Floating

Floating explains why a wooden log stays on water while a coin sinks. It depends on density and on two opposite forces: weight pulling down and upthrust (buoyancy) pushing up.

Key ideas

• Density is how much mass fits into a given volume: $\rho = \tfrac{m}{V}$.
• Float rule: An object floats in a liquid if its density is less than the liquid’s density.
• When floating, the upward upthrust equals the object’s weight.

Forces on an object in a liquid

Weight acts down: $W = mg$. The liquid pushes up with an upthrust. If upthrust is smaller than weight, the object sinks. If upthrust equals weight, it floats at a level where just enough liquid is pushed aside (displaced) to support it.

Using density to predict floating

Compare densities:

$$\rho_{\text{object}} < \rho_{\text{liquid}} \; \Rightarrow \; \text{object floats} \quad\quad \rho_{\text{object}} > \rho_{\text{liquid}} \; \Rightarrow \; \text{object sinks}$$

If it floats, the fraction that is underwater is about: $$\text{fraction submerged} = \frac{\rho_{\text{object}}}{\rho_{\text{liquid}}}.$$

Liquids floating on liquids

Two liquids that do not mix form layers. The less dense liquid floats on top of the more dense liquid (e.g., oil above water). You can decide the order by comparing their densities.

Everyday connections and notes

• A steel ship floats because its overall (average) density, including the air inside, is less than water.
• Ice floats in water because ice is less dense than liquid water.
• Floating is easier in the sea than in a lake because salt water is more dense.

Common misconceptions

• “Heavy things sink.” Not always. A large, heavy object can float if its density is lower than the liquid.
• “Shape does not matter.” Shape can trap air and change average density (boats, life jackets).