Final Answer:
a) The stress acting on the rod would be approximately 1.45 x 10^9 N/m^2.
b) The strain felt by the rod would be approximately 2.04 x 10^-4.
c) The change in length of the rod would be approximately 1.63 cm.
Step-by-step explanation:
a) Calculate the stress:
Convert the given values to SI units:
Length (L) = 8.0 ft = 2.44 m
Diameter (d) = 0.25 mm = 2.5 x 10^-4 m
Young's modulus (Y) = 71.3 GPa = 71.3 x 10^9 N/m^2
Force (F) = 175 N
Calculate the cross-sectional area (A):
A = π * (d/2)^2
A ≈ 4.91 x 10^-7 m^2
Calculate the stress (σ):
σ = F / A
σ ≈ 1.45 x 10^9 N/m^2
b) Calculate the strain:
Strain (ε) is the change in length (ΔL) divided by the original length (L):
ε = ΔL / L
We haven't calculated the change in length yet. However, we know the stress and Young's modulus:
σ = Y * ε
2.04 x 10^-4 = 71.3 x 10^9 N/m^2 * ε
ε ≈ 2.04 x 10^-4
c) Calculate the change in length:
Substitute the strain into the strain definition:
ΔL = ε * L
ΔL ≈ 2.04 x 10^-4 * 2.44 m
ΔL ≈ 0.00163 m = 1.63 cm
Therefore:
The stress acting on the rod is approximately 1.45 x 10^9 N/m^2.
The strain felt by the rod is approximately 2.04 x 10^-4.
The change in length of the rod is approximately 1.63 cm.