## Origins of buoyancy forces

Physics Narrative for 11-14

#### Explaining buoyancy

Back to boat: the larger the hole it made in the water, the greater the support force – the buoyancy force.

The physical origin of the buoyancy force is a challenge to explain. It involves appreciating that the pressure in a fluid increases as you go deeper. For water, just think about deep-sea divers and the special suits they have to wear to withstand the water pressures of the deep sea.

This extra pressure arises from the increased density, which leads to more bombardment of the bottom surface, as compared to the top surface. This extra pressure on the bottom of the object is the source of the upward force on the object. So whatever the force of gravity acting on the object, if it floats we can be confident that a force equal in size to the force of gravity acting on the object is pushing upwards. This is the buoyancy force. Let's look at that line of reasoning using diagrams, focussing on the boat as an example.

First simplify the boat to a box.

Then look at how the pressure changes with depth.

We can re-imagine the increasing depth of water as increasing pressures at different depths – caused by increasing bombardment by the particles of the fluid.

This bombardment leads to forces acting on the sides and the bottom of the model of the boat.

These forces add, and the vertical supporting forces balance the pull of gravity on the boat.

#### Buoyancy forces on fully-immersed objects

What about sinkers? The upward force doesn't disappear just because an object sinks. There are still more particles in each cubic metre at the bottom of the object than at the top. So there is still more bombardment, and so more pressure, at the bottom than at the top. You will notice that objects sink slowly, more slowly in water than in air. In such cases, the buoyancy force is still there pushing up on the object, but it is just not big enough to balance the gravity force.

Add a lid to the model of the boat and submerge the model. As the depth increases the vertical forces due to bombardment on the top and bottom surfaces both increase, but the difference stays the same. The buoyancy force, which is the result of this difference, also stays the same.

So there are still two forces acting but they are not balanced. The force of gravity acting on the object is the greater force and so the object sinks. For all objects denser than the surrounding fluid, as they sink the buoyancy force pushing on them is less than their force of gravity acting on the objects. The resultant force is downwards: the buoyancy force is smaller than the gravity force and the object sinks. For all objects less dense than the surrounding fluid, as they sink the buoyancy force pushing on them is greater than the gravity force. The resultant force is upwards: the buoyancy force is greater than the gravity force and the object rises.

For a floating boat, the bombardment on the underside is enough to balance the pull of gravity. If you get into the boat, the force of gravity acting on the boat and you increases, and more of the boat is immersed in the fluid. There is a greater rate of bombardment than before you got in (the bottom of the boat is further down in the fluid and there are more particles in each cubic metre to do the bombarding). If this new level of bombardment is enough to support the force of gravity acting on both you and the boat then you still float. If not, it sinks.