Archimedes Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. Thus, for an object of density 0 floating partly submerged in a fluid of density f, the buoyant force is given by F f t y 0 2h As yd dy, where t is the acceleration due to gravity and As yd is the area of a typical cross-section of the object (see the figure). The weight of the object is given by W 0 t y L2h 2h As yd dy (a) Show that the percentage of the volume of the object above the surface of the liquid is 100 f 2 0 f (b) The density of ice is 917 kgym3 and the density of seawater is 1030 kgym3 . What percentage of the volume of an iceberg is above water? (c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts? (d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is 1000 kgym3 .

# Archimedes Principle states that the buoyant force on an

## Solution for problem 6 Chapter 6

Calculus | 8th Edition

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Get Full SolutionsCalculus was written by and is associated to the ISBN: 9781285740621. The answer to “Archimedes Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. Thus, for an object of density 0 floating partly submerged in a fluid of density f, the buoyant force is given by F f t y 0 2h As yd dy, where t is the acceleration due to gravity and As yd is the area of a typical cross-section of the object (see the figure). The weight of the object is given by W 0 t y L2h 2h As yd dy (a) Show that the percentage of the volume of the object above the surface of the liquid is 100 f 2 0 f (b) The density of ice is 917 kgym3 and the density of seawater is 1030 kgym3 . What percentage of the volume of an iceberg is above water? (c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts? (d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is 1000 kgym3 .” is broken down into a number of easy to follow steps, and 211 words. This full solution covers the following key subjects: Object, Density, Water, ice, weight. This expansive textbook survival guide covers 16 chapters, and 250 solutions. The full step-by-step solution to problem: 6 from chapter: 6 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since the solution to 6 from 6 chapter was answered, more than 230 students have viewed the full step-by-step answer.

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Archimedes Principle states that the buoyant force on an