Calculate density and pressure
Relate density to mass per volume and pressure to perpendicular force per area, keeping units consistent.
Section 4 · Forces, density and pressure
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 4. These original explanations and numerical practice support theory study; they do not demonstrate supervised practical competence. Full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use SI units, resolve perpendicular components, and distinguish force from pressure.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which equation defines density?
What you will learn
- Define and calculate density
- Define and calculate pressure
- Use consistent units for mass, volume, force and area
Density describes mass packed into a volume
Density is mass per unit volume: ρ = m/V. It is a property of the material in a specified state. The SI unit is kg m⁻³; convert dimensions to metres before calculating volume in m³.
For a regular solid, volume can be calculated from its dimensions. For an irregular object, an appropriate displacement method may estimate volume, but a written or simulated method cannot by itself demonstrate practical measurement skill.
Pressure spreads a force over an area
Pressure is the normal force per unit area: p = F/A, where F is perpendicular to the surface. Its SI unit is Pa, equivalent to N m⁻². The same force gives greater pressure when it acts over a smaller area.
If the force is angled, use its component perpendicular to the surface for normal pressure. Keep area in square metres and distinguish pressure, which is force per area, from force itself.
Pause and explain
What happens to pressure if the same normal force is spread over twice the area?
Worked example
A metal block has mass 2.7 kg and volume 1.0 × 10⁻³ m³. Find its density. Then find the pressure from a 120 N normal force over 0.020 m².
Show the worked solution
- Density = 2.7/(1.0 × 10⁻³) = 2700 kg m⁻³.
- Pressure = 120/0.020 = 6000 Pa.
- The two quantities have different definitions and units.
Answer Density 2.7 × 10³ kg m⁻³; pressure 6.0 × 10³ Pa.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A sample has mass 0.60 kg and volume 2.0 × 10⁻⁴ m³. Calculate its density.
Give me a hint
Divide mass by volume and preserve the powers of ten.
Compare my reasoning
- ρ = m/V.
- ρ = 0.60/(2.0 × 10⁻⁴).
- Write the result in kg m⁻³.
3.0 × 10³ kg m⁻³.
Look for these in your work
- Relationship used
- Division correct
- SI unit stated
A 500 N student stands on two shoes with a total contact area of 0.025 m². Find the average pressure on the floor.
Give me a hint
Use the total contact area of both shoes and the normal force.
Compare my reasoning
- p = F/A.
- p = 500/0.025.
- Report pascals or N m⁻².
2.0 × 10⁴ Pa.
Look for these in your work
- Total force and area used
- Pressure calculated
- Pa unit included
A cube of side 5.0 cm has mass 0.50 kg. Find its density in kg m⁻³. State the pressure on a horizontal floor if the cube rests on one face and g = 10 N kg⁻¹.
Give me a hint
Convert centimetres to metres before finding volume and contact area.
Compare my reasoning
- Side = 0.050 m; volume = 0.050³ = 1.25 × 10⁻⁴ m³, so ρ = 0.50/(1.25 × 10⁻⁴) = 4000 kg m⁻³.
- Weight = mg = 0.50 × 10 = 5.0 N; face area = 0.050² = 0.0025 m².
- Pressure = 5.0/0.0025 = 2000 Pa.
Density 4.0 × 10³ kg m⁻³; average pressure on the floor 2.0 × 10³ Pa.
Look for these in your work
- Length converted to metres
- Density uses the full cube volume
- Pressure uses weight over one face area
Common mistakes
- Using cm³ with mass in kilograms without converting
- Using total surface area instead of the contact area in a pressure problem
- Using a force component parallel to the surface
What can you explain now?
Which equation defines density?
Compare with the explanation
ρ = m/V
Density is mass per unit volume.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do the units and equations show the difference between density and pressure?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.