Force which supports objects in fluids

The buoyant force on an object equals the weight of the fluid it displaces. This principle is named after the Greek mathematician and inventor Archimedes ca. The force that provides the pressure of a fluid acts on a body perpendicular to the surface of the body.

In other words, the force due to the pressure at the bottom is pointed up, while at the top, the force due to the pressure is pointed down; the forces due to the pressures at the sides are pointing into the body.

Therefore a net upward force acts on the body. This upward force is the force of buoyancy, or simply buoyancy. Some say it all started in a bathtub.

To read the story, explore Scientific American to learn more. If you drop a lump of clay in water, it will sink. But if you mold the same lump of clay into the shape of a boat, it will float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same is true of steel ships. The average density of an object is what ultimately determines whether it floats.

The reason is that the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. That is, apparent weight loss equals weight of fluid displaced, or apparent mass loss equals mass of fluid displaced. More force is required to pull the plug in a full bathtub than when it is empty.

Explain your answer. Not at all. The reason that the full tub requires more force to pull the plug is because of the weight of the water above the plug. Will the same ship float higher in salt water than in freshwater? The buoyant force is equal to the weight of the fluid displaced.

The greater the density of the fluid, the less fluid that is needed to be displaced to have the weight of the object be supported and to float. Since the density of salt water is higher than that of fresh water, less salt water will be displaced, and the ship will float higher. Marbles dropped into a partially filled bathtub sink to the bottom. 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 The buoyant force is the weight of this volume of water. The mass of water displaced is found from its relationship to density and volume, both of which are known.

That is,. The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking. The average density of an object is what ultimately determines whether it floats.

If its average density is less than that of the surrounding fluid, it will float. This is because the fluid, having a higher density, contains more mass and hence more weight in the same volume.

The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink. In Figure 4, for example, the unloaded ship has a lower density and less of it is submerged compared with the same ship loaded.

We can derive a quantitative expression for the fraction submerged by considering density. The fraction submerged is the ratio of the volume submerged to the volume of the object, or. The volume submerged equals the volume of fluid displaced, which we call V fl. Since the object floats, its mass and that of the displaced fluid are equal, and so they cancel from the equation, leaving.

Figure 4. An unloaded ship a floats higher in the water than a loaded ship b. We use this last relationship to measure densities. This is done by measuring the fraction of a floating object that is submerged—for example, with a hydrometer. It is useful to define the ratio of the density of an object to a fluid usually water as specific gravity :. If an object floats, its specific gravity is less than one.

If it sinks, its specific gravity is greater than one. 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.