A Buoyant Force Experiment

Here is a simple experiment that might help you understand certain things about buoyant force, equilibrium, and Newton's third law. Before describing the experiment, please understand that in equilibrium problems, any force units are ok, even mass units. Physics books do not use grams or kilograms for force, but in real life it is common. Look on a can of beans or a bag of potatoes. Anyway in this experiment, let us use gram force units (gf), where a gram force is the gravitational force (at sea level and 45^o latitude if you want to be fussy) on a gram of mass.

If you want to avoid gram force units, multiply grams by g, 980 dyne/gram and you will have dynes of force. Or for newtons, convert to kg then multiply by 9.8 N/kg.

The experiment (or demo): Put a beaker of water on a triple beam balance or similar platform balance and obtain the mass reading. Rig up a pulley above it, using a tall post and a clamp, and hang two equal masses on two ends of a string passing over the pulley, say 50 grams each. Those two masses are in equilibrium. Arrange it so that one of the masses is directly above the beaker of water. Add ten grams to that one, and it will want to move downward. Ease it gently into the water and check the balance reading again when equilibrium is achieved. It should be 10 grams higher! Explain why before you read beyond this point.

The explanation: The buoyant force had to be 10 gf to achieve equilibrium if it is not touching the bottom of the beaker, so if the water exerts an upward force on the hanging mass, there must be an equal downward force on the water, resulting in the increased balance reading. Even if the thing rests on the bottom of the beaker the result is the same, because the total force up (buoyant force plus the normal force of the bottom of the beaker on the mass) must be 10 gf to achieve equilibrium. If it is not touching the bottom, how could there be an increased force against the bottom? Answer that before reading on.

The water level rises when the thing is immersed, and that increases the pressure at the bottom and thus increases the force against the bottom.

Repeat for other masses.

If you do this same sort of thing using a graduated cylinder, you can measure the volume of water displaced. The density of water is 1 g/cm³, so in the 10 gf buoyant force example, the water displaced should be 10 cm³.

What causes buoyant force? The deeper you go in a fluid, the greater the pressure. So when a body is immersed in a fluid, there is a greater pressure on the bottom of it than on the top, so the upward force on the bottom is greater than the downward force on the top. Imagine a sphere immersed in water. Now remove the sphere and imagine the sphere-shaped region of water that took its place. It is in equilibrium, so the downward force of gravity on it must equal the upward force due to the pressures on it. Thus the buoyant force must equal the weight of fluid displaced: Archimedes’ Principle.

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