases with area: P &propto F, P &propto 1/A. Use P = F/A and its rearrangements to solve problems quickly.

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