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IGCSE Physics 0625 · Chapter 5 notes · ~7 min read

Pressure

Why a knife cuts, why skis stop you sinking, and why a dam wall is thicker at the bottom — pressure in solids and liquids.

Pressure = force ÷ areaEveryday examplesLiquid pressure, depth & densityΔp = ρgΔh
RSby Riyaz Sir
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No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • Pressure = force ÷ area. The same force on a smaller area gives a bigger pressure.
  • Unit: the pascal (Pa), which is 1 N for every m².
  • Liquid pressure increases with depth and with the density of the liquid.
  • EXT The extra pressure at depth is Δp = ρgΔh.

By the end you can

  • Use p = F ÷ A, changing cm² into m² first.
  • Explain everyday examples with large and small areas.
  • State how liquid pressure depends on depth and density.
  • Calculate liquid pressure with Δp = ρgΔh. EXT

1Pressure on a surface

Force and area

Pressure — the force acting on each unit of area, at right angles to the surface.

p = FA
pressure (Pa) = force (N) ÷ area (m²)
60 N60 Narea 0.12 m² → p = 500 Paarea 0.04 m² → p = 1500 Pasame force, smaller area = bigger pressure
The same 60 N force acts on two areas. The smaller area gives three times the pressure.
  • 1 Pa = 1 N/m². A pascal is tiny, so you often see kPa (1000 Pa). Atmospheric pressure at sea level is about 100 000 Pa.
  • Rearrange: F = pA and A = F ÷ p.
  • To get a high pressure: increase the force or decrease the area. To get a low pressure: decrease the force or increase the area.
ExampleAreaEffect
knife edge, nail, drawing-pin tipvery smallhuge pressure, so it cuts or pierces
skis, snowshoes, caterpillar trackslargelow pressure, so you do not sink
wide rucksack strapslargethe load is spread over your shoulders
high heelsmallhigh pressure that can dent a floor
Worked example

An 80 kg person stands on two feet, each of area 0.020 m². Find the pressure. Then find it on one foot. (g = 10 N/kg)

  1. Force = weight = mg = 80 × 10 = 800 N
  2. Two feet: A = 0.040 m², p = 800 ÷ 0.040 = 20 000 Pa
  3. One foot: A = 0.020 m², p = 800 ÷ 0.020 = 40 000 Pa (double)
Worked example

A force of 200 N acts on an area of 5.0 cm². Find the pressure in pascals.

  1. Convert first: 1 cm² = 0.0001 m², so 5.0 cm² = 5.0 × 10⁻⁴ m²
  2. p = F ÷ A = 200 ÷ (5.0 × 10⁻⁴)
  3. = 4.0 × 10⁵ Pa
Worked example

The air presses with 1.0 × 10⁵ Pa on a table top of area 0.80 m². Find the force. Why doesn't it crush the table?

  1. F = pA = 1.0 × 10⁵ × 0.80 = 8.0 × 10⁴ N (80 000 N)
  2. The air also presses upwards on the underside of the table with the same force, so the forces balance
Common mistakeUsing cm² with pascals. Convert to m² first (1 m² = 10 000 cm²).
Common mistakeMixing up force and pressure. Force is the push; pressure is how concentrated that push is.
Picture itStand on soft snow in shoes and you sink. Strap on skis and the same weight is spread over a bigger area, so the pressure is lower and you stay on top.
  • Gas pressure comes from particles hitting the walls — see Thermal physics.

2Pressure in liquids

Liquid pressure

  • Liquid pressure increases with depth. At greater depth there is more liquid above, pressing down.
  • It also increases with density. A denser liquid at the same depth gives more pressure.
  • At a given depth the pressure acts equally in all directions, and pushes on side walls at right angles.
  • At the same depth in the same liquid, the pressure is the same whatever the shape of the container.
depthp = ρ g h (more depth = more pressure)
The arrows on the wall get longer as the depth increases. That is why dam walls, submarines and deep-sea equipment are built extra strong.
Picture itIn a stack of books the bottom book carries every book above it. In a liquid, the deeper you go, the taller the "stack of liquid" pressing on you.
EXT Δp = ρ g Δh
pressure change (Pa) = density (kg/m³) × g (N/kg) × change in depth (m)
Worked example

EXT Find the increase in pressure for a diver who goes down 25 m in sea water. (ρ = 1030 kg/m³, g = 9.8 N/kg)

  1. Δp = ρgΔh = 1030 × 9.8 × 25
  2. = 252 350 Pa
  3. ≈ 2.5 × 10⁵ Pa, on top of the atmospheric pressure at the surface
Worked example

EXT A tank is filled to a depth of 0.80 m with water of density 1000 kg/m³. Find the pressure due to the water on the base. (g = 9.8 N/kg)

  1. Δp = ρgΔh = 1000 × 9.8 × 0.80
  2. = 7840 Pa
Exam tipLiquid pressure depends only on depth and density — not on how wide the container is or how much liquid there is in total.
Common mistake"A wider tank has more pressure at the bottom." Only depth and density count.

3Test yourself

Test yourself — cover the answers first

Quick check

  1. A 500 N person stands on a total area of 0.050 m². What is the pressure?
  2. Why do skis stop you sinking into snow?
  3. Convert 4.0 cm² to m².
  4. What two things does liquid pressure depend on?
  5. Why is a dam wall thicker at the bottom?

Exam-style

  1. A tank has a weight of 600 000 N. Its tracks create a pressure of 40 000 Pa. What area of track is in contact with the ground?
  2. Explain why a sharp knife cuts better than a blunt one. [2]
  3. EXT Oil of density 800 kg/m³ fills a tank. Find the pressure due to the oil at a depth of 3.0 m. (g = 9.8 N/kg)
  4. EXT A diver is 10 m below the surface of a lake (water density 1000 kg/m³, atmospheric pressure 1.0 × 10⁵ Pa, g = 9.8 N/kg). Find the total pressure on the diver.
Show answers
  1. 500 ÷ 0.050 = 10 000 Pa
  2. They spread your weight over a larger area, so the pressure is smaller.
  3. 4.0 × 10⁻⁴ m²
  4. the depth and the density of the liquid
  5. The pressure is bigger at greater depth, so the wall must be stronger there.
  6. A = F ÷ p = 600 000 ÷ 40 000 = 15 m²
  7. The sharp edge has a smaller area
    so the same force produces a larger pressure
  8. Δp = ρgΔh = 800 × 9.8 × 3.0 = 23 520 Pa ≈ 2.4 × 10⁴ Pa
  9. pressure due to water = 1000 × 9.8 × 10 = 9.8 × 10⁴ Pa
    total = 9.8 × 10⁴ + 1.0 × 10⁵ = 1.98 × 10⁵ Pa ≈ 2.0 × 10⁵ Pa
Practise this chapter
PressureDensity
Next chapterThermal physics →
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