Question

The answor of a is 95.5 and the answor of b is 2.75 please show work

11.0 (20 pts) A unidirectional fiber-epoxy resin composite contains a 89 % fiber volume with epoxy resin for the remaining volumne fraction. Determine the (a) % composition of fiber by weight and (b) the average density of the composite. The fiber and resin densities are 2.95 and 1.21 g/cm^3, respectively. Fiber comp (wt%) = _____95.5___ ? = ____2.75____

The answor of a is 95.5 and the answor of b is 2.75 please show work

Answer 1

Let the total Volume of composite is V & Total mass is M

So

Fiber volume = 0.89V & epoxy resin volume = 0.11V

we know-

Mass = Density x Volume

M = m₁ + m₂ ( where m₁ and m₂ are the masses of Fiber and Epoxy resin respectively)

now:

m₁= 2.95 x 0.89V

m₁ = 2.6255V

m₂= 1.21 x 0.11V

m₂ = 0.1331V

M=2.6255V+0.1331V

M=2.7586V

(A) % composition of fiber by weight = (fiber weight / total weight) x 100 %

= (m₁ / M) x100 %

= (2.6255V / 2.7586V) x 100 %

= 95.17% Ans.

(B) The average density of the composite = total mass / total volume

= M / V

=2.7586V / V

= 2.7586 Ans.