. Have you heard about the Egyptian Lighthouse (one of the seven wonders of the ancient worlds) that was found in the sea? Well, people are proposing lifting the 70-ton sections of the lighthouse with balloons. Can a balloon do this? What special aspect of the balloon will lift 70-ton bricks? What kind of balloon would be used?
I would guess that they intend to use balloons in the water. The blocks are at the bottom of the sea, so they must be lifted up to a boat. A balloon experiences an upward net force that is equal to the difference between the upward buoyant force on it and its downward weight. If the balloon displaces air, then the buoyant force on it is rather small and it would have to be extraordinarily big to displace enough air to lift a 70-ton block. But if it displaces water, then the buoyant force on it is much greater. To displace 70 tons, it would only have to displace about 65 cubic meters of water. That's not hard at all. The balloon could be made of heavy reinforced canvas and still work just fine underwater.
. How can a balloon support the air around it (pressure wise) and still rise?
If you could have filled a balloon with nothing at all, it would float very nicely because it would have had no weight and the only force on it would have been the buoyant force upward. But an empty balloon will be crushed by the surrounding air, which will push inward on its surface with enormous forces. To keep the balloon from crushing, you must fill it with gas. Since this gas will weight the balloon down, you should choose the lightest gases around: hot air or helium. In the case of hot air, a relatively small number of air molecules create the pressure needed to keep the balloon inflated. With helium atoms, lots of helium atoms are needed to create the pressure but helium atoms are very light and their total weight is less than that of an equal volume of air. Thus the upward force on the helium filled balloon is more than its weight and floats upward.
. How do clouds exist? If oxygen molecules, which must weight less than water vapor are drawn toward earth, then why aren't the clouds?
First, water molecules are lighter than the average air molecule so a balloon filled with water vapor would actually float in air. But that isn't what you're asking. Clouds exist because when water condenses from vapor to liquid, it often forms extremely tiny water droplets. These droplets are so small that they experience lots of air resistance as they try to move about. They begin to fall but quickly reach terminal velocity at perhaps a millimeter per second. The water droplets drift downward so slowly that they hardly move. That's what's happening in a cloud. The water droplets are trying to fall, but air resistance is slowing their descents.
. How do submarines sink if they have air inside?
The net force on the submarine depends on its average density, not on the density of one of its constituents. If the average density of the submarine is less than that of water, it will float upward in water. If the average density of the submarine is more than that of water, it will sink downward in water. To determine the submarine's average density, you need to divide its overall mass by its overall volume. While the submarine does contain air, a low-density material, it also contains steel, a high-density material. The submarine's average density turns out to be very nearly that of water. Fine adjustments to its density, made by pumping water in and out of ballast tanks, determines whether the submarines floats or sinks.
. How does altitude affect the presence of molecules?
As you travel upward, the air around you has less and less pressure. That's because it's supporting less and less weight above it. As long as the temperature isn't changing much, this decrease in pressure is caused by a decrease in density: the air molecules are become less tightly packed together. The result is that at high altitude, each breath you take delivers fewer air molecules into your lungs. Actually, air usually gets colder at higher altitudes, a change which keeps the air's density from decreasing so rapidly. The higher you go, the colder the air gets and the more molecules you need in each liter of air to maintain its pressure.
. If you don't want your tires to blow up from too much thermal energy, then why aren't tires white (to absorb less sunlight and thus receive less thermal energy)?
That's an interesting question. It's probably difficult to manufacture white tires and they'd probably look terrible after they'd been driven a while. The old white-wall tires where difficult to keep clean. Because the pressure in a tire varies with its temperature, your tires will probably go over their optimum pressure on a hot sunny day. But driving them on the road also heats them, probably more than sunlight does. Because their temperatures increase during hard use, the tires are evidently capable of handling pressures much higher than their normal fill pressures.
. Many large boats seem to taper down toward the water line. If their hulls follow this trend, their centers of mass will be high above their centers of buoyancy, making the boats unstable (like standing in a canoe). How do these things stay upright?
You're right that the boats must keep their centers of gravity lower than their centers of buoyancy. A boat with its center of gravity above its center of buoyancy will flip over, just as an upright broomstick will flip over if you support it only from below. But because a boat with a narrow tapered hull will go deeper into the water than one with a wide flat hull, the boat with the tapered hull may actually have a lower center of gravity than the boat with the wide flat hull. For example, imagine adding a long thin vertical plate to the bottom of a canoe, effectively converting the canoe's wide flat hull into a thin tapered hull. That canoe will be much more stable than before. So the shape of a boat's hull isn't as important as where the boat's weight located is relative to its center of buoyancy (the effective location of the buoyant force on the boat).
. What is the buoyant force?
When you displace a volume of air and replace that volume with something else, the air around the volume still pushes on it as before. If that volume had remained air, then it would have just floated there, suspended by a force from the surrounding air. Now that the volume has been replaced by something else, it still experiences the same suspending force. That suspending force is the buoyant force. It's actually created by a slight imbalance in the pressures around the volume. The pressure at the bottom of the volume is slightly higher than on top, so the air exerts a net upward on the volume. This pressure imbalance is in turn created by gravity and the fact that the air near the ground must support the air above it against the force of gravity.
. Why do high altitude places have different cooking temperatures than sea-level places?
The air pressure is lower at high altitudes than it is near sea level because there is less atmosphere overhead to support. This decreased air pressure affects the way water boils. Molecules can always evaporate from the surface of a pot of water, even when that water is cold, but above a certain temperature, water molecules can begin to evaporate from the interior of the water as steam, the gaseous form of water, in a process we call boiling. The temperature at which boiling occurs depends on the ambient air pressure because it can only proceed when there is enough pressure inside the steam bubbles to make them grow larger. At high altitudes, the lower air pressure makes it easier for these steam bubbles to form and grow, so they occur at lower temperatures. That's why water boils at a lower temperature at high altitudes. Once water reaches its boiling temperature, any heat that you add to it tends to cause the water molecules to boil away rather than to make the water hotter—so it's hard to heat water-containing food hotter than the boiling temperature of water. Since food needs high temperatures to cook, they don't cook as easily at high altitude where the low boiling temperature of water tends to keep the food from getting very hot.
. Why does a balloon collapse without air inside it while a vacuum bell jar does not?
A balloon's skin is too weak to support the air around it. If you don't put any gas inside the balloon, the atmosphere around it will push it inward and it will collapse. But a vacuum bell jar is made of an extremely strong plastic that easily supports the weight of the atmosphere on top of it. Even with nothing inside it, it remains full size.