Sample 1, Original Length 250 mm and 10 mm Diameter, Length after testing 250.23 mm the force used for the test was 15KN

Calculate the Stress and Strain for each of the Samples and from this and, assuming the material has remained within the elastic limit, determine their modulus of elasticity.

please help

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To calculate the stress and strain, we will need to use the formulas:

1. Stress (σ) = Force (F) / Area (A)
2. Strain (ε) = Change in Length (ΔL) / Original Length (L0)

We have the following information:
Original Length (L0) = 250 mm
Change in Length (ΔL) = 250.23 mm - 250 mm = 0.23 mm
Diameter (D) = 10 mm

First, we need to calculate the area (A) of the sample using the formula for the area of a circle:
Area (A) = π * (D/2)^2

Substituting the values into the formula:
A = π * (10 mm / 2)^2
= π * (5)^2
= 3.14 * 25
= 78.5 mm^2

Now we can calculate the stress (σ):
Stress (σ) = Force (F) / Area (A)
= 15 kN / 78.5 mm^2
≈ 0.191 kN/mm^2

Next, we can calculate the strain (ε):
Strain (ε) = Change in Length (ΔL) / Original Length (L0)
= 0.23 mm / 250 mm
≈ 0.00092

To determine the modulus of elasticity, we can use the formula:

Modulus of Elasticity (E) = Stress (σ) / Strain (ε)

Substituting the values:
Modulus of Elasticity (E) = 0.191 kN/mm^2 / 0.00092
≈ 207.61 kN/mm^2 (or 207.61 GPa)

Therefore, the calculated modulus of elasticity for this sample, assuming it remains within the elastic limit, is approximately 207.61 GPa.