Buoyancy: why things float or sink
A fluid pushes up on anything in it: this is buoyant force, or upthrust. A body floats if it is less dense than the fluid and sinks if denser.
The upward push of a fluid
Push a wooden block or a capped empty bottle under water. You feel the water pushing it up. Let go, and it bounces back to the surface. The upward force a fluid exerts on a body in it is the buoyant force, or upthrust. Every body in a liquid or a gas feels it. A mug of water feels lighter inside a bucket of water than when you lift it out. This upward push is the reason.
Float or sink?
| Compare | Result | Example |
|---|---|---|
| Body less dense than the liquid | Floats, partly above the surface | Wood, cork or ice in water |
| Body denser than the liquid | Sinks | An iron nail or a stone in water |
| Body as dense as the liquid | Stays wherever it is placed, fully under | An egg in salt water of just the right strength |
Why density decides
- When a body is fully under water, the buoyant force equals the weight of water of the same volume as the body.
- If the body is denser than water, its weight is more than this push, so it sinks.
- If it is less dense, the push is more than its weight. So it rises, and floats with part of it above the surface.
- An iron ship floats because its hollow shape displaces a lot of water. Its average density is less than that of water.
- An egg sinks in plain water but floats in very salty water. Salt water is denser, so it pushes up more.
Activity (practical): density of a solid with a spring balance and a measuring cylinder
You need a small stone or metal piece that sinks, a thread, a spring balance, a measuring cylinder and water.
- 1Check that the spring balance pointer is at zero, and note its least count.
- 2Hang the solid from the balance by the thread. Read its mass m in grams: the balance measures weight, but its scale is marked in grams.
- 3Fill the measuring cylinder about half with water. Read the level V₁ at the bottom of the curved surface, with your eye level with it.
- 4Lower the solid gently on the thread until it is fully under water. Read the new level V₂.
- 5The volume of the solid is V = V₂ − V₁, in cm³ (1 mL = 1 cm³).
- 6★Find the density = m ÷ V in g cm⁻³. Compare it with water (1 g cm⁻³) to predict whether the solid floats or sinks.
★ key step
Worked example: from the practical
A stone has a mass of 75 g. When it is lowered into a measuring cylinder, the water level rises from 40 mL to 70 mL. Find its density. Will it float in water?
- Volume V = 70 mL − 40 mL = 30 mL = 30 cm³.
- Density = m/V = 75 g ÷ 30 cm³ = 2.5 g cm⁻³.
- In SI units, 2.5 g cm⁻³ = 2500 kg m⁻³.
2.5 g cm⁻³ (2500 kg m⁻³). It is denser than water (1 g cm⁻³), so it sinks
How to draw the measuring cylinder readings
- Draw two tall, narrow measuring cylinders side by side, with marks up the side.
- In the first, draw water up to a level and label it V₁.
- In the second, draw the solid hanging on a thread, fully under water, not touching the bottom.
- Draw the higher water level and label it V₂.
- Add the labels measuring cylinder, water, solid and thread. Write V = V₂ − V₁ beside them.
Fishing communities on the coast tie floats of light wood or plastic to their nets, so the nets hang near the surface. A life jacket adds a large, light volume that the water pushes up on.
2 marks: “A plastic ball is held under water and then released. Why does it shoot up? Name one factor that decides how strong this push is.” Water exerts an upward buoyant force on the ball that is greater than its small weight, so it rises. The push is larger when more of the ball's volume is under water, or when the liquid is denser.
2 marks: “A steel spoon sinks in a bucket of water, but an empty steel katori (bowl) of the same metal floats. Explain why.” The spoon is solid steel, which is denser than water, so its weight is more than the buoyant force. The hollow katori pushes aside a large volume of water, so the buoyant force balances its weight; its average density is less than water's.
3 marks: “A metal block of mass 540 g has a volume of 200 cm³. Find its density in g cm⁻³ and in kg m⁻³. Will it float on water?” Density = 540 ÷ 200 = 2.7 g cm⁻³ = 2700 kg m⁻³. It is denser than water (1 g cm⁻³), so it sinks.
Less dense than water, it floats; denser than water, it sinks.