Final answer:
To calculate the final volume of the stretched copper rod, stress and strain due to the applied force are computed, the change in length is determined, and this is used to calculate the final volume of the rod.
Step-by-step explanation:
The question asks to calculate the final volume of a cylindrical copper rod when it is stretched with a load. To find the final volume, we need to determine the change in length of the rod due to the stress applied and then calculate the new volume. Using Hooke's law, stress (σ) is equal to the force (F) divided by the cross-sectional area (A), and strain (ε) is equal to stress (σ) divided by the modulus of elasticity (E).
First, we calculate the stress using the formula σ = F / A. Substituting the given values, we get σ = (4.0*10^5 N) / (1.2 cm²). Next, we calculate strain using the formula ε = σ / E. The modulus of elasticity for copper (E) is given as 70 GPa, which we need to convert to the same units as stress (N/cm²).
After finding the strain, we use it to calculate the change in length (ΔL) using the formula ΔL = ε * L, where L is the original length of the rod. Finally, the final volume (Vₓ) is determined by the formula Vₓ = V₀ + (A * ΔL), where V₀ is the original volume of the rod.
It's important to mention that the student should confirm that the stress applied does not exceed the yield strength (σy) or the tensile strength (σTS) of copper, to ensure that the material does not fail or deform in an irreversible way.