## Why do things float better in salt water than in fresh water?

A floating object is displacing fluids that would otherwise fill the space it occupies. For example, a ball floating motionless on water is displacing the water and air that would normally be where the ball is. If we remove the ball, water and air will fill its space and soon everything will be motionless again.

Just because that ball-shaped portion of water and air is motionless doesn’t mean that it’s weightless. It does have a weight! But its weight is supported by the water and air that surround it. Because of the earth’s gravity, the pressure of stationary water or air decreases steadily with altitude, so pressure exerted on the bottom of this ball-shaped portion is greater than the pressure exerted on its top. This unbalanced pressure produce a net upward force on the ball-shaped portion of water and air.

That upward force is known as the buoyant force and it’s evidently just strong enough to support the weight of the ball-shaped portion of water and air. If it weren’t the ball-shaped portion would accelerate up or down.

When we put the real ball back where it was and let it again float motionless on the water, the surrounding water and air continue to exert the same buoyant force on the real ball that they exerted on the ball-shaped portion of water and air. So the ball experiences an upward buoyant force that’s equal in amount to the weight of the water and air it displaces. That observation is known as Archimedes’ principle.

Which brings me to your question. Here are two identical balls floating motionless on fresh water (left) and on salt water (right). In each case, the ball is experiencing a buoyant force that exactly cancels its weight. To obtain that exact buoyant force, the ball must displace a portion of water and air that weighs exactly as much as the ball weighs.

Salt water is denser than fresh water, meaning that salt water has more mass per volume (more kilograms per liter) than fresh water. A liter of salt water consequently weighs more than a liter of fresh water. Displacing a liter of salt water therefore produces a stronger upward buoyant force than displacing a liter of fresh water. That’s why the ball is floating higher on the container of salt water than it does on the container of fresh water.

The ball doesn’t need to displace as much salt water to obtain a buoyant force that supports its weight, so it rises higher on the salt water than it does on the fresh water. In each case, the ball finds just the right mix of water and air so that it displaces exactly its own weight in those two fluids.

## Why does adding salt to water make an egg float?

#### I am a 3rd grade student and would like to do a science project for the science fair. My question is why does salt make objects float? (small objects like eggs, paperclips) — MP, Brooklyn, New York

Adding salt to water won’t make everything float, but it will work for an object that just barely sinks in pure water. A hard-boiled egg is the most famous example: the egg will sink in pure water, but float in concentrated salt water. To explain why that happens, I need to tell you about the two forces that act on the egg when it’s in the water.

First, the egg has its weight—it’s being pulled downward by gravity. That weight force tends to make the egg sink. Second, the egg is being pushed upward by the water around it with a force known as “the buoyant force.” The buoyant force tends to make the egg float. It’s a battle between those two forces and the strongest one wins.

The buoyant force exists because the water that is now surrounding the egg used to be surrounding an egg-shaped blob of water and it was pushing up on that blob of water just hard enough to support the blob’s weight. Now that the egg has replace the egg-shaped blob of water, the surrounding water is still pushing up the same amount as before and that upward force on the egg is the buoyant force.

Since the buoyant force on the egg is equal in amount to the weight of the water that used to be there, it can support the egg only if the egg weighs no more than the egg-shaped blob of water. If the egg is heavier than that blob of water, the buoyant force will be too weak to support it and the egg will sink.

It so happens that a hard-boiled egg weighs slightly more than an egg-shaped blob of pure water, so it sinks in pure water. But that egg weighs slightly less than an egg-shaped blob of very salty water. Adding salt to the water increases the water’s weight significantly while having only a small effect on the water’s volume. Salt water is heavier, cup for cup, than fresh water and it produces stronger buoyant forces.

In general, any object that weighs more than the fluid it displaces sinks in that fluid. And any object that weighs less than the fluid it displaces floats. You are another good example of this: you probably sink in fresh water, particularly after letting out all the air in your lungs. But you float nicely in extremely salty water. The woman in this photograph is floating like a cork in the ultra-salty water of the Dead Sea.

## Will shaking a container of gas warm it up?

#### Will the temperature of a gas in a closed container rise if is is vibrated in a vacuum? — TJC, California

Yes, the temperature of the gas will rise as you shake it. It’s a subtle effect, so insulating the container by putting it in vacuum is probably a good idea. As you shake the container, its moving walls bat the tiny gas molecules around, sometimes adding energy to them and sometimes taking it away. On average however, those moving walls add energy to the gas molecules and thereby increase the gas’s temperature.

