Monday, January 19, 2009

Why do the glass blocks at the Desert Botanical Gardens float on the water?

So, we went to the Desert Botanical Gardens in the Phoenix. They had a show exhibiting the art of Dale Chihuly. He's an artist who works with glass (blowing, shaping, etc.).

We saw this there and Sonny boy asked how does the glass float on the water.

Buoyancy, baby!

Basically, buoyancy works because of two properties of fluids:

1) In a fluid (water in this instance), pressure increases with depth.
2) Pressure, at any given depth, is exerted in all directions.

So, what this means is that for any real object that is submersed, the bottom of the object will experience a greater, upward-directed force than the downward-directed force on the top of the object. This results, after all the forces exerted by the fluid are summed, in an upward-directed force being applied to the object by the fluid.

So, why don't all objects float in water?

Well, there are other forces acting besides the buoyancy forces. Specifically, gravity.

Let's imagine two balls of equal size, one made of cork and one made of lead, say 1 m^3.

The density of cork is about 240 kg/m^3, so a 1 m^3 ball of cork has a mass of 240 kg, and will weigh 2352 newtons.
The density of lead is 11340 kg/m^3, so a 1m^3 ball of lead has a mass of 11340 kg and will weigh 111132 newtons.
The density of water is 1000 kg/m^3, so a 1m^3 ball of water has a mass of 1000 kg and will weigh 9800 newtons.

So, if you displace 1 m^3 of water with 1 m^3 of cork, you've replaced 9800 newtons of water with 2352 newtons of cork. Since the 1m^3 of water was sitting where it was, happily not moving (let's assume the water has a constant temperature throughout its depth), we can successfully argue that the water was feeling a buoyant force of 9800 newtons. That is, the weight of the water (mass * gravity) was perfectly balanced by the buoyant force of the water.

Now, let's put that 1m^3 of cork (2352 newtons) in place of the water. Suddenly, the buoyant, upward force of 9800 newtons is being opposed by only 2352 newtons of downward force. The water pressure pushes the cork up.

When we put the 1m^3 of lead in place of the water, the 9800 newtons of buoyant, upward force is met with 111132 newtons of downward force. The lead sinks.

Specific gravity is the term used to tell you if something will sink or float in water, but all it really is is a ratio of densities. Something less dense than water will float on the water; the volume of the water displaced times the density of the water times the gravitational acceleration tells you the weight of the water displaced and that tells you the buoyant force that must be met for an object to sink in water (or any fluid, once you know the fluid's density).

Now, hang on! The density of glass is higher than the density of water!

Ah, but the glass sculptures are filled with air, decreasing their bulk density to less than water. This is the same way boats float. The volume of the water they displace is very high, allowing a high weight of water displaced, which means a large buoyant force opposing a (relatively) small downward force due to gravitational acceleration; the boat/water bulb floats.

[aside] When I say "weigh" above, I mean it will produce a force of xxx newtons at the Earth's surface, at the equator. People often mix-and-match the concept of weight and mass. An object's mass is a fundamental quantity that defines how much material there is. An object with mass has weight when a gravitational acceleration is applied to it. Weight (w) is defined by:
w = m*g
where w is the weight, m is the mass, and g is the gravitational acceleration. You'll notice that weight has the units of force. That's because it is a force.
You can't (correctly) interchange your weight in pounds with mass in kilograms. It's often done, especially in popular literature, and even by many conversion tables. It's incorrect. A kilogram of lead on the Earth is the same as a kilogram on the moon, but it'll weigh about 1/6 on the moon.

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