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Question: Why does soap float in water?
Answer: Not all soaps float in water. Some sink in water, depending on their chemical composition, or if insufficient amount of air was trapped in them during the manufacturing process. The trapped air tends to 'puff up' the volume of the soap bar, and this makes it less dense, enabling it to float in water. So, in order to answer your query, let us discuss a broader question: what determines whether an object will float or sink in a liquid?
We'll first mention some relevant concepts. All material objects have a characteristic property called density, which is simply the mass of an object divided by its volume. For example, at room temperature, one gram of pure water has a volume close to one cubic centimeter (or one milliliter). So, water has a density of 1.0 gram/milliliter. The Weight (W) of an object is the downward force acting on the object due to earth's gravitational pull. This is what causes an object you drop to undergo free fall. Another force we need to recognize is called Buoyancy. Based on an easily performed experiment outlined below, or from a relatively simple analysis, it can be shown that any liquid exerts an upward force on an object, when the object is fully or partly immersed in the liquid. This upward force on an immersed object is termed Buoyancy (B), and it can be measured as follows.
Using, say, a spring balance, first weigh a piece of solid iron in air, and then find its apparent weight while it is immersed - either partly or fully in water. The apparent weight in water is always less than its weight in air. The magnitude of B is the difference between the two weights. As the immersed volume (V) of iron increases, an identical volume of water is displaced by it. It turns out that the buoyancy B is directly proportional to V, and the magnitude of B is exactly equal to the weight of the liquid displaced by the object.
Now consider a soap bar, or even a ship, which floats in water, with a fraction of its volume immersed in water. Since the floating object is at rest, its weight is being supported only by water. We thus conclude that the buoyancy acting on the object due to water must exactly counteract the weight of the object, i.e. the two have equal magnitude. So, a partially immersed object floats in a liquid when the buoyancy B acting on it equals the weight of the object, W. A large ship at sea floats precisely because the weight of the seawater it displaces, i.e. buoyancy acting on the ship, equals the total weight of the ship. For a solid piece of iron, even if B is maximized by fully immersing it in water, its weight always exceeds B. That is why it sinks in water.
An equivalent and useful criterion for flotation of any object is that it will float in a liquid, if the density of the object is less than that of the liquid. This is true, for example, for wood or ice, both of which have a lower density than water. A solid piece of iron sinks in water because the density of iron is greater than that of water. However, a thin walled, hollow ball of iron, with adequate volume of air trapped within it, floats in water. In this case, the trapped air has lowered the average density of the ball, so that it is less than that of water.
A given object may sink in one liquid, but float in another liquid. For example, a solid piece of iron sinks in water, but it will float, partially submerged, in a pool of mercury. We can thus conclude that mercury must have a higher density than iron, which is true.
Caution: since mercury is an extremely hazardous and toxic substance, this demonstration should only be performed with your teacher's approval and close supervision, in a carefully controlled laboratory setting.
Air or any gas surrounding an object also behaves like a liquid, and exerts buoyancy upon an object. As a result, the apparent weight of an object in air is slightly less than its 'true weight' measured in a vacuum. For many objects we deal with, this buoyancy effect due to air - which equals the weight of the air displaced by the object, is quite small when compared to the overall weight of the object itself. So, we normally tend to ignore the effects of buoyancy due to air, as in our discussion above. However, the buoyancy of air becomes strikingly evident when one lets go of sealed, helium filled balloon. It doesn't just float in air, but rapidly ascends, defying earth's gravity! Clearly, in this case, the buoyancy due to air must exceed the total weight of the balloon, thereby causing a net upward force on the balloon, and enabling it to accelerate upwards! This is a vivid demonstration of the upward direction of buoyancy.
There is even more to why objects may float on a liquid that we haven't addressed here due to lack of space. Here is a teaser. With some care and deftness, a small, solid needle made of steel can be made to float lengthwise on the surface of water. In light of our entire discussion above, this is indeed puzzling, since steel has a higher density than water. You may wish to investigate this phenomenon, and perhaps 'Ask a Scientist' about it in future!
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