This document contains solutions to problems 4.5, 4.6, and 4.11 from a materials science textbook. Problem 4.5 involves calculating values using exponential notation. Problem 4.6 calculates mechanical properties for three different fiber-reinforced composites: E-glass with polyester, S-glass with epoxy, and carbon fiber with vinyl ester. It provides values for tensile strength, tensile modulus, and other mechanical properties. Problem 4.11 asks the reader to consider two failure theories for composites: maximum stress theory and maximum strain theory.

1. Problem 4.5
= 230 *10^9 =4.6 *10^9
= 92*10^9 = 1.769*10^9
=0.25 =0.3
= 0.4
Solution
= 9.476 *10^10
= 7.566 *10^9
= 0.28
= 2.911*10^9
Problem 4.6
= 0.55 so
a) E-glass - Polyster
= 72.345 Gpa = 3.4 Gpa
= 3.45 Gpa = 75.9 Mpa
So
= 4.31*10^10 7.145*10^9
= 01.6425*10^8 0.292
b) S-glass – epoxy (9310)
= 85 Gpa = 3.12 Gpa
= 4.8 Gpa = 75.8 Mpa

2. So
= 4.8154*10^10 6.6356*10^9
= 1.6525*10^8 0.292
c) Carbon(T300) – Vinyl ester
= 230 Gpa = 3.4 Gpa
= 3.53 Gpa = 82.7 Mpa
So
= 1.2803*10^11 7.421*10^9
= 1.7866*10^9 0.292
Problem 4.11
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