Question

What is buoyancy force? Compare the relative magnitudes of the buoyancy force acting on a body immersed in these media: \((a)\) air, \((b)\) water, \((c)\) mercury, and \((d)\) an evacuated chamber.

Short answer

Question: Arrange the given media in increasing order of the buoyancy force experienced by an object when submerged: air, water, mercury, and an evacuated chamber. Answer: Evacuated Chamber < Air < Water < Mercury

Step-by-step solution

Understanding Buoyancy and Archimedes' Principle

Buoyancy is the upward force experienced by an object submerged in a fluid (gas or liquid). This force occurs because the pressure in the fluid increases with depth, and there is a pressure difference acting on the bottom and top surfaces of the object. Archimedes' principle states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object. Mathematically, this can be represented as \(Buoyancy\ Force = Weight\ of\ Displaced\ Fluid\), or in terms of density, volume, and gravitational acceleration: \(F_b = \rho V g\), where \(F_b\) is the buoyancy force, \(\rho\) is the density of the fluid, \(V\) is the volume of the displaced fluid, and \(g\) is the gravitational acceleration.

Computing Buoyancy Force for Each Medium

In this step, we will determine the buoyancy force acting on the object when immersed in air, water, mercury, and an evacuated chamber. To make a valid comparison, we need to use a fixed volume (\(V\)) for the object and gravitational acceleration (\(g\)), keeping these values constant for all cases. The densities of air, water, and mercury are approximately: - Air density: \(\rho_{air} \approx 1.2\ kg/m^3\) - Water density: \(\rho_{water} \approx 1000\ kg/m^3\) - Mercury density: \(\rho_{mercury} \approx 13,600\ kg/m^3\) For an evacuated chamber, the density of the fluid medium is considered to be \(0\ kg/m^3\) since there is no fluid present. Using the density values, we can find the buoyancy force for each medium using Archimedes' principle, \(F_b = \rho V g\): \((a) F_{b,air} = \rho_{air} V g\) \((b) F_{b,water} = \rho_{water} V g\) \((c) F_{b,mercury} = \rho_{mercury} V g\) \((d) F_{b,evacuated} = 0 \cdot Vg = 0\)

Comparing the Relative Magnitudes of Buoyancy Force

Based on the buoyancy force calculations, we can compare the magnitudes for each medium as follows: - Air has the lowest fluid density, leading to a relatively small buoyancy force. - Water's buoyancy force is significantly greater than air's due to its higher density. - Mercury provides the largest buoyancy force among the given media due to its extremely high density. - In the evacuated chamber, there is no fluid present, meaning there is no buoyancy force acting on the object. In conclusion, the relative magnitudes of buoyancy force for the given media are: Evacuated Chamber < Air < Water < Mercury