Final answer:
To calculate Young's modulus for a metal rod subjected to tensile stress, divide the tensile force by the cross-sectional area to get stress, then divide the change in length by the original length to get strain. Young's modulus is the ratio of stress to strain. For the given rod with a tensile force of 8,052 N and a stretch of 0.78 cm, Young's modulus is 1.61 x 10¹ N/m².
Step-by-step explanation:
To calculate the Young's modulus for the metal of the rod, we need to use the formula defining Young's modulus (Y), which relates tensile stress (σ) to tensile strain (ε):
Y = σ / ε
Firstly, we calculate the tensile stress by dividing the tensile force (F) by the cross-sectional area (A), σ = F / A. Secondly, we calculate tensile strain by dividing the change in length (ΔL) by the original length (L), ε = ΔL / L.
Given: F = 8,052 N, A = 0.41 cm² = 0.41 x 10⁻´ m², ΔL = 0.78 cm = 0.78 x 10⁻² m, and L = 6.4 m.
Tensile stress (σ) = 8,052 N / (0.41 x 10⁻´ m²) = 1.96341 x 10⁸ N/m².
Tensile strain (ε) = 0.78 x 10⁻² m / 6.4 m = 1.21875 x 10⁻´.
Now, we can find Young's modulus (Y) by dividing stress by strain.
Y = (1.96341 x 10⁸ N/m²) / (1.21875 x 10⁻´) = 1.61 x 10¹ N/m².
Therefore, the Young's modulus for this metal is 1.61 x 10¹ N/m².