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Physics · 03 / 12

Density and pressure

Middle school · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Units: numbers have dimensionsEquations: keep the balance level
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

Density relates mass to volume through ρ=m/V, in kg/m³. Pressure is normal force per area p=F/S, in pascals or N/m². These ratios describe different quantities. At fixed force, a smaller area increases pressure.

p=F/S
THE PICTURE TO REMEMBERDensity and pressure
  1. 01Required quantity
  2. 02Volume or area
  3. 03SI units
  4. 04Ratio and meaning

WORKED EXAMPLE

From principle to reasoning

2 kg in 0.001 m³ gives 2,000 kg/m³. A normal force of 100 N on 0.02 m² gives 5,000 Pa. Convert volume and area first.

Solve a problem in this subject

  1. Draw the system

    Define the studied object, reference frame and positive axis. A force diagram shows external interactions acting on the system.

  2. Sort quantities

    Separate data and unknowns; convert units before substitution. 36 km/h = 10 m/s, so never insert 36 into a formula expecting SI speed.

  3. Write the model

    Choose a law matching assumptions: constant acceleration, thin lens, ohmic resistor. Isolate the unknown symbolically before rounding.

  4. Interpret

    Check dimensions and signs. Negative velocity gives direction on the chosen axis. Discuss scale and model limitations.

YOUR TURN

01 · Try before checking

Find pressure for 60 N over 0.03 m².

One hint

Divide normal force by area.

Reveal and understand the solution

60/0.03=2,000 Pa; N/m² confirms the dimension.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

A 270 g object occupies 100 cm³. Find density in g/cm³.

A hint to get started

ρ = mass/volume, keeping units consistent.

Step-by-step solution
  1. ρ = 270/100.
  2. ρ = 2.7 g/cm³.
  3. This is 2,700 kg/m³.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

A normal force of 100 N acts on 0.02 m². Find pressure.

A hint to get started

Use square metres for area.

Step-by-step solution
  1. p = F/S.
  2. p = 100/0.02 = 5,000.
  3. Pressure is 5,000 Pa.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

Why do skis reduce sinking into snow at the same body weight?

A hint to get started

Compare contact areas.

Step-by-step solution
  1. The supported weight is approximately unchanged.
  2. Larger area reduces F/S.
  3. Pressure falls; deformation also depends on snow properties.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

1 cm² is 10⁻⁴ m² and 1 cm³ is 10⁻⁶ m³. Powers matter in unit conversion.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

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