IGCSE Physics · Unit 1: Motion, Forces and Energy · Core + Extended
Pressure CoreExtended adds liquid pressure equation
Pressure explains why a sharp knife cuts easily, why snowshoes stop you sinking, and why a dam is built thicker at its base. This short but important topic covers pressure from a solid force on a surface, and how pressure changes with depth in a liquid.
1. Pressure as Force per Unit Area
Pressure is defined as force per unit area.
p = F / A
Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². For the same force, a smaller area produces a greater pressure, and a larger area produces a smaller pressure.
Worked example — calculating pressure
A crate exerts a force of 200 N on the floor through a base of area 0.5 m². Find the pressure on the floor.
p = F / A = 200 / 0.5 = 400 Pa
A crate exerts a force of 200 N on the floor through a base of area 0.5 m². Find the pressure on the floor.
p = F / A = 200 / 0.5 = 400 Pa
Worked example — rearranging for force
A hydraulic press produces a pressure of 5000 Pa over a piston of area 0.02 m². Find the force produced.
F = p × A = 5000 × 0.02 = 100 N
A hydraulic press produces a pressure of 5000 Pa over a piston of area 0.02 m². Find the force produced.
F = p × A = 5000 × 0.02 = 100 N
Everyday examples
A drawing pin has a very sharp point (a tiny area), so a modest push produces a huge pressure, easily piercing a surface. Snowshoes work the opposite way — they spread a person’s weight over a much larger area, greatly reducing the pressure on the snow so the person doesn’t sink. A sharp knife cuts more easily than a blunt one for the same reason: a thinner blade edge means a smaller contact area, and hence a much larger pressure for the same applied force.
A drawing pin has a very sharp point (a tiny area), so a modest push produces a huge pressure, easily piercing a surface. Snowshoes work the opposite way — they spread a person’s weight over a much larger area, greatly reducing the pressure on the snow so the person doesn’t sink. A sharp knife cuts more easily than a blunt one for the same reason: a thinner blade edge means a smaller contact area, and hence a much larger pressure for the same applied force.
Try it — Pressure and Area
- A force of 150 N acts over an area of 0.3 m². Calculate the pressure.
- A pressure of 2500 Pa is produced over an area of 0.04 m². Calculate the force.
- Explain, using p = F/A, why a stiletto heel can damage a wooden floor while a flat shoe of the same weight does not.
Show answers
- p = 150/0.3 = 500 Pa
- F = p × A = 2500 × 0.04 = 100 N
- A stiletto heel has a very small contact area, so for the same weight (force), the pressure exerted on the floor (p = F/A) is much greater than for a flat shoe with a much larger contact area — this larger pressure can be enough to dent or damage the floor.
2. Pressure in Liquids
The pressure beneath the surface of a liquid increases with both depth and density of the liquid — deeper down, there is more liquid above pushing down, and a denser liquid weighs more for the same volume.
Δp = ρgΔh Extended
Worked example — pressure at depth
Find the pressure due to water at a depth of 5 m (density of water = 1000 kg/m³, g = 9.8 N/kg).
Δp = ρgΔh = 1000 × 9.8 × 5 = 49000 Pa
Find the pressure due to water at a depth of 5 m (density of water = 1000 kg/m³, g = 9.8 N/kg).
Δp = ρgΔh = 1000 × 9.8 × 5 = 49000 Pa
Worked example — comparing liquids
Compare the pressure at 0.5 m depth in water (density 1000 kg/m³) and in mercury (density 13600 kg/m³), with g = 9.8 N/kg.
Water: Δp = 1000 × 9.8 × 0.5 = 4900 Pa
Mercury: Δp = 13600 × 9.8 × 0.5 = 66640 Pa
Mercury produces a much greater pressure at the same depth, because it is far denser than water.
Compare the pressure at 0.5 m depth in water (density 1000 kg/m³) and in mercury (density 13600 kg/m³), with g = 9.8 N/kg.
Water: Δp = 1000 × 9.8 × 0.5 = 4900 Pa
Mercury: Δp = 13600 × 9.8 × 0.5 = 66640 Pa
Mercury produces a much greater pressure at the same depth, because it is far denser than water.
Why dams are thicker at the base
Since liquid pressure increases with depth, the water pushes hardest against the lowest part of a dam wall. Dams are therefore built much thicker at the base than at the top, so the structure can withstand this much larger pressure where it is greatest.
Since liquid pressure increases with depth, the water pushes hardest against the lowest part of a dam wall. Dams are therefore built much thicker at the base than at the top, so the structure can withstand this much larger pressure where it is greatest.
Try it — Liquid Pressure
- Find the pressure due to water at a depth of 3 m (density 1000 kg/m³, g = 9.8 N/kg).
- A liquid has a density of 800 kg/m³. Find the pressure at a depth of 2.5 m (g = 9.8 N/kg).
- Explain, in terms of the liquid above, why pressure increases with depth in a liquid.
Show answers
- Δp = 1000 × 9.8 × 3 = 29400 Pa
- Δp = 800 × 9.8 × 2.5 = 19600 Pa
- At a greater depth, there is a taller column of liquid above that point, so its weight presses down with a greater force over the same area — since pressure is force per unit area, this greater force means a greater pressure the deeper you go.
Common mistakes to watch for
- Forgetting that pressure DECREASES as area increases for the same force — smaller area always means greater pressure, not the other way round.
- Using the wrong density (mixing up kg/m³ and g/cm³) when calculating liquid pressure — Δp = ρgΔh requires SI units (kg/m³, m/s², m) to give an answer in Pa.
- Forgetting that liquid pressure depends on depth and density only, not on the shape or width of the container.
Key Vocabulary Recap
Pressure — force per unit area (p = F/A), measured in pascals (Pa)
Pascal (Pa) — the SI unit of pressure; 1 Pa = 1 N/m²
Liquid pressure — depends on depth and density (Δp = ρgΔh)
Syllabus Reference
This note covers Cambridge IGCSE Physics (0625) section 1.8, Pressure — Core: defining pressure as force per unit area (p = F/A), how pressure varies with force and area in everyday examples, and the qualitative effect of depth and density on liquid pressure; Supplement: the equation for the change in pressure beneath the surface of a liquid (Δp = ρgΔh).
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