Pressure due to Solids

Pressure in solids

Definition

Pressure in solids is the force exerted per unit area when a solid object applies a force to a surface.

Formula

$$\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A}$$

P = Pressure (in Pascals, Pa or N/m²) F = Force applied (in Newtons, N) A = Area over which the force is applied (in square meters, m²)

Key concept

The smaller the area on which a force acts, the greater the pressure it produces.

Example 1: Block of wood

Given:

• Force = 30 N
• Dimensions of the block = 10 m × 5 m × 4 m

Step 1: Calculate pressure on the large base

$$\text{Area}_{\text{large}} = 10 \times 5 = 50 \, \text{m}^2$$ $$\text{Pressure}_{\text{large}} = \frac{30}{50} = 0.6 \, \text{N/m}^2$$

Step 2: Calculate pressure on the small base

$$\text{Area}_{\text{small}} = 5 \times 4 = 20 \, \text{m}^2$$ $$\text{Pressure}_{\text{small}} = \frac{30}{20} = 1.5 \, \text{N/m}^2$$

The block exerts more pressure when placed on the smaller base.

Example 2: Needle tip

Given:

• Force = 20 N
• Area of needle tip = $1 \times 10^{-6} \, \text{m}^2$

Apply the formula:

$$\text{Pressure} = \frac{20}{1 \times 10^{-6}} = 2.0 \times 10^7 \, \text{N/m}^2$$

The pressure at the tip of the needle is extremely high due to the very small area.