   Chapter 9, Problem 29P

Chapter
Section
Textbook Problem

A sample of an unknown material appears to weigh 300. N in air and 200. N when immersed in alcohol of specific gravity 0.700. What are (a) the volume and (b) the density of the material?

(a)

To determine
The volume of the material.

Explanation
The difference between the weight of the unknown material in air and the apparent weight of the material in liquid is equal to the buoyant force on that material and it defined as B=(ρalcoholV)gWairWalcohol=(ρalcoholV)g . This expression is rearranged for the volume of the unknown material.

Given info: The weight of the unknown material in air is 300N and in alcohol is 200N , density of alcohol is 700kg/m3 , and acceleration due to gravity is 9.80m/s2 .

The formula for the volume of the unknown material is,

V=WairWalcoholρalcoholg

• Wair is weight of the unknown material in air.
• Walcohol is weight of the unknown material when immersed in alcohol.
• ρalcohol is density of alcohol.
• g is acceleration due to gravity

(b)

To determine
The density of the material.

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