What do p, F, and A represent in the formula `p = F / A`?

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Detailed Solution

The formula p = F / A defines pressure as the normal (perpendicular) force acting per unit area.

Symbol meanings

p (pressure): The amount of force applied per unit area and perpendicular to the surface.
SI unit: pascal (Pa), where 1 Pa = 1 N·m⁻².
Type: Scalar (in elementary contexts).
Dimensions: [M L⁻¹ T⁻²].
F (force): The perpendicular (normal) component of the total force acting on the surface.
If a force makes an angle θ with the surface, use the component F_normal = F·cosθ that is perpendicular to the surface.
SI unit: newton (N).
Type: Vector (but only its magnitude, perpendicular to the area, enters the formula).
A (area of contact): The surface area over which the force is distributed.
SI unit: square metre (m²).
Use the area actually in contact and perpendicular to the applied force.

A force of 200 N acts normally on an area of 0.02 m².
Pressure: p = F / A = 200 / 0.02 = 10,000 Pa (10 kPa).

Forces at an angle: use only the normal component in the formula.
Unit conversions: convert cm² to m² (1 cm² = 1×10⁻⁴ m²).
“More area → less pressure” (for the same force), which explains wide tractor tyres, snowshoes, etc.

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