Sec 3 Physics Pressure notes

Pressure is the force acting perpendicularly per unit area: pressure = force ÷ area, with the unit pascal (1 Pa = 1 N/m²). It explains why a stiletto heel dents a wooden floor a flat shoe does not: the same weight squeezes through a heel a hundred times smaller in area, so the pressure is a hundred times bigger.

Watch the areas: questions quote cm² as often as m², and 1 m² = 10 000 cm². Converting sloppily by a factor of 100 or 10 000 is the single biggest mark-loser in this topic. The force must also act perpendicularly to the surface — a foot pressing squarely, not a leaning ladder.

Density is the mass per unit volume: ρ = m ÷ V. Water has ρ = 1000 kg/m³, which equals 1 g/cm³ — a useful bridge because questions mix the two unit families freely. Densities decide floating (less dense floats on more dense) and enter the liquid-pressure formula directly.

Converting between the unit families: to turn g/cm³ into kg/m³ multiply by 1000 (there are a million cm³ in a m³ but a thousand grams in a kilogram). So 2.7 g/cm³ = 2700 kg/m³ (aluminium), 0.92 g/cm³ = 920 kg/m³ (oil, which floats on water).

A liquid column of height h and density ρ presses down with the weight of the liquid above: pressure p = hρg. The shape and width of the container are irrelevant — a deep narrow tube and a wide lake give the same pressure at the same depth. Liquid pressure also acts equally in all directions at a point, which is why a dam wall is thicker at the bottom: the water there pushes hardest.

Liquids are nearly incompressible, so pushing a piston raises the pressure everywhere in the connected liquid by the same amount (pressure transmits equally in all directions). A second piston of larger area then feels a larger force: F = p × A. This is the hydraulic press, the car jack, the dentist’s chair and the excavator arm all at once.

The force-multiplying ratio equals the area ratio: F₂ ÷ F₁ = A₂ ÷ A₁. But the small piston must travel proportionally further — volume pushed in at one end equals volume delivered at the other — so energy is conserved: small force × big distance = big force × small distance.

Real systems add a note worth quoting for full marks: the liquid must have no air bubbles (air compresses and makes the control spongy) and the pistons must not leak — the equal-transmission principle assumes an enclosed, continuous liquid.

The atmosphere presses on everything at about 100 kPa — the weight of a kilometres-deep ocean of air. A liquid-column barometer measures it: the atmosphere balances a column of liquid, and at equilibrium atmospheric pressure = hρg for the column. With water (ρ = 1000 kg/m³) the column would stand 100 000 ÷ (1000 × 10) = 10 m tall — hopeless for a lab bench. Mercury, 13.6 times denser, stands about 0.76 m, which is why old barometers used it and why pressure is still quoted in "mm Hg".

A manometer is a U-tube of liquid comparing two pressures. With one arm open to the air, the height difference h between the arms gives the excess of the gas pressure over atmospheric: Δp = hρg. If the gas pushes its arm down, the gas is above atmospheric; if it lets its arm rise, the gas is below (a partial vacuum). Denser liquids read shorter columns for the same pressure — the measuring liquid is chosen for the range needed.