\n When an object is immersed in a fluid, the fluid exerts an upward force on the object. This force is known as buoyant force, and this phenomenon is known as buoyancy. The magnitude of the bouyant force acting on an object depends on the density of the fluid and the volume of fluid displaced by the object.\r\n
\r\n\n Consider a cylindrical object completely submerged in a fluid. The buoyant force acting on an object immersed in a fluid arises from the pressure exerted on the object by the fluid.\r\n The fluid exerts pressure on all sides of the immersed object. However, since the fluid pressure increases with depth, the pressure exerted at the bottom surface of the cylinder is greater than the pressure exerted on the top. This results in a net upward force, which is the buoyant force.\r\n
\r\n\n Let's calculate the magnitude of buoyant force on a cylindrical can (completely submerged in a fluid) by adding up all the forces acting on the object.\r\n First, we note that pressure exerted by a fluid varies with depth \\(h\\) as follows:\r\n $$P = \\rho_f g h$$\r\n where \\(\\rho_f\\) is the density of the fluid, \\(g \\) is the acceleration due to gravity and \\(h \\) is the depth. The pressures at the top and the bottom of the cylindrical can thus be obtained as \\(P_1 = \\rho_f g h_1\\) and \\(P_2 = \\rho_f g h_2\\).\r\n Now, we calculate the force acting on the top face as:\r\n $$F_\\text{Top} \\text{(acts downward)} = P_1 A = \\rho_f g A h_1$$\r\n Similarly, the force acting on the bottom face of the cylindrical can is obtained as:\r\n $$F_\\text{Bot} \\text{(acts upward)} = P_2 A = \\rho_f g A h_2 $$\r\n Note that \\(F_\\text{Bot} > F_\\text{A}\\) due to the fact that \\(h_2 > h_1\\).\r\n The sum of lateral forces is zero. Thus, the net force acting on the cylindrical can (which is the Buoyant force) is:\r\n $$F_{Buo}\\text{(acts upward)} = F_\\text{Bot} - F_\\text{Top} = \\rho_f g A (h_2 - h_1) = \\rho_f g A l$$\r\n where \\(l = h_2 -h_1\\) is the height of the cylindrical can.\r\n
\r\n\n The Archimedes principle states that the buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. Stated in simple terms — the buoyant force acting on an object can be calculated by assuming the submerged portion of the object is made of the fluid that the object is submerged in and then by calculating the weight of that mass of fluid. Expressed as an equation, the Archimedes principles reads as\r\n $$F_\\text{Buo} = \\rho_f g V_\\text{Sub}$$\r\n where \\(V_\\text{sub}\\) is the volume of the object submerged in the fluid.\r\n For an object of volume \\(V\\) that is completely submerged in a fluid, the Archimedes principle becomes\r\n $$F_\\text{Buo} = \\rho_f g V$$\r\n The Archimedes principle is valid for any fluid whether its a liquid (such as water) or a gas (such as air).\n
\r\nHave you ever noticed that an object feels lighter when it is submerged in water (or as a matter of fact in any fluid). This is a consequence of buoyancy. The weight of the object acts downward while the buoyant force due to the fluid acts upward. Thus, the weight of the object is opposed by the buoyant force exerted on it by the fluid — as a result the object feels lighter in water. By measuring the weight of the object inside and outside of the fluid, the buoyant force acting on the object can be measured. Through this interactive session, you will learn about —
\r\n\n Kettlebells are out of stock this year — courtesy of COVID-19.\r\n You are a fitness enthusiast and you really need a kettlebell for your daily exercise.\r\n One day a mysterious salesman shows up to your door. He has several expensive kettlebells to sell — each made of a different metal.\r\n Your job is to figure out what metal the kettlebell is made of, and if it is worth the asking price.\n
\r\n\n Follow the steps below to accomplish this task.\r\n