Concept explainers
A unidirectional carbon fiber–epoxy resin composite contains 68% by volume of carbon fiber and 32% epoxy resin. The density of the carbon fiber is 1.79 g/cm3 and that of the epoxy resin is 1.20 g/cm3. (a) What are the weight percentages of carbon fibers and epoxy resin in the composite? (b) What is the average density of the composite?
(a)
The weight percentage of carbon fibers in the composite.
The weight percentage of epoxy resin in the composite.
Answer to Problem 40AAP
The weight percentage of carbon fibers in the composite is
The weight percentage of epoxy resin in the composite is
Explanation of Solution
Write the expression to calculate mass of carbon fiber in the composite
Here, density of carbon fiber is
Write the expression to calculate mass of epoxy resin in the composite
Here, density of epoxy resin is
Write the expression to calculate total mass of the composite
Here, density of epoxy resin is
Write the expression to calculate weight percentage of carbon fiber in the composite
Write the expression to calculate weight percentage of epoxy resin in the composite
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the weight percentage of carbon fibers in the composite is
(b)
The average density of the composite.
Answer to Problem 40AAP
The average density of the composite is
Explanation of Solution
Write the expression to calculate average density of the composite
Here, total volume of composite is
Conclusion:
Substitute
Thus, the average density of the composite is
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