Limitless Physics
Menu

Topic 1.8 · Unit 1

Pressure

Pressure as force per unit area, how changing the force or the area changes the pressure in everyday situations, and how the pressure in a liquid depends on depth and density.

Key points

  • Pressure is the force per unit area: p = F / A.
  • The force F is the force acting at right angles (perpendicular) to the surface.
  • The unit of pressure is N/m2. If the area is in cm2, the pressure is in N/cm2.
  • The pascal (Pa) is another name for the same unit: 1 Pa = 1 N/m2. Extended
  • For the same area, a larger force gives a larger pressure.
  • For the same force, a smaller area gives a larger pressure. A larger area gives a smaller pressure.
  • Everyday examples where a small area gives a high pressure:
    • A sharp knife has a very thin edge, so its area is tiny. The same push gives a high pressure, which cuts the food easily.
    • A drawing pin has a sharp point with a tiny area. The high pressure pushes the point into a board.
    • A person in high-heeled shoes sinks into soft sand more than a person in flat sandals. The weight is the same, but the area of the heels is smaller, so the pressure on the sand is larger.
  • Everyday examples where a large area gives a low pressure:
    • The head of a drawing pin is wide. The pressure on your thumb is low, so it does not hurt.
    • Wide tyres on a heavy truck or tractor spread its weight over a larger area. The pressure on soft ground is lower, so the wheels do not sink.
    • A wide strap on a heavy bag spreads the force over your shoulder, so the pressure is lower and it is more comfortable.
    • Buildings stand on wide foundations, so the pressure on the ground below is low enough for the ground to support them.
  • Pressure in a liquid is caused by the weight of the liquid above.
  • The pressure in a liquid increases with depth. Deeper down, there is more liquid above, so its weight is larger.
  • The pressure in a liquid increases with the density of the liquid. At the same depth, a denser liquid above has a larger mass, so a larger weight.
  • Examples:
    • Make holes at different depths in a can of water. Water leaves the deeper hole faster, because the pressure there is greater.
    • A dam is built thicker at the bottom, because the pressure of the water is greatest at the bottom.
    • A diver feels more pressure on the ears the deeper the diver goes.
    • At the same depth, the pressure in seawater is a little greater than in fresh water, because seawater is denser.
  • Extra detail: at any point in a liquid, the pressure acts in all directions.
  • Extra detail: the pressure at a given depth does not depend on the shape or width of the container. It depends only on the depth and the density of the liquid.
  • The change in pressure beneath the surface of a liquid: Δp = ρgΔh. Extended
  • Δh is the change in depth, measured vertically. Use the density in kg/m3, Δh in m and g = 9.8 N/kg. Then Δp is in Pa. Extended
  • Δp is the extra pressure caused by the liquid. Example: going from the surface down to a depth h, Δp = ρgh. Extended
  • Extra detail: the total pressure at a depth also includes the pressure of the atmosphere pushing on the surface of the liquid.
  • Extra detail: where Δp = ρgΔh comes from. Imagine a column of liquid with base area A and height Δh. Its mass is ρ × A × Δh. Its weight is ρ × A × Δh × g. Pressure = weight ÷ area = ρgΔh.

Model

No model for this topic yet.

Equations

  • Pressure

    p = F / A

    p = pressure (N/m2 or N/cm2; Pa in Extended); F = force acting at right angles to the surface (N); A = area (m2 or cm2)

  • Change in pressure beneath the surface of a liquidExtended

    Δp = ρgΔh

    Δp = change in pressure (Pa); ρ = density of the liquid (kg/m3); g = gravitational field strength (9.8 N/kg); Δh = change in depth (m)

Pressure

A motorbike and its riders weigh 2500 N. The area of the tyres touching the road is 0.010 m2. Find the pressure on the road.

  • Given: F = 2500 N, A = 0.010 m2
  • p = F / A
  • p = 2500 ÷ 0.010
  • p = 250 000 N/m2
  • In pascals, this is 250 000 Pa (250 kPa). Extended

A student of weight 600 N stands on both feet. The total area of the shoes touching the floor is 300 cm2. Find the pressure in N/cm2. What happens to the pressure if the student stands on one foot?

  • Given: F = 600 N, A = 300 cm2
  • p = 600 ÷ 300
  • p = 2.0 N/cm2
  • On one foot, the area halves to 150 cm2. The force is the same.
  • p = 600 ÷ 150 = 4.0 N/cm2. The pressure doubles.

Change in pressure beneath the surface of a liquid Extended

A diver swims down from the surface to a depth of 10 m in seawater. The density of the seawater is 1030 kg/m3. Find the increase in pressure. Use g = 9.8 N/kg.

  • Given: ρ = 1030 kg/m3, g = 9.8 N/kg, Δh = 10 m
  • Δp = ρgΔh
  • Δp = 1030 × 9.8 × 10
  • Δp = 100 940 Pa = 101 000 Pa (3 s.f.), or 1.01 × 105 Pa

A fish moves from 2.0 m deep to 5.0 m deep in a freshwater tank. The density of the water is 1000 kg/m3. Find the change in pressure on the fish.

  • Δh = 5.0 − 2.0 = 3.0 m (the change in depth, not the final depth)
  • Δp = 1000 × 9.8 × 3.0
  • Δp = 29 400 Pa (an increase, because the fish moved deeper)

Common mistakes

  • Students write pressure = force × area. / The mark scheme wants force ÷ area: p = F / A.
  • Students say a sharp knife cuts better because it has a bigger force. / The mark scheme wants: the same force acts on a smaller area, so the pressure is greater.
  • Students mix units, for example a force in N with an area in cm2, then write the answer in N/m2. / The mark scheme wants the unit to match the area: N/cm2 for cm2, N/m2 for m2. To change cm2 to m2, divide by 10 000.
  • Students say the pressure in a liquid depends on the amount of liquid in the container. / The mark scheme wants: the pressure depends on the depth and the density of the liquid.
  • Students put a density in g/cm3 into Δp = ρgΔh. / The mark scheme wants the density in kg/m3: 1.03 g/cm3 = 1030 kg/m3. Extended
  • Students use the final depth when an object moves between two depths. / The mark scheme wants Δh, the change in depth. Extended

Exam tips

  • Define pressure in words: “force per unit area”. Then give p = F / A.
  • Describe an everyday example in three parts: is the force the same or different? Is the area larger or smaller? So is the pressure larger or smaller?
  • Describe how the pressure in a liquid changes: it increases with depth and with the density of the liquid. Name both factors if the question asks for both.
  • Calculate: check whether the area is in m2 or cm2, and give the matching unit.
  • Calculate with Δp = ρgΔh: write the equation, substitute with units in kg/m3 and m, and give the answer in Pa. Extended
  • A typical 1-mark answer: “Pressure is the force per unit area.”
  • A typical 2-mark answer to “Why do wide tyres stop a tractor sinking into mud?”: “The weight is spread over a larger area (1), so the pressure on the mud is smaller (1).”
  • A typical 2-mark answer to “Why is a dam thicker at the bottom?”: “The pressure in water increases with depth (1). So the force on the bottom of the dam is greatest, and it must be strongest there (1).”