A simple way to see why that’s the case is to picture the gas as composed of many little bouncing balls inside the container. Those balls are perfectly elastic so they rebound from a stationary wall without changing their speeds at all. But the walls of the container aren’t stationary, they move back and forth as you shake the container. Because of the moving walls, the balls change their speeds as they rebound. A ball that bounces off a wall that is moving toward it gains speed during its bounce, like a pitched ball rebounding from a swung bat. On the other hand, a ball that bounces off a wall that is moving away from it loses speed during its bounce, like a pitched ball rebounding from a bat during a bunt. If both types of bounces were equally common in every way then, on average, the balls (or actually the gas molecules) would neither gain nor lose speed as the result of bounces off the walls and the gas temperature would remain unchanged.

But the bounces aren’t equally common. It’s more likely that a moving ball will hit a wall that is moving toward it than that it will hit a wall that is moving away from it. It’s a geometry problem; you get wet faster when you run toward a sprinkler than when you run away from the sprinkler. So, on average, the balls (or gas molecules) gain speed as the result of bounces off the walls and the gas temperature increases.

How large this effect is depends on the relative speeds of the gas molecules and the walls. The effect becomes enormous when the walls move as fast or faster than the gas molecules but is quite subtle when the gas molecules move faster than the walls. Since air molecules typically move at about 500 meters per second (more than 1000 mph) at room temperature, you’ll have to shake the container pretty violently to see a substantial heating of the gas.

## How do you calculate how much weight a helium balloon can lift? – C & S

#### How do you calculate how much weight a helium balloon can lift? – C & S

A helium balloon experiences an upward force that is equal to the weight of the air it displaces (the buoyant force on the balloon) minus its own weight. At sea level, air weighs about 0.078 pounds per cubic foot, so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift, which is about 0.067 pounds per cubic foot. To lift a 100 pound person, you’ll need about 1500 cubic feet of helium in your balloon.

## Is it true that the buoyancy of an incompressible bathysphere doesn’t change whe…

#### Is it true that the buoyancy of an incompressible bathysphere doesn’t change when it plunges to great depths in the ocean, even though the pressure exerted on it increases enormously? – AM

A submerged object’s buoyancy (the upward force exerted on it by a fluid) is exactly equal to the weight of the fluid it displaces. In this case, the upward buoyant force on the bathysphere is equal in amount to the weight of the water it displaces. Since the bathysphere is essentially incompressible, it always displaces the same volume of water. And since water is essentially incompressible, that fixed volume of water always weighs the same amount. That’s why the bathysphere experiences a constant upward force on it due to the surrounding water. To sink the bathysphere, they weight it down with heavy metal particles. And to allow the bathysphere to float back up, they release those particles and reduce the bathysphere’s total weight.

## I am twelve years old and weigh 85 pounds. How much helium would it take to lift…

#### I am twelve years old and weigh 85 pounds. How much helium would it take to lift me off the ground?

While helium itself doesn’t actually defy gravity, it is lighter than air and floats upward as descending air pushes it out of the way. Like a bubble in water, the helium goes up to make room for the air going down. The buoyant force that acts on the helium is equal to the weight of air that the helium displaces.

A cubic foot of air weighs about 0.078 pounds so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift; about 0.067 pounds. Since you weigh 85 pounds, it would take about 1300 cubic feet of helium to lift you and a thin balloon up into the air. That’s a balloon about 13.5 feet in diameter.

## The force of gravity decreases as we go down toward the center of the earth and …

#### The force of gravity decreases as we go down toward the center of the earth and becomes equalized at the center. So why does pressure increase with depth, for example in the ocean? — HN, Vancouver, British Columbia

It’s true that the force of gravity decreases with depth, so that if you were to find yourself in a cave at the center of the earth, you would be completely weightless. However, pressure depends on more than local gravity: it depends on the weight of everything being supported overhead. So while you might be weightless, you would still be under enormous pressure. Your body would be pushing outward on everything around you, trying to prevent those things from squeezing inward and filling the space you occupy. In fact, your body would not succeed in keeping those things away and you would be crushed by their inward pressure.

More manageable pressures surround us everyday. Our bodies do their part in supporting the weight of the atmosphere overhead when we’re on land or the weight of the atmosphere and a small part of the ocean when we’re swimming at sea. The deeper you go in the ocean, the more weight there is overhead and the harder your body must push upward. Thus the pressure you exert on the water above you and the pressure that that water exerts back on you increases with depth. Even though gravity is decreasing as you go deeper and deeper, the pressure continues to increase. However, it increases a little less rapidly as a result of the decrease in local gravity.

## After a party at work, a friend tied a helium balloon to his car’s gearshift lev…

#### After a party at work, a friend tied a helium balloon to his car’s gearshift lever and drove off. As he started driving forward, the balloon first went forward and then backward. That’s not what happens to everything else. Why does it happen for the helium balloon? — S

The helium balloon is the least dense thing in the car and is responding to forces exerted on it by the air in the car. To understand this, consider what happens to you, the air, and finally the helium balloon as the car first starts to accelerate forward.

