Pressure–Force–Area (Rearrange)

Statement

The relationship between pressure, force, and area is given by:

\[ p = \frac{F}{A}, \quad F = pA, \quad A = \frac{F}{p} \]

Why it’s true

• Pressure is defined as force per unit area.
• Rearranging gives force = pressure × area, or area = force ÷ pressure.
• This allows switching between the three depending on which quantities are known.

Recipe (how to use it)

1. If finding pressure: divide force by area.
2. If finding force: multiply pressure by area.
3. If finding area: divide force by pressure.

Spotting it

This formula is used in physics/mechanics problems involving surfaces, hydraulics, or weight spread over an area.

Common pairings

• Units: pressure in Pascals (Pa), force in Newtons (N), area in m².
• Applied in fluids, gases, solids contact problems.

Mini examples

1. Given: Force=200 N, Area=4 m².
   Answer: \(p=200/4=50\) Pa.
2. Given: Pressure=100 Pa, Area=2 m².
   Answer: \(F=100*2=200\) N.

Pitfalls

• Forgetting to convert area into square metres (e.g., cm² → m²).
• Confusing pressure with force (they are not the same).

Exam strategy

• Always write the correct rearranged version of the formula first.
• Check units: pressure must be in Pascals (N/m²).
• Draw a triangle memory aid: F on top, P and A at the bottom corners.

Summary

The formula triangle links pressure, force, and area: \(p=F/A\), \(F=pA\), \(A=F/p\). It is fundamental in mechanics and physics problem-solving.