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). This weight is equal to the mass of the displaced fluid multiplied by the gravitational acceleration:īuoyant force: The fluid pushes on all sides of a submerged object. The buoyancy force on the cylinder is equal to the weight of the displaced fluid. Now, we’ll calculate this force using Archimedes’ principle. In the previous section, we calculated the buoyancy force on a cylinder (shown in ) by considering the force exerted on each of the cylinder’s sides. We will explore this further as we discuss applications of the principle in subsequent sections.Īrchimedes’ Principle – Simple Example: We use Archimedes’ Principle to determine the number of penguins an ice float can dryly support. The Archimedes principle is valid for any fluid-not only liquids (such as water) but also gases (such as air). Therefore, the buoyancy force on the original object is equal to the weight of the “displaced fluid” (in this case, the water inside the dashed region (b)). However, we also know that the buoyancy force on the fluid must be equal to its weight, as the fluid does not sink in itself. The buoyancy force on this amount of fluid must be the same as on the original object (the ship).
Imagine that we replace the submerged part of the object with the fluid in which it is contained, as in (b). The reasoning behind the Archimedes principle is that the buoyancy force on an object depends on the pressure exerted by the fluid on its submerged surface. The principle can be stated as a formula: He discovered the relation between the surface and volume of a sphere and its circumscribing cylinder. In other words, to calculate the buoyant force on an object we assume that the submersed part of the object is made of water and then calculate the weight of that water (as seen in ).Īrchimedes principle: The buoyant force on the ship (a) is equal to the weight of the water displaced by the ship-shown as the dashed region in (b). Archimedes, the most famous mathematician and inventor in ancient Greece. A simpler method follows from the Archimedes principle, which states that the buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces. Thus, the net upward force on the cylinder due to the fluid is:Īlthough calculating the buoyant force in this way is always possible it is often very difficult. Because it is cylindrical, the net force on the object’s sides is zero-the forces on different parts of the surface oppose each other and cancel exactly. Similarly, the force on the bottom surface is:Īnd points upwards. The magnitude of the force on the top surface is:
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