Thrust and pressure

Why does a nail go into wood?

Hammer a nail point first and it goes in; hammer it head first and it does not. The force is the same. What changes is the area it acts on.

Thrust and pressure

Thrust is a force pushing straight onto a surface, in newtons. Pressure is the thrust on each square metre:

The unit is the pascal: $1\ \text{Pa} = 1\ \text{N/m}^2$.

The same brick presses hardest when it stands on its smallest face.

You should find that halving the area doubles the pressure. A sharp edge has a tiny area, so even a small push gives a large pressure.

Using pressure

• Large area, small pressure: wide tyres on tractors, broad straps on a school bag, snow shoes, foundations of buildings.
• Small area, large pressure: knives, needles, nails, the studs on football boots.

Watch out. Change square centimetres to square metres: $1\ \text{cm}^2 = 0.0001\ \text{m}^2$, not $0.01\ \text{m}^2$.

A worked example

A $600\ \text{N}$ person stands on two flat shoes ($0.04\ \text{m}^2$ in all), on one shoe ($0.02\ \text{m}^2$), and on one stiletto heel ($1\ \text{cm}^2$). Find each pressure.

1. Two shoes. $\dfrac{600\ \text{N}}{0.04\ \text{m}^2} = 15000\ \text{Pa}$.
2. One shoe. $\dfrac{600\ \text{N}}{0.02\ \text{m}^2} = 30000\ \text{Pa}$.
3. One heel. $\dfrac{600\ \text{N}}{0.0001\ \text{m}^2} = 6000000\ \text{Pa}$: four hundred times as much, enough to dent a wooden floor.

Practise with new numbers

Try it in Python

The program works out the three pressures.

Remember these

• Pressure $=$ thrust $\div$ area, in pascals.
• Small area, big pressure; big area, small pressure.
• $1\ \text{cm}^2 = 0.0001\ \text{m}^2$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A force of $50\ \text{N}$ acts on $0.5\ \text{m}^2$. What is the pressure?

2. Why do school bags have wide straps?

3. Why is a sharp knife better for cutting?

4. What is one pascal?