Pressure Revision Notes

Pressure is defined as the amount of force applied on a surface divided by the area of that surface. Mathematically, pressure (P) is given by the formula P = F / A, where F is the force in newtons (N) and A is the area in square metres (m²). The unit of pressure is pascals (Pa), where 1 Pa = 1 N/m².

This means that pressure depends directly on the force applied and inversely on the area over which the force is distributed. If the force increases while the area remains the same, pressure increases. Conversely, if the area increases while the force remains constant, pressure decreases.

• Pressure (P) = Force (F) ÷ Area (A)
• Units: Force in newtons (N), Area in square metres (m²), Pressure in pascals (Pa)
• Pressure increases if force increases (area constant)
• Pressure decreases if area increases (force constant)

When the area over which a force acts remains constant, increasing the force increases the pressure proportionally. For example, if you press your hand harder against a wall, the force increases, so the pressure on the wall increases.

Conversely, if the force decreases, the pressure decreases. This relationship is linear because pressure is directly proportional to force when area is fixed.

Example: If a force of 10 N is applied over an area of 0.5 m², the pressure is P = 10 N ÷ 0.5 m² = 20 Pa. If the force doubles to 20 N, pressure doubles to 40 Pa.

• Pressure ∝ Force (if area constant)
• Doubling force doubles pressure
• Example: 10 N over 0.5 m² → 20 Pa; 20 N over 0.5 m² → 40 Pa

When the force remains constant, changing the area changes the pressure inversely. Decreasing the area increases the pressure because the same force is concentrated on a smaller surface.

For example, a sharp knife has a very small edge area, so when you apply a force to cut, the pressure is high, making it easier to slice through materials. A blunt knife has a larger edge area, so the pressure is lower, making cutting harder.

If the area increases, pressure decreases. For instance, snowshoes have a large surface area, distributing the weight of a person over a larger area, reducing pressure on the snow and preventing sinking.

• Pressure ∝ 1/Area (if force constant)
• Smaller area → higher pressure
• Larger area → lower pressure
• Examples: sharp knife edge vs blunt knife; snowshoes vs regular shoes

Calculate the pressure exerted by a person weighing 600 N standing on one foot with an area of 0.02 m² in contact with the ground.

Using P = F / A, substitute F = 600 N and A = 0.02 m²:

P = 600 N ÷ 0.02 m² = 30,000 Pa (or 3.0 × 10⁴ Pa) which is a high pressure due to the small area of one foot.

• P = F / A = 600 N / 0.02 m² = 30,000 Pa
• High pressure due to small contact area

Understanding pressure helps explain many everyday situations:

High heels exert more pressure on the ground than flat shoes because the area of the heel is smaller, which can damage soft flooring.

Car tyres have a larger contact area than bicycle tyres, so the pressure on the road is lower, affecting grip and wear rates.

• High heels → small area → high pressure → potential floor damage
• Snowshoes → large area → low pressure → prevents sinking
• Knives → sharp edge → small area → high pressure → easier cutting

Pressure is a measure of how a force is spread over a surface area. It tells us how concentrated or distributed a force is on a particular area. For example, standing on snow with flat shoes applies less pressure than standing on the same snow with high heels because the force (your weight) is spread over a larger area with flat shoes, reducing pressure.

Pressure is not just about the size of the force but also about how that force is applied over an area. A small force over a tiny area can produce high pressure, while a large force over a large area can produce low pressure.

• Pressure relates force to area, indicating force intensity per unit area.
• It helps explain phenomena like why sharp knives cut better (high pressure) and why snowshoes prevent sinking (low pressure).

Pressure (P) is calculated by dividing the force (F) applied perpendicular to a surface by the area (A) of that surface. The formula is:

P = F / A, where: P is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m²).

This formula shows that pressure increases if force increases while area stays the same, and pressure decreases if area increases while force stays the same.

• Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m².
• Force must be perpendicular to the surface for this formula to apply directly.
• Area must be in square metres to keep units consistent.

Suppose a person weighing 600 N stands on one foot with a sole area of 0.02 m². To find the pressure exerted on the ground:

Use P = F / A: P = 600 N / 0.02 m² = 30,000 Pa (or 30 kPa).

This high pressure explains why standing on one foot can leave a noticeable mark on soft ground.

• Identify force and area with correct units.
• Substitute values into the formula carefully.
• Calculate and include units in the final answer.

If the force applied increases but the area remains constant, pressure increases proportionally. For example, pushing harder with a finger on a surface increases pressure.

If the area over which the force acts increases while the force remains constant, pressure decreases. For example, lying down spreads your weight over a larger area, reducing pressure on any one point.

Understanding this helps explain why snowshoes prevent sinking into snow by increasing area and reducing pressure.

• Pressure ∝ Force (if area constant).
• Pressure ∝ 1/Area (if force constant).
• Practical applications include footwear design, tyre pressure, and hydraulic systems.

Pressure is commonly measured in pascals (Pa), but other units like kilopascals (kPa) or atmospheres (atm) are also used in different contexts.

1 kPa = 1000 Pa. Atmospheric pressure at sea level is approximately 101 kPa.

Always convert units to SI before calculations to avoid errors.

• Use pascals (Pa) as the standard unit in calculations.
• Convert cm² to m² by dividing by 10,000 (since 1 m² = 10,000 cm²).
• Check units carefully to ensure correct answers.