Pressure and Buoyancy: Quick Revision

A brief note on Pressure and Buoyancy. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Thrust is a force pressing at right angles on a surface. Pressure is thrust per unit area: $P = \dfrac{F}{A}$, in pascals ($1\ \text{Pa} = 1\ \text{N/m}^2$).
• The same force on a smaller area gives a bigger pressure: that is why knives are sharp and school bags have wide straps.
• In a liquid the pressure grows with depth, $P = \rho gh$, and pushes equally in all directions.
• The air presses on us with about $1.0 \times 10^{5}\ \text{Pa}$.
• Archimedes' principle: an object in a liquid is pushed up by a force equal to the weight of the liquid it pushes aside.
• An object floats if it is less dense than the liquid; then a part $\dfrac{\rho_\text{object}}{\rho_\text{liquid}}$ of it is under the surface.
• Relative density $=$ density of the substance $\div$ density of water, a pure number.

The facts at a glance

A worked example

An $11\ \text{kg}$ wooden box of volume $0.025\ \text{m}^3$ is pushed under water and let go. Does it float, and how much of it stays under?

1. Buoyant force. $1000\ \text{kg/m}^3 \times 0.025\ \text{m}^3 \times 9.8\ \text{m/s}^2 = 245\ \text{N}$.
2. Weight. $11\ \text{kg} \times 9.8\ \text{m/s}^2 = 107.8\ \text{N}$, less than $245\ \text{N}$, so it rises.
3. So it floats. Its density is $\dfrac{11\ \text{kg}}{0.025\ \text{m}^3} = 440\ \text{kg/m}^3$, so $44\%$ of it stays under the water.

Practice with new numbers

A program to try

The program works out the box.

Mistakes to avoid

• Areas in square centimetres. Change to square metres first: $1\ \text{cm}^2 = 1 \times 10^{-4}\ \text{m}^2$.
• Using the mass as the thrust. The thrust is the weight, $mg$, in newtons.
• 'Heavy things sink.' Dense things sink; a huge iron ship floats.
• Adding the air pressure when only the water's part is asked for. Read the question.

Check yourself

1. A $500\ \text{N}$ crate rests on an area of $0.25\ \text{m}^2$. What pressure does it put on the floor?

2. Why are the walls of a dam thicker at the bottom?

3. A stone weighs $15\ \text{N}$ in air and $9\ \text{N}$ in water. What is the buoyant force on it?

4. Wood of density $700\ \text{kg/m}^3$ floats in water. What part of it is under the surface?

5. What is the relative density of a metal of density $8900\ \text{kg/m}^3$?