Section 1 of 6The Equation
The effect of a force depends on how concentrated it is.
Definition
- Pressure is the force acting at right angles to a surface divided by the area of that surface.
Equation
- p = F ÷ A, where p is the pressure in pascals, F is force in newtons and A is area in square metres.
Rearranged
- The same relationship gives F = pA and A = F ÷ p, which a formula triangle can help you remember.
Large or small area
- A force spread over a large area gives a small pressure, whereas a force on a small area gives a large pressure.
Unit
- One pascal is a pressure of one newton on every square metre, so 1 Pa = 1 N/m².
Section 2 of 6Calculating Pressure
Unit conversions are the usual source of errors.
1
Find the force acting at right angles to the surface; for an object resting on the ground this is its weight.
2
Find the area of contact and convert it to square metres, because 1 cm² = 0.0001 m².
3
Substitute into p = F ÷ A and calculate the answer in pascals.
4
Convert to kilopascals by dividing by 1000 if the number is large.
5
Check that the unit is right: newtons divided by square metres gives pascals.
Section 3 of 6Large Pressure, Small Area
Large Pressure, Small Area
Knife
- A sharp knife has a very thin edge, so the area is tiny and a modest force gives a large pressure that cuts.
Nail
- The point of a nail has a small area and the head has a large one, so the point penetrates wood under the same force.
Stiletto heel
- A narrow heel concentrates the whole weight on a tiny area, which can dent soft floors.
Spikes
- Studs on boots press into the ground with high pressure to give grip.
Section 4 of 6Small Pressure, Large Area
Tractor tyres
- Wide tyres spread the weight of the tractor, so the pressure on soft ground is low and the tractor does not sink.
Snow shoes
- The large area reduces pressure on the snow, which stops a person from sinking in.
Foundations
- Buildings use wide foundations so that the pressure on the ground stays low and the building is stable.
Section 5 of 6Worked Example
Question
- A drawing pin is pushed with a force of 20 N.
- The area of the head is 1.0 × 10⁻⁴ m² and the area of the point is 2.0 × 10⁻⁷ m².
- Find the pressure on the thumb and on the wall.
- Pressure on the thumb = F/A = 20 / (1.0 × 10⁻⁴) = 2.0 × 10⁵ Pa.
- Pressure on the wall = 20 / (2.0 × 10⁻⁷) = 1.0 × 10⁸ Pa.
Answer The point produces a pressure 500 times larger: 1.0 × 10⁸ Pa compared with 2.0 × 10⁵ Pa on the thumb.
Section 6 of 6Exam Checklist & Tips
15.2.2 – Key Points for the Exam
- Pressure Force per unit area acting at right angles to a surface.
- Contact area The area of a surface that is touching another surface.
- Pascal The unit of pressure, 1 N per square metre.
- Weight The force of gravity on an object, found from mass × gravitational field strength.
Common Mistakes
- Using the area in cm² or mm² without converting to m².
- Mixing up pressure and force; pressure depends on area as well.
- Using the mass of an object as the force instead of its weight.
- Saying that a sharp point has a larger force; it has the same force but a smaller area.