|MLA Citation:||Bloomfield, Louis A. "Balloons" How Everything Works 18 Jun 2018. Page 4 of 4. 18 Jun 2018 <http://www.howeverythingworks.org/prints.php?topic=balloons&page=4>.|
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.
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.
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.
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.
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.
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.
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