Moreover, the fraction of a floating object that is submerged equals its specific gravity. Scuba divers try to obtain this state so that they can hover in the water.
We measure the specific gravity of fluids, such as battery acid, radiator fluid, and urine, as an indicator of their condition. One device for measuring specific gravity is shown in Figure 5. Figure 5. This hydrometer is floating in a fluid of specific gravity 0. The glass hydrometer is filled with air and weighted with lead at the bottom.
It floats highest in the densest fluids and has been calibrated and labeled so that specific gravity can be read from it directly. Suppose a What is her average density? Her density is less than the fluid density. We expect this because she floats. See Figure 6. Figure 6. The subject must completely empty his lungs and hold a metal weight in order to sink. Corrections are made for the residual air in his lungs measured separately and the metal weight.
His corrected submerged weight, his weight in air, and pinch tests of strategic fatty areas are used to calculate his percent body fat. Less obvious examples include lava rising in a volcano and mountain ranges floating on the higher-density crust and mantle beneath them.
Even seemingly solid Earth has fluid characteristics. Figure 7. These two measurements are used to calculate the density of the coin. An object, here a coin, is weighed in air and then weighed again while submerged in a liquid.
The density of the coin, an indication of its authenticity, can be calculated if the fluid density is known. This same technique can also be used to determine the density of the fluid if the density of the coin is known.
The object suffers an apparent weight loss equal to the weight of the fluid displaced. Alternatively, on balances that measure mass, the object suffers an apparent mass loss equal to the mass of fluid displaced. That is. The mass of an ancient Greek coin is determined in air to be 8. When the coin is submerged in water as shown in Figure 7, its apparent mass is 7.
Calculate its density, given that water has a density of 1. The volume of the coin equals the volume of water displaced. This is also the volume of the coin, since it is completely submerged. We can now find the density of the coin using the definition of density:. You can see from Table 1 that this density is very close to that of pure silver, appropriate for this type of ancient coin. Most modern counterfeits are not pure silver. As the story goes, the king of Syracuse gave Archimedes the task of determining whether the royal crown maker was supplying a crown of pure gold.
The purity of gold is difficult to determine by color it can be diluted with other metals and still look as yellow as pure gold , and other analytical techniques had not yet been conceived. Even ancient peoples, however, realized that the density of gold was greater than that of any other then-known substance. Archimedes purportedly agonized over his task and had his inspiration one day while at the public baths, pondering the support the water gave his body.
How are density mass and volume related? How do you calculate mass using density and volume? How do you convert mass to density? How do you determine the density of a gas? What is the density of water? What is linear mass density? Why does density change with temperature? Buoyant force : The fluid pushes on all sides of a submerged object. However, because pressure increases with depth, the upward push on the bottom surface F2 is greater than the downward push on the top surface F1.
Therefore, the net buoyant force is always upwards. However and this is the crucial point , the cylinder is entirely submerged, so the volume of the displaced fluid is just the volume of the cylinder see , and:. Archimedes principle : The volume of the fluid displaced b is the same as the volume of the original cylinder a.
This is the same result obtained in the previous section by considering the force due to the pressure exerted by the fluid. Consider the USS Macon, a helium-filled airship shown in. Ignoring the small volume of the gondola, what was the buoyancy force on this airship?
If the airship weighed , kg, how much cargo could it carry? Assume the density of air is 1. The buoyancy force on an airship is due to the air in which it is immersed. To find the cargo capacity of the airship, we subtract the weight of the airship from the buoyancy force:. The buoyant force is always present, whether the object floats, sinks, or is suspended in a fluid.
If you put a metal coin into a glass of water it will sink. But most ships are built of metal, and they float. So how is this possible? An object will float if the buoyancy force exerted on it by the fluid balances its weight, i.
But the Archimedes principle states that the buoyant force is the weight of the fluid displaced. So, for a floating object on a liquid, the weight of the displaced liquid is the weight of the object. Consider a one-ton block of solid iron. Suppose the same iron block is reshaped into a bowl.
Part of their weight is supported by buoyant force, yet the downward force on the bottom of the tub increases by exactly the weight of the marbles. Explain why. What fraction of ice is submerged when it floats in freshwater, given the density of water at. A rock with a mass of g in air is found to have an apparent mass of g when submerged in water.
Is this consistent with the value for granite? Suppose a chunk of iron with a mass of Calculate the buoyant force on a 2. Neglect the volume of the rubber. This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water.
A simple compass can be made by placing a small bar magnet on a cork floating in water. You may assume that the buoyant force is. Calculate the volume of air he inhales—called his lung capacity—in liters.
Skip to content 14 Fluid Mechanics. Figure Buoyant Force The buoyant force is the upward force on any object in any fluid. If the object were not in the fluid, the space the object occupied would be filled by fluid having a weight This weight is supported by the surrounding fluid, so the buoyant force must equal the weight of the fluid displaced by the object. If is less than the weight of the object, the object sinks.
Some say it all started in a bathtub. Example Calculating Average Density Suppose a Measuring Density One of the most common techniques for determining density is shown in Figure. These two measurements are used to calculate the density of the coin.
0コメント