Can someone please help with this problem?

A burnout test was performed to determine the volume fractions of constituents in a
glass/epoxy composite. The following observations were made:
Weight of empty crucible = 47.6504 g
Weight of the crucible and small piece of composite = 50.2417 g
Weight of the crucible and glass after burnout = 49.7576 g

(a)Calculate the weight and volume fractions of glass fiber and epoxy resin. Assume that the
densities of the fibers and the resin are 2.5 and 1.2 g/cm3 respectively.

(b) Can the burn out test be used for kevlar/epoxy composites? Explain.

a) The mass of glass in the sample is the remaining mass that does not burn, 49.7576 - 47.6504 = 2.1072 g

The total mass of sample before burnout was 50.2417 - 47.6504 = 2.5913 9
The difference of those numbers is the original resin content, 0.4841 g.
Divide those numbers by the respective densities to get the volumes, and the volume fractions.

b) This analysis method will not work for Kevlar/epoxy, because the Kevlar can be oxidized.

Thank you very much.

Sure, I can help you with this problem step-by-step.

(a) To calculate the weight and volume fractions of glass fiber and epoxy resin, we need to first find the weight of the composite, the weight of the glass fiber, and the weight of the epoxy resin. We can then use these weights to calculate the volume fractions.

1. Weight of the composite:
Weight of the crucible and small piece of composite = 50.2417 g
Weight of empty crucible = 47.6504 g
Weight of the composite = (Weight of the crucible and small piece of composite) - (Weight of empty crucible)
= 50.2417 g - 47.6504 g
= 2.5913 g

2. Weight of the glass fiber:
Weight of the crucible and glass after burnout = 49.7576 g
Weight of empty crucible = 47.6504 g
Weight of the glass fiber = (Weight of the crucible and glass after burnout) - (Weight of empty crucible)
= 49.7576 g - 47.6504 g
= 2.1072 g

3. Weight of the epoxy resin:
Weight of the epoxy resin = Weight of the composite - Weight of the glass fiber
= 2.5913 g - 2.1072 g
= 0.4841 g

Now, let's calculate the volume fractions:

4. Volume fraction of glass fiber:
Volume fraction of glass fiber = (Weight of the glass fiber) / (Density of the fiber)
= 2.1072 g / 2.5 g/cm³
= 0.8429 cm³ / cm³

5. Volume fraction of epoxy resin:
Volume fraction of epoxy resin = (Weight of the epoxy resin) / (Density of the resin)
= 0.4841 g / 1.2 g/cm³
= 0.4034 cm³ / cm³

So, the weight fraction of glass fiber is approximately 0.8429 and the weight fraction of epoxy resin is approximately 0.4034.

(b) The burnout test cannot be used for Kevlar/epoxy composites. This is because the burnout test relies on the fact that one of the constituents (in this case, the glass fiber) can be burned away, leaving the other constituent (in this case, the epoxy resin) behind. However, Kevlar is a synthetic fiber made from aramid, which does not burn away during the burnout test. Therefore, the burnout test cannot be used to determine the volume fractions in Kevlar/epoxy composites.

To solve this problem, we need to calculate the weight and volume fractions of glass fiber and epoxy resin in the composite. We can use the following formulas:

Weight fraction = (Weight of component / Weight of composite) * 100
Volume fraction = (Weight fraction / Density of component) * (Density of composite / 100)

Let's calculate the weight fraction and volume fraction for each component:

(a) For the glass fiber:
Weight of glass fiber = Weight of composite - Weight of crucible = 50.2417 g - 47.6504 g = 2.5913 g
Weight fraction of glass fiber = (2.5913 g / 50.2417 g) * 100 = 5.15%

Volume fraction of glass fiber = (5.15% / 2.5 g/cm3) * (1.2 g/cm3 / 100) = 0.0206 or 2.06%

For the epoxy resin:
Weight of epoxy resin = Weight of glass after burnout - Weight of empty crucible = 49.7576 g - 47.6504 g = 2.1072 g
Weight fraction of epoxy resin = (2.1072 g / 50.2417 g) * 100 = 4.19%

Volume fraction of epoxy resin = (4.19% / 1.2 g/cm3) * (1.2 g/cm3 / 100) = 0.0349 or 3.49%

(b) The burnout test cannot be used for Kevlar/epoxy composites. The burnout test relies on the fact that one of the components can be burned off completely, leaving only the other component. In the case of glass/epoxy composites, the epoxy resin can be burned off, leaving only the glass fiber. However, Kevlar is a synthetic fiber made of aramid, which cannot be easily burned off. Therefore, the burnout test cannot be used to separate the Kevlar fiber from the epoxy resin in Kevlar/epoxy composites.