Weight and upthrust

1. Any object in a fluid, which can be a liquid or a gas, has two vertical forces acting on it.
2. Its weight acts vertically downwards, caused by gravity pulling on its mass.
3. The upthrust from the fluid acts vertically upwards.
4. If the weight is greater than the upthrust, the resultant force is downwards and the object sinks.
5. If the upthrust is greater than the weight, the resultant force is upwards and the object rises.
6. If the upthrust equals the weight, the forces are balanced, so the object floats at the surface or stays still within the fluid.
7. A floating object sinks into the fluid only until the upthrust has grown to match its weight, and then it stays at that level.

Upthrust and displaced fluid

1. An object placed in a fluid pushes some of the fluid out of the way, and this is the displaced fluid.
2. The upthrust on an object is equal to the weight of the fluid it displaces.
3. The more of an object that sits below the surface, the more fluid it displaces and the larger the upthrust.
4. Once an object is completely under the surface it cannot displace any more fluid, so the upthrust stops increasing.
5. An object therefore floats only if it can displace its own weight of fluid before it is completely submerged.
6. A floating ship displaces a weight of water exactly equal to its own weight, which is why a ship's mass is often quoted as its displacement.

Comparing densities

1. Whether an object floats or sinks depends on its average density compared with the density of the fluid.
2. If the object's average density is less than the fluid's density, it floats with only part of it below the surface.
3. If the object's average density is greater than the fluid's density, it sinks, because even when fully submerged it displaces less than its own weight of fluid.
4. If the two densities are equal, the object neither rises nor sinks and stays at whatever depth it is placed.
5. Water has a density of $1000{kg/m}^3$, so oak at about $750{kg/m}^3$ floats and steel at about $7900{kg/m}^3$ sinks.
6. The closer an object's density is to the fluid's density, the more of it lies below the surface, which is why about nine-tenths of an iceberg is hidden under the sea.

Factors that affect floating

1. Shape: a solid lump of steel sinks, but the same steel shaped into a hollow hull encloses a large volume of air, so the ship's average density is less than that of water.
2. The wide hull also lets the ship displace a large volume of water, giving enough upthrust to balance its weight.
3. Load: adding cargo increases a ship's weight, so it settles lower in the water until it displaces enough extra water to balance the extra weight.
4. The Plimsoll line painted on a ship's hull marks the lowest safe level, because an overloaded ship has too little hull above the water and can be swamped by waves.
5. Density of the fluid: a denser fluid gives more upthrust for the same displaced volume, so objects float higher in sea water than in fresh water.
6. Swimmers float with almost no effort in the Dead Sea, whose water is about a quarter denser than fresh water.
7. Changing average density: a submarine floods its ballast tanks with sea water to increase its average density and dive, and blows the water out with compressed air to decrease its average density and surface.
8. Floating also happens in gases, because a helium balloon rises when the weight of air it displaces is greater than the total weight of the balloon, the helium and the string.