### How much water does it take to float something weighing a kilogram?

If you want to float a thing that weighs one kilogram in water, how much water do you need?

First, of course, the thing must float in water: a piece of wood, a can of peanuts or glass of instant coffee, any closed container weighing one kilogram (2.2 lb) that is larger than one liter of water (because a liter of water weighs one kilogram). The one kilogram is just used as an example; one pound or any fraction of a pound or kilo just changes the amount of water needed to float the object.

So how much water does one need to float it?

You know, of course, that an object floats when it is lighter than water, because **its volume displaces an amount of water that weighs more than the object**. That is why a steel ship floats; its hull is full of air. Or, for an example in the kitchen, a soup plate floats, until it is filled with water. Ice floats because water expands when it is colder that 4° Celsius, even before it solidifies.

So, does one need that volume of water to float your piece of wood, can of peanuts, glass of instant coffee, whatever? Of course, it will float in a basin full of water, but it will also float in a very much smaller container. If the container fits closely around the object, it will float in much less than its own weight in water. Really!

You can experiment with this in the kitchen. I played around with a couple of cylindrical measuring vessels, eventually finding a jar that fit quite closely in one of them. Empty, it floated immediately. Filling it with water caused it to sink to the bottom of measuring vessel, but adding more water in the vessel made it float again. At the end of the experiment, 60 grams of water caused the jar partially filled with water to float. The kitchen scale gave the jar’s weight as 410 grams.

Why? How could 60 grams float 410 grams? Because the small amount of water in the measuring vessel rose in the narrow area around the jar to a level that, if the jar had not been there, would have weighed as much as the 410 grams of the jar. The jar **displaced water that was never there** and floated.

Is there any practical application for this? There has been. The lenses of rotating lighthouse beacons were floated on mercury, virtually frictionless. Mercury is a metal that is liquid at common temperatures and is thirteen times heavier than water, heavy enough to float the weight of the rotating lens (lenses) around a constantly burning source, the intervals between the “flashes” noted on coastal charts. Now this is usually achieved by flashing an electric light

on and off.

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## 3 Comments

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Happy New Year!

Updated experiment:

an empty :-) bottle of champagne weighing 900 gm floats in 200 gm of water in my wine cooler.

Myoarin

Surprisingly, none of the viewers of this Quezi has commented to say that my experiments were demonstrations of the Archimedes Paradox, related to the Hydrostatic Paradox (which is also known as the Pascal Paradox):

http://en.wikipedia.org/wiki/Archimedes_paradox

Duh! I should have known that, but only discovered it while perusing a link to a question on Uclue.com.

You explained it so well that we all think of it as the Myoarin Paradox rather than the Archimedes Paradox.