Density and Pressure » Pressure
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 5.5
- What pressure means and how to use pressure = force ÷ area
- The units of pressure: the pascal and N/cm2, and how to change cm2 to m2
- Why a small area gives a large pressure and a large area gives a small pressure
- How to rearrange the equation to find a force or an area
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Unlock This CourseWhat is pressure?
Push your thumb against a wooden board and nothing happens. Push a drawing pin with the same force and the point goes straight in. The force has not changed. What has changed is the area that the force acts on.
Pressure tells you how concentrated a force is. The same force squeezed onto a tiny area gives a large pressure. The same force spread over a big area gives a small pressure.
Key terms:
- Pressure: the force acting on each unit of area, for example on each square metre.
- Pascal (Pa): the unit of pressure. One pascal is one newton per square metre, so 1 Pa = 1 N/m2.
The pressure equation
pressure = force ÷ area
p = F ÷ A
This equation is not given in the exam. You must learn it.
| Quantity | Symbol | Unit |
|---|---|---|
| pressure | p | pascal (Pa) |
| force | F | newton (N) |
| area | A | metre squared (m2) |
The force is the one that presses at right angles onto the surface. For an object resting on level ground, that force is its weight. If a question gives a mass, find the weight first with W = m × g, using g = 10 N/kg.
One pascal is a very small pressure, so answers in thousands or even millions of pascals are normal. You may also see the kilopascal: 1 kPa = 1000 Pa.
Worked example 1: a box on the floor
A box of weight 600 N rests on a floor. Its base measures 0.50 m by 0.40 m. Calculate the pressure on the floor.
area = 0.50 × 0.40 = 0.20 m2
p = F ÷ A = 600 ÷ 0.20 = 3000 Pa
One block, three pressures
A concrete block has a weight of 120 N. It measures 0.40 m by 0.20 m by 0.10 m. Its weight never changes, but the pressure under it depends on which face it stands on.
| Face on the ground | Area in m2 | Pressure = 120 ÷ area |
|---|---|---|
| 0.40 m × 0.20 m (largest face) | 0.08 | 1500 Pa |
| 0.40 m × 0.10 m | 0.04 | 3000 Pa |
| 0.20 m × 0.10 m (smallest face) | 0.02 | 6000 Pa |
Look at the pattern. Each time the area halves, the pressure doubles. The smallest face gives the largest pressure and the largest face gives the smallest pressure. Exam questions often ask for the greatest or the least pressure a block can exert, so pick the face before you calculate.
Areas in cm2
Small areas are often given in cm2. There are two ways to deal with this.
Change to m2. Remember that 1 m2 = 10 000 cm2, because a square metre is 100 cm long and 100 cm wide. To change cm2 to m2, divide by 10 000. So 300 cm2 = 0.030 m2. Your answer is then in pascals.
Or keep the cm2. A force in newtons divided by an area in cm2 gives a pressure in N/cm2. This is a perfectly good unit, as long as you write it on your answer. 1 N/cm2 = 10 000 Pa.
Worked example 2: standing on two feet
A man of mass 60 kg stands on both feet. The total area of his shoes touching the floor is 300 cm2. Calculate the pressure on the floor in Pa.
W = m × g = 60 × 10 = 600 N
area = 300 ÷ 10 000 = 0.030 m2
p = F ÷ A = 600 ÷ 0.030 = 20 000 Pa
In the other unit: 600 ÷ 300 = 2.0 N/cm2.
Small area, large pressure
Things that are made to cut or pierce have a very small area, so a modest force gives a huge pressure.
📌 Drawing pins
The point has a tiny area, so the pressure on the board is very large and the pin goes in. The head is wide, so the pressure on your thumb is small and it does not hurt.
🔪 Knife edges
A sharp blade has a very thin edge. The force from your hand acts on a tiny area, so the pressure is large enough to cut. A blunt knife has a wider edge, so it needs more force.
👠 Stiletto heels
A stiletto heel has a very small area. When the wearer's weight rests on the heel, the pressure is large enough to dent a wooden floor.
Large area, small pressure
When you do not want something to sink in, you spread the force over a large area.
⛄ Snowshoes
Snowshoes are much wider and longer than boots. They spread the walker's weight over a large area, so the pressure on the snow is small and the walker does not sink.
🚜 Tractor tyres
A tractor is heavy and works on soft soil. Its wide tyres have a large area touching the ground. This keeps the pressure small, so the tractor does not sink into the mud.
🏠 Building foundations
The walls of a building stand on foundations that are wider than the walls. The weight of the building is spread over a larger area of ground, so the pressure is smaller and the building does not sink.
To explain any of these in the exam, use three steps: say whether the area is large or small, quote pressure = force ÷ area, then say what happens to the pressure for the same force.
Rearranging the equation
The equation can be rearranged to find the force or the area:
- force = pressure × area, F = p × A
- area = force ÷ pressure, A = F ÷ p
Worked example 3: finding the force
The tyres of a tractor exert a pressure of 50 000 Pa on a field. The total area of tyre touching the ground is 0.80 m2. Calculate the weight of the tractor.
F = p × A = 50 000 × 0.80 = 40 000 N
Worked example 4: finding the area
A walker has a weight of 700 N. The snow can support a pressure of 2000 Pa before it gives way. Calculate the smallest total area of snowshoe the walker needs.
A = F ÷ p = 700 ÷ 2000 = 0.35 m2
Common mistakes
Using the mass in kilograms as the force. The force must be in newtons, so find the weight first. Dividing by an area in cm2 and then writing Pa. Either change the area to m2 or write N/cm2. Dividing by 100 to change cm2 to m2. It is 10 000. Forgetting to count every area that touches the ground, such as both feet or all four legs of a chair. Saying a sharp knife 'has more force'. It has a smaller area, so the same force gives a larger pressure.
Exam-style question
A table has a mass of 24 kg. It stands on four legs on a level floor.
(a) State the equation linking pressure, force and area. [1 mark]
(b) Calculate the weight of the table. Use g = 10 N/kg. [2 marks]
(c) Each leg touches the floor with an area of 4.0 cm2. Calculate the pressure that the table exerts on the floor. Give your answer in Pa. [4 marks]
(d) The table is moved onto a soft lawn and its legs sink into the ground. Explain why placing a flat wooden board under the legs stops the table from sinking. [2 marks]
Model answer
(a) pressure = force ÷ area, or p = F ÷ A (1).
(b) W = m × g = 24 × 10 (1) = 240 N (1).
(c) total area = 4 × 4.0 = 16 cm2 (1). 16 ÷ 10 000 = 0.0016 m2 (1). p = F ÷ A = 240 ÷ 0.0016 (1) = 150 000 Pa (1).
(d) The board has a much larger area touching the ground than the four legs (1). The weight is the same, so the pressure on the ground is much smaller (1).
Exam tip
Before you divide, check two things: is the force a weight in newtons, and have you added up the area of every leg? Then look at the unit the question asks for. If it wants Pa, the area must be in m2, so divide the cm2 by 10 000 first.