6.1 Pressure

Two Bags, One Puzzle

Megha and Pawan carry identical, equally heavy bags to a picnic — yet Pawan’s shoulders hurt and Megha’s don’t. The only difference? Pawan’s bag has narrow straps; Megha’s has broad straps. Same weight, very different comfort. How can the width of a strap change how heavy a bag feels?

The bag’s weight (the force of gravity) is the same for both. What differs is the area over which that force is pressed onto the shoulder. Narrow straps squeeze the whole weight onto a small area; broad straps spread it over a large area. The crowding of force onto an area is a quantity all its own.

The Definition Pressure is the force acting per unit area:

\text{Pressure} = \frac{\text{Force}}{\text{Area}}

(Here we mean force acting perpendicular to the surface.) Its SI unit is newton per square metre (N/m²), also called the pascal (Pa). So the same force over a smaller area gives higher pressure; over a larger area, lower pressure.

Worked Example

A force of 100 N presses on a cardboard of area 2 m². Find the pressure.

\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{100\ \text{N}}{2\ \text{m}^2} = 50\ \text{N/m}^2 = 50\ \text{Pa}.

Use the calculator to feel the relationship — change the force and the area and watch the pressure respond.

Pressure calculator
Pressure = Force ÷ Area. Small area → big pressure.



Why we use this every day

Once you know pressure = force ÷ area, dozens of everyday choices make sense:

  • A bucket with a broad handle is comfier than one with a thin handle — the same weight, spread over more skin.
  • People carry head-loads on a round cloth pad, spreading the weight over a bigger area.
  • A knife’s sharp edge and a nail’s pointed tip have a tiny area, so even a modest force makes a huge pressure — which is exactly why the sharp edge cuts and the pointed nail drives in easily.

The Two-Way Rule To reduce pressure, increase the area (broad straps, wide pads, a camel’s broad feet on sand). To increase pressure, reduce the area (sharp knives, pointed nails, ice-skate blades). Same force — opposite results, just by changing the area.

Exam Tip In numerical problems, always use Pressure = Force ÷ Area, with force in newtons and area in square metres, giving pressure in pascals (Pa). Watch the units: a weight given in “kg” must be treated as a force only after it is expressed in newtons.