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Density & Pressure

📋 Module Overview & Key Units

General Learning Outcomes:

  • 5.1 Use the following units: degree Celsius (°C), Kelvin (K), joule (J), kilogram (kg), kg/m³, metre (m), m², m³, m/s, m/s², newton (N), and pascal (Pa).

This module covers the fundamental concepts of density and pressure, including how pressure behaves in fluids. Correct units are crucial for all calculations.

⚖️ 1. Density

Learning Outcomes:

  • 5.3 Know and use the relationship between density, mass, and volume.
  • 5.4 Practical: Investigate density using direct measurements of mass and volume.

Density measures how compact a substance is — how much mass is packed into a given volume. A dense material (like iron) has a lot of mass in a small space, while a less dense material (like wood) is lighter for the same size.

ρ = m ÷ V

Density (kg/m³) = Mass (kg) ÷ Volume (m³)

Example: A metal block has mass 400 g and volume 50 cm³.
Density = 400 g ÷ 50 cm³ = 8 g/cm³ = 8 000 kg/m³

📊 Common Material Densities

MaterialDensity (kg/m³)Float or Sink?
Cork240🟢 Floats
Wood (oak)600🟢 Floats
Ice917🟢 Floats
Water1 000—
Aluminium2 700🔴 Sinks
Iron7 874🔴 Sinks
Copper8 960🔴 Sinks
Gold19 320🔴 Sinks

🌊 Simulation: Float or Sink?

Click a material to drop it into the water tank and see whether it floats or sinks. Objects with density < 1 000 kg/m³ float; objects with density ≥ 1 000 kg/m³ sink.

🧮 Density Calculator

🔬 Practical: Measuring Density

🛠️ Materials:
  • Electronic balance
  • Regular-shaped objects (blocks, cylinders)
  • Irregular-shaped objects (stones, metal samples)
  • Ruler or vernier calipers
  • Eureka can / displacement vessel
  • Measuring cylinder, water, string

📐 Method A — Regular-Shaped Objects

1
Measure the mass on an electronic balance. Record in grams.
2
Measure dimensions with a ruler/calipers. For a block: length × width × height. For a cylinder: diameter and height.
3
Calculate volume: V = l × w × h (block) or V = π r² h (cylinder).
4
Calculate density: ρ = m ÷ V. Convert units as needed.

🌊 Method B — Irregular-Shaped Objects (Displacement)

Rock 🤚 Eureka Can Measuring Cylinder overflow 50.0 g Electronic Balance
1
Measure the mass of the object using the electronic balance.
2
Fill the Eureka can until water is level with the overflow spout (or record initial volume in a measuring cylinder).
3
Tie string to the object and gently lower it completely into the water.
4
Collect displaced water in a measuring cylinder and record the volume. (1 mL = 1 cm³)
5
Calculate density: ρ = mass ÷ displaced volume.
⚠️ Note: Repeat measurements several times and calculate an average to improve accuracy.
Example: A stone has mass 50 g. It displaces 20 mL of water.
ρ = 50 g ÷ 20 cm³ = 2.5 g/cm³ = 2 500 kg/m³

💪 2. Pressure

Learning Outcomes:

  • 5.5 Know and use the relationship between pressure, force, and area: P = F ÷ A.

Pressure is the force applied perpendicular to a surface, divided by the area over which it acts. The same force spread over a smaller area creates much higher pressure.

P = F ÷ A

Pressure (Pa) = Force (N) ÷ Area (m²)

Example: 500 N applied to 0.25 m².
P = 500 ÷ 0.25 = 2 000 Pa (2 kPa)

🔧 Simulation: Pressure vs Area

The same force is applied to both surfaces. Drag the sliders to see how changing force or area affects pressure. The colour intensity shows pressure level.

500 N
1.00 m²
0.20 m²

🧮 Pressure Calculator

🌊 3. Pressure in Fluids

Learning Outcomes:

  • 5.6 Understand how pressure at a point in a fluid at rest acts equally in all directions.
  • 5.7 Know and use the relationship: p = h × ρ × g.

In fluids (liquids and gases), pressure at any given point acts equally in all directions. This is called Pascal's Principle. Pressure also increases with depth because of the weight of fluid above.

Pressure acts equally in all directions Fluid at rest

At any point in a fluid at rest, pressure pushes equally in every direction. This is why submarines must be uniformly strong on all sides, and why water leaks from a hole in any direction.

p = h × ρ × g

Pressure difference (Pa) = height (m) × density (kg/m³) × gravitational field strength (m/s²)

Example: Pressure at 5 m depth in freshwater (ρ = 1 000 kg/m³):
p = 5 × 1 000 × 9.8 = 49 000 Pa = 49 kPa

🤿 Simulation: Depth Pressure Explorer

Drag the depth slider to move the submarine deeper. Watch how pressure increases with depth. Try different fluids!

10 m
Depth
10
metres
Fluid Density
1 000
kg/m³
Hydrostatic Pressure
98 000
Pa
Total Pressure
199 325
Pa (incl. atm)

⚙️ Simulation: Hydraulic Press

A hydraulic press uses Pascal's Principle: pressure applied to one piston is transmitted equally to the other. A larger output piston creates a larger force — a mechanical advantage!

200 N
5 cm²
100 cm²
Pressure in fluid
400 000
Pa
Output force
4 000
N
Mechanical advantage
20
×

🧮 Fluid Pressure Calculator

🌍 Real-life applications:
  • Submarine hulls must withstand pressure from all sides equally.
  • Water leaks through pipe holes in every direction.
  • Deep-sea creatures evolved to withstand enormous equal pressure.
  • Hydraulic brakes in cars transmit force through fluid pressure.

✅ Knowledge Check

1. What is the density of a substance with mass 150 g and volume 30 cm³?

2. A force of 200 N is applied to an area of 0.5 m². What is the pressure?

3. What happens to pressure as the area decreases (force stays constant)?

4. If you take a partially inflated balloon deep underwater, what happens?

5. In a hydraulic press, what property of fluids allows force to be transmitted?

6. A diver is 20 m below the surface of seawater (ρ = 1 025 kg/m³, g = 9.8 m/s²). What is the hydrostatic pressure?

7. Why do snowshoes stop you sinking into snow?

8. An object floats with 75% of its volume submerged. What is its density if the fluid is water (1 000 kg/m³)?