
Interpretation:
The comparison of cost of material in the composite quarter with the quarter made up of nickel should be determined.
Concept introduction:
The rule of mixtures for particulate composites is:
Where
Volume fraction is defined as
Density is defined as the ratio of mass per unit volume expressed as
Where,
m is the mass of material in kg.
V is the volume of material in cubic meter.
The unit of density is kg/cubic meter.

Answer to Problem 17.56P
The cost of quarter made up of copper and nickel is
The cost of quarter made up of nickel is
Thus, the cost of quarter made up of copper and nickel is half of the cost of quarter made up of nickel.
Explanation of Solution
Given information:
Diameter of US quarter =
Thickness of US quarter =
Cost of copper =
Cost of nickel =
From given information, the volume of copper in US quarter =
The volume of nickel in US quarter =
Volume fraction of copper
Volume fraction of nickel
Calculation of volume of quarter,
Conversion of d from inch to cm, by multiplying it with 2.54 cm,
Conversion of thickness to cm, by multiplying it with 2.54 cm,
Thus, the volume of quarter =
Calculation of volume of copper using rule of mixing concept,
Volume fraction is defined as the ratio of volume of copper to the volume of quarter. On rearranging the equation,
Volume fraction of copper
Putting the values,
Therefore, the volume of copper
Calculation of volume of nickel using volume fraction relation,
Volume fraction of nickel
Thus, the volume of nickel
Calculation of weight of copper using the relationship of weight with density given as,
The values of density and volume are,
Putting the values in the formula of weight,
Calculation of weight of nickel using the relationship of weight with density given as,
The values of density and volume are,
Putting the values,
Calculation of cost of copper and nickel using the relation,
Conversion of per pound to per kg by multiplying it with 2.205
Cost of copper per kg =
Calculation of cost of nickel,
Conversion of per pound to per kg by multiplying it with 2.205,
Cost of nickel per kg =
Putting the values,
The total cost of quarter is the sum of cost of nickel and copper,
Thus, the total cost of quarter
Weight of nickel based on the volume of quarter is calculated as,
Calculation of cost of quarter, if it is made of nickel,
Thus, the cost of quarter made up of nickel
The comparison of total cost of quarter made up of copper and nickel with cost of quarter made up of only nickel is given by,
Thus, the cost of quarter made up of copper and nickel is half of the cost of quarter made up of nickel.
The cost of quarter made up of copper and nickel is
The cost of quarter made up of nickel is
Thus, the cost of quarter made up of copper and nickel is half of the cost of quarter made up of nickel.
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Chapter 17 Solutions
Essentials of Materials Science and Engineering, SI Edition
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