Density and pressure
Cambridge A-Level Physics (9702) · Unit 4: Forces, density and pressure · 7 flashcards
Density and pressure is topic 4.3 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 4 — Forces, density and pressure , alongside Turning effects of forces and Equilibrium of forces. In one line: Density (ρ) is mass per unit volume. It is calculated as ρ = m/V, where m is mass and V is volume. Common units are kg/m³ or g/cm³.
Marked as AS Level: examined at AS Level in Paper 1 (Multiple Choice), Paper 2 (AS Structured Questions) and Paper 3 (Advanced Practical Skills). The same content may also be assumed in Paper 4 (A Level Structured Questions).
The deck below contains 7 flashcards — 3 definitions, 1 key concept, 2 calculations and 1 derivation — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Density
Density (ρ) is mass per unit volume. It is calculated as ρ = m/V, where m is mass and V is volume. Common units are kg/m³ or g/cm³.
What the Cambridge 9702 syllabus says
Official 2025-2027 spec · AS LevelThese are the exact learning outcomes Cambridge sets for this topic. The candidate is expected to be able to do each of these on the relevant paper.
- define and use density
- define and use pressure
- derive, from the definitions of pressure and density, the equation for hydrostatic pressure ∆p = ρg∆h
- use the equation ∆p = ρg∆h
- understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure
- calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in Density and pressure
- › Ensure the 'total weight' in buoyancy calculations includes every part of the submerged or floating system.
- › Define upthrust strictly as the force due to the pressure difference (pb – pt)A between the top and bottom surfaces.
- › Use the formula Upthrust = ρgV, where V is the volume of the submerged part of the object and ρ is the density of the fluid.
- › Recognize that scale readings indicate the normal contact force; use R - mg = ma to solve for acceleration.
- › Recall that the torque of a couple is the product of one of the forces and the perpendicular distance between the forces.
Define density.
Density (ρ) is mass per unit volume. It is calculated as ρ = m/V, where m is mass and V is volume. Common units are kg/m³ or g/cm³.
Define pressure.
Pressure (p) is the force acting perpendicularly per unit area. It is calculated as p = F/A, where F is the force and A is the area. The SI unit is Pascal (Pa), which is equivalent to N/m².
Derive the formula for hydrostatic pressure (∆p = ρg∆h).
Consider a column of fluid of height ∆h, area A, and density ρ. The weight of the fluid column is mg = ρVg = ρA∆hg. The pressure difference ∆p is the weight divided by the area: ∆p = (ρA∆hg)/A = ρg∆h.
A submarine is at a depth of 50m in seawater (density 1030 kg/m³). Calculate the hydrostatic pressure acting on it.
Using ∆p = ρg∆h, where ρ = 1030 kg/m³, g = 9.81 m/s², and ∆h = 50m, we get: ∆p = 1030 * 9.81 * 50 = 505115 Pa. Therefore, the hydrostatic pressure is approximately 505 kPa.
Explain why an object submerged in a fluid experiences upthrust.
Upthrust occurs because the pressure at the bottom of the object is greater than the pressure at the top. This pressure difference creates a net upward force, known as upthrust (Archimedes' principle).
State Archimedes' principle.
Archimedes' principle states that the upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, Upthrust = ρgV where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid displaced (which is the volume of the submerged object).
A stone of volume 0.01 m³ is fully submerged in water (density 1000 kg/m³). Calculate the upthrust on the stone.
Using F = ρgV, where ρ = 1000 kg/m³, g = 9.81 m/s², and V = 0.01 m³, the upthrust is: F = 1000 * 9.81 * 0.01 = 98.1 N.
Review the material
Read full revision notes on Density and pressure — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 4 — Forces, density and pressure
Density and pressure sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Density and pressure deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
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