When the car starts forward, inertia tries to keep all of the objects in the car from moving forward. An object at rest tends to remain at rest. So the car must push you forward in order to accelerate you forward and keep you moving with the car. As the car seat pushes forward on you, you push back on the car seat (Newton’s third law) and dent its surface. Your perception is that you are moving backward, but you’re not really. You’re actually moving forward; just not quite as quickly as the car itself.

The air in the car undergoes the same forward acceleration process. Its inertia tends to keep it in place, so the car must push forward on it to make it accelerate forward. Air near the front of the car has nothing to push it forward except the air near the back of the car, so the air in the front of the car tends to “dent” the air in the back of the car. In effect, the air shifts slightly toward the rear of the car. Again, you might think that this air is going backward, but it’s not. It’s actually moving forward; just not quite as quickly as the car itself.

Now we’re ready for the helium balloon. Since helium is so light, the helium balloon is almost a hollow, weightless shell that displaces the surrounding air. As the car accelerates forward, the air in the car tends to pile up near the rear of the car because of its inertia. If the air can push something out of its way to get more room near the rear of the car, it will. The helium balloon is that something. As inertia causes the air to drift toward the rear of the accelerating car, the nearly massless and inertialess helium balloon is squirted toward the front of the car to make more room for the air. There is actually a horizontal pressure gradient in the car’s air during forward acceleration, with a higher pressure at the rear of the car than at the front of the car. This pressure gradient is ultimately what accelerates the air forward with the car and it’s also what propels the helium balloon to the front of the car.

Finally, when the car is up to speed and stops accelerating forward, the pressure gradient vanishes and the air returns to its normal distribution. The helium balloon is no longer squeezed toward the front of the car and it floats once again directly above the gear shift.

One last note: OGT from Lystrup, Denmark points out that when you accelerate a glass of beer, the rising bubbles behave in the same manner. They move toward the front of the glass as you accelerate it forward and toward the back of the glass as you bring it to rest.

## I once read that if you were in a boat and dropped a cannonball into the water, …

#### I once read that if you were in a boat and dropped a cannonball into the water, the water level would actually go down. It had to do with mass and displacement. Please explain in layman’s terms. — MJB, Lafayette, LA

While the cannonball is in your boat, its great weight pushes the boat deeper into the water. To support the cannonball, the boat must displace the cannonball’s weight in water—a result known as Archimedes principle. Since the cannonball is very dense, the boat must displace perhaps 8 cannonball volumes of water in order to obtain the buoyancy needed to support the cannonball. This displaced water appears on the surface of the lake so that the lake’s level rises.

Now suppose that you throw the cannonball overboard. The cannonball quickly sinks to the bottom. The boat now floats higher than before because it no longer needs to displaces the extra 8 cannonball volumes of water. Although the cannonball itself is displacing 1 cannonball volume of water, there are still 7 cannonball volumes less water being displaced by objects in the water. As a result, the water level of the lake drops slightly when you throw the cannonball overboard.

## What are the effects of water pressure on fish, submarines and divers?

#### What are the effects of water pressure on fish, submarines and divers?

All three of these objects contain solids, liquids, and gases, so I’ll begin by describing how pressure affects those three states of matter. Solids and liquids are essentially incompressible, meaning that as the pressure on a solid or a liquid increases, its volume doesn’t change very much. Without extraordinary tools, you simply can’t squeeze a liter of water or liter-sized block of copper into a half-liter container. Gases, on the other hand, are relatively compressible. With increasing pressure on it, a certain quantity of gas (as measured by weight) will occupy less and less volume. For example, you can squeeze a closet full of air into a scuba tank.

Applying these observations to the three objects, it’s clear that the solid and liquid portions of these objects aren’t affected very much by the pressure, but the gaseous portions are. In a fish or diver, the gas-filled parts (the swim bladder in a fish and the lungs in a diver) become smaller as the fish or diver go deeper in the water and are exposed to more pressure. In a submarine, the hull of the submarine must support the pressure outside so that the pressure of the air inside the submarine doesn’t increase. If the pressure did reach the air inside the submarine, that air would occupy less and less volume and the submarine would crush. That’s why the hull of a submarine must be so strong—it must hide the tremendous water pressure outside the hull from the air inside the hull.

Apart from these mechanical effects on the three objects, there is one other interesting effect to consider. Increasing pressure makes gases more soluble in liquids. Thus at greater depths and pressures, the fish and diver can have more gases dissolved in their blood and tissues. Decompression illness, commonly called “the bends”, occurs when the pressure on a diver is suddenly reduced by a rapid ascent from great depth. Gases that were soluble in that diver’s tissue at the initial high pressure suddenly become less soluble in that diver’s tissue at the final low pressure. If the gas comes out of solution inside the diver’s tissue, it causes damage and pain.