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Chapter 9: Problem 5

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

Short Answer

Expert verified
Question: Arrange the following mediums in decreasing order of buoyancy force acting on an object of the same volume submerged in each medium: air, water, mercury, and an evacuated chamber. Answer: Mercury, Water, Air, Evacuated Chamber

Step by step solution

01

Understand Archimedes' Principle

Archimedes' principle states that the upward buoyancy force (F_b) exerted on an object immersed in a fluid equals the weight of the fluid displaced by the object. Mathematically, it can be expressed as: F_b = ρ × V × g, where ρ is the fluid density, V is the volume of the fluid displaced by the object, and g is the gravitational acceleration.
02

Find the density of each medium

The density ρ of each medium is as follows: - Air: \(\rho_a \approx 1.225 kg/m^3\) - Water: \(\rho_w \approx 1,000 kg/m^3\) - Mercury: \(\rho_m \approx 13,600 kg/m^3\) - Evacuated chamber: In an evacuated chamber, there's no fluid, so the density ρ in this case is assumed to be 0 kg/m^3.
03

Compare buoyancy forces in different mediums

Now, we will compare the buoyancy forces for a body of the same volume, V, immersed in these different mediums. The buoyancy force acting on the body can be calculated using the Archimedes' principle (F_b = ρ × V × g). (a) Air: \(F_{b_{air}} = \rho_a × V × g = 1.225 kg/m^3 × V × g\) (b) Water: \(F_{b_{water}} = \rho_w × V × g = 1,000 kg/m^3 × V × g\) (c) Mercury: \(F_{b_{mercury}} = \rho_m × V × g = 13,600 kg/m^3 × V × g\) (d) Evacuated chamber: \(F_{b_{evacuated}} = 0 kg/m^3 × V × g = 0\)
04

Determine the relative magnitudes of the buoyancy forces

Comparing the buoyancy forces, we can see that \(F_{b_{mercury}} > F_{b_{water}} > F_{b_{air}} > F_{b_{evacuated}}\). The buoyancy force is greatest when the body is submerged in mercury, followed by water, then air, and finally, no buoyancy force is present in an evacuated chamber.

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Most popular questions from this chapter

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