Science Content: Why Things Float

A fluid is a material that can flow, like water or air. The kinds of energy that are important to a fluid are kinetic energy (because it can move) and gravitational energy (because it has weight). Water flowing downhill is converting gravitational energy into kinetic energy.

a pond with a wavy surface and a pond with a flat surface We can use the energy concept to explain why the surface of a pond is flat. Suppose there is a pond whose surface is not flat. Then the "hill" of water on one side can move into the "valley" on the other. Water has moved downwards, decreasing its potential energy. The surface is flat because this gets the water as low as possible.

That explanation depends on the assumption that the water has mass and occupies a volume that is proportional to the mass. If we could pack more mass into the same volume, the water wouldn't have to move from one side of the lake to the other). The ratio of mass to volume is called the density.
density = mass/volume
The density of liquid water is 1000 Kg/m3 (that may seem like a big number, but a cubic meter of water is a lot!).

Buoyancy

Objects seem to weigh less under water -- indeed, some objects float to the top instead of sinking to the bottom, as if their weight were negative. We can explain this using energy ideas.
As the rock moves up ... ...water moves down
Consider what happens as we raise an underwater object --let's say, a rock -- from one level to another. When the rock moves, some water has moved, too: away from the place the rock will be, and into the place where it was. The net effect is that a "piece of water" exactly the same shape as the rock has moved downward as the rock itself has moved up, as if they had changed places with each other. The gravitational energy of the rock has increased, but the gravitational energy of the piece of water has decreased, and so the energy we need to supply is just the difference between these two amounts of energy. The "piece of water" serves as a counterweight for the rock. The energy we supply in lifting the rock while it is underwater is less than the energy we supply in lifting it in air, and since

energy transferred = force x distance

this means the force we exert is less. The apparent weight of the rock is the actual weight minus the weight of the piece of water it displaces. Lifting a bag full of water while it is under water requires no force at all.

If an object has a small weight and a large volume, it might displace more than its own weight of water, and then the object will float. The condition can be stated simply in terms of densities: if the average density is less than the density of water, the object will float.

Helium balloons and hot air balloons work the same way, only now it is air that is displaced, instead of water.

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Discussion of the unit on buoyancy