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Pressure

Heat and matter · level 5, lesson 1 of 6

A question to start

Why can you walk on deep snow in snowshoes but sink in trainers? And why does a rover in soft sand want wide wheels?

The idea

Pressure is how hard a force presses on each square metre:

\[p = \frac{F}{A}.\]

It is measured in pascals (Pa): 1 Pa is 1 newton on each square metre. The same force spread over a bigger area gives a smaller pressure.

small area: sinksbig area: stays on top

Worked examples

1. A person. A weight of 600 N standing on two feet with a total area of 0.04 m²: \(p = 600/0.04 = 15{,}000\) Pa.

2. With snowshoes. The same 600 N on 0.25 m²: \(p = 600/0.25 = 2{,}400\) Pa, about six times less.

3. Perseverance on Mars. Mass 1,025 kg, so its weight on Mars is \(1025 \times 3.71 = 3{,}800\) N. Suppose each of its six wheels touches the ground over 0.01 m²:

Perseverance's wheels pressing on the ground Mars Earth
Weight 3,800 N 10,060 N
Pressure, if the wheels touch 0.06 m² in all 63,000 Pa 168,000 Pa

On Mars the same rover presses on the sand with only 38% of the pressure it would on Earth.

Try it

  1. What is the unit of pressure?
  2. A box weighing 200 N rests on 0.5 m². What pressure does it make?
  3. Why do knives cut better when they are sharp?
  4. Why do tractors and rovers have wide tyres?
Answers
  1. The pascal, Pa, one newton per square metre.
  2. \(200/0.5 = 400\) Pa.
  3. A sharp edge has a tiny area, so the same push gives a huge pressure.
  4. The wide tyres spread the weight over a bigger area, so the pressure is lower and they sink less.

Common mistake

"A bigger force always means more pressure." Not if the area grows too. A heavy lorry on many wide tyres can press on the road less than a person in stiletto heels.

Where it leads