Force and pressure — types of forces, pressure in fluids, atmospheric pressure

Question

A block of weight 100 N rests on a table. Its base area is 0.05 m². Find the pressure exerted on the table. Why does a sharp nail pierce easily but a flat book does not, even with the same force?

Solution — Step by Step

$\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{100}{0.05} = \mathbf{2000 \text{ Pa (N/m}^{2}\text{)}}$

A nail has a tiny tip area (say 1 mm² = $10^{-6}$ m²). Apply 10 N of force: pressure = $10/10^{-6} = 10^7$ Pa (10 million pascals). A book’s flat surface might be $0.05$ m². Same 10 N force gives pressure = $200$ Pa. The nail’s pressure is 50,000 times higher — enough to pierce skin or wood.

Same force, smaller area → much higher pressure. This is why sharp objects cut and pierce.

Why This Works

graph TD
    A["Types of Forces"] --> B["Contact Forces"]
    A --> C["Non-Contact Forces"]
    B --> D["Muscular force"]
    B --> E["Friction"]
    B --> F["Normal force"]
    B --> G["Tension"]
    C --> H["Gravitational force"]
    C --> I["Magnetic force"]
    C --> J["Electrostatic force"]
    A --> K["Pressure = Force/Area"]
    K --> L["Same force, less area → more pressure"]
    K --> M["Applies to solids, liquids, and gases"]

Pressure is force distributed over an area. When force is concentrated on a small area, the effect per unit area is intense. When spread over a large area, the effect is mild.

Pressure in fluids acts in all directions (unlike solids where pressure acts only on the contact surface). The pressure at a depth $h$ in a liquid of density $\rho$ is: $P = \rho g h$ . This is why divers experience more pressure at greater depths, and why dams are thicker at the bottom.

Atmospheric pressure = $1.013 \times 10^5$ Pa (1 atm). This enormous pressure does not crush us because our internal body pressure balances it. We demonstrated this with the Magdeburg hemispheres experiment — two hemispheres could not be pulled apart even by horses because of the external atmospheric pressure.

Alternative Method

Practical applications to remember for exams:

Broad straps on bags — distribute weight over larger area, less pressure on shoulder
Tank treads (caterpillar wheels) — spread heavy vehicle weight over large area to avoid sinking
Cutting tools are sharp — tiny contact area creates huge pressure for the same applied force
Lying on bed of nails — weight spread over hundreds of nails, so pressure per nail is bearable

Common Mistake

Confusing force with pressure. Force is measured in Newtons and has direction. Pressure is force per unit area, measured in Pascals (N/m²), and in fluids it acts equally in all directions. A heavy elephant exerts less pressure than a woman in high heels because the heel area is tiny. The question “which exerts more pressure?” and “which exerts more force?” have different answers. Always check what is being asked.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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