Convert areas and rearrange pressure calculations
Square length conversions correctly and find missing force or contact area.
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- Use p = F/A.
- Convert centimetres and millimetres as lengths.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many square metres is 1 cm²?
What you will learn
- Convert cm² and mm² to m² before obtaining pascals.
- Use F = pA and A = F/p with physically consistent data.
An area conversion squares the length factor
One centimetre is 0.01 m, so 1 cm² is 0.0001 m². One millimetre is 0.001 m, so 1 mm² is 0.000001 m². A 3 cm by 2 cm rectangular contact has area 6 cm² = 0.0006 m². A normal 30 N over that contact gives 50 000 Pa. Converting cm² by only dividing by 100 would be a length conversion, not the required area conversion.
If a contact's dimensions are both supplied, multiply their consistently converted lengths. For a 20 mm by 10 mm patch, area is 200 mm² = 0.0002 m². Do not divide by an object's total external surface area when only one face or a small patch touches the support.
Rearrange without changing the meaning
From p = F/A, force is F = pA and contact area is A = F/p. For pressure 20 kPa over 0.0060 m², F = 20 000 × 0.0060 = 120 N. To keep average pressure at 10 kPa with force 120 N, the required area is 120/10 000 = 0.012 m² or 120 cm².
Use a positive non-zero area for a finite-contact average. A zero normal force on a finite area gives zero pressure in this simple model. If both supplied F and p are zero, F/p is 0/0 and does not determine a unique area. A non-zero force with zero requested pressure cannot be achieved on a finite area by this model.
Sources for this lesson
Pause and explain
Do F = 0 and p = 0 establish a unique contact area by A = F/p?
Worked example
A normal 30 N acts on a 3 cm by 2 cm rectangular patch. Find pressure, then find the area needed for 120 N at 10 kPa.
Show the worked solution
- The patch is 6 cm² = 0.0006 m².
- Pressure is 30/0.0006 = 50 000 Pa.
- Required area is 120/10 000 = 0.012 m² = 120 cm².
Answer 50 000 Pa; 0.012 m² or 120 cm².
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.
Find pressure for normal 30 N on a 3 cm by 2 cm rectangular contact.
Give me a hint
Multiply the lengths and convert the resulting squared unit.
Compare my reasoning
- Area = 6 cm².
- Area = 0.0006 m².
- Pressure = 30/0.0006 = 50 000 Pa.
50 000 Pa.
Look for these in your work
- Convert the whole area correctly.
- Use the normal force.
Find force at 20 kPa on 0.0060 m², and the area for 120 N at 10 kPa.
Give me a hint
Use F = pA and A = F/p after converting kPa to Pa.
Compare my reasoning
- 20 kPa = 20 000 Pa, giving F = 120 N.
- 10 kPa = 10 000 Pa, giving A = 0.012 m².
- 0.012 m² is 120 cm².
120 N; 0.012 m² or 120 cm².
Look for these in your work
- Choose the right rearrangement.
- Convert pressure and area units.
A 20 mm by 10 mm patch carries normal 10 N. A student uses 200 m² as its area. Correct the area and pressure.
Give me a hint
The numeric product retains mm² until that squared unit is converted.
Compare my reasoning
- Area = 200 mm² = 0.0002 m².
- Pressure = 10/0.0002 = 50 000 Pa.
- Using 200 m² would describe a completely different contact.
0.0002 m²; 50 000 Pa.
Look for these in your work
- Preserve the original squared unit.
- Calculate with m² for Pa.
Common mistakes
- Square the conversion factor.
- Use the area that actually touches.
- Zero divided by zero does not determine an area.
What can you explain now?
How many square metres is 200 mm²?
Compare with the explanation
0.0002 m².
Each square millimetre is one millionth of a square metre.
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Make it stick
Convert contact areas, rearrange pressure for force or area and explain a zero-data limit.
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.