Edexcel IGCSE Physics · Spec 5.3-5.5
Pressure: Using the Equations
Worked examples using the pressure equations.
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Pressure: Using the Equations
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Explained
Two pressure equations, and knowing which to use
Pressure equals force divided by area, p equals F over A. Pressure difference in a liquid equals density times gravitational field strength times depth, p equals rho g h.
Choosing between them is straightforward once you notice what each is about. The first is about something pressing on a surface. The second is about being underneath a fluid.
Force over area
Force in newtons, area in square metres, pressure in pascals, where one pascal is one newton per square metre.
A 600 N person standing on two shoes with a total area of 0.03 square metres exerts 600 divided by 0.03, which is 20 000 Pa. The same person on skis with a total area of 0.6 square metres exerts 1000 Pa, which is why they do not sink into snow.
Watch the area units. Areas are often given in square centimetres, and there are 10 000 square centimetres in a square metre, not 100. Squaring the conversion factor is the step people miss.
If the object is a block, its weight is the force, so you may need W equals m g first.
Density times g times depth
Density in kilograms per cubic metre, g in newtons per kilogram, depth in metres, pressure in pascals.
Water has a density of about 1000 kg per cubic metre, so at 38 m depth in seawater of density 1030, the pressure due to the water is 1030 times 10 times 38, which is about 390 000 Pa, or 390 kPa.
The h is vertical depth below the surface, not the width of the container or a distance along a slope. And this gives the pressure from the liquid alone, so add atmospheric pressure for the total on a submerged object.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards a mark simply for stating pressure difference equals density times g times height. It allows standard symbols, condones d for density and gfs for gravitational field strength, and instructs the examiner to ignore the word gravity.
On the calculation that follows it allows the use of 9.8 or 9.81 for g, and asks for the evaluation in kilopascals. Its note then records that an answer of 391 400 kPa scores one mark rather than two, which is the pascal answer left unconverted. The physics was right and the unit was not.
On a question about lying on a board of nails, the same mark scheme accepts two different routes and credits both. One argues that the board increases the area over which the force acts, so for a given force the pressure is inversely proportional to the area. The other argues that the force on each individual nail is smaller, so for a given area the pressure is proportional to the force.
Either reasoning earns the marks, provided the middle step naming the proportionality is there. Saying the pressure is less, without saying which quantity changed and how, is the half answer.
Which equation, and a check
If the question mentions a surface, a contact area, a footprint or a blade, use force over area. If it mentions depth, a diver, a dam or a manometer, use rho g h.
Then sanity check. Reducing the area should increase the pressure, so a sharp knife gives a larger number than a blunt one. Going deeper should increase the pressure, so a bigger h must give a bigger answer. If your result moved the other way, the fraction is inverted.
Spec 5.3-5.5
What you need to know
- Use pressure equals force over area
- Use p equals rho g h for liquids
- Rearrange each equation
Active recall
Quick check
Answer each question before opening the answer.
What pressure does a 200 N force exert on an area of 4 m²?
p = F ÷ A = 200 ÷ 4 = 50 Pa.
What are the units of pressure?
Pascals (Pa), equal to N/m².
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