A wire of length 5.0m and diameter 2.0mm extends by 0.025mm when a force of 50N was used to stretch it from one end. Calculate:
a.)Stress on the wire
b.)Strain on the wire
c.) Young's Modulus
To solve this problem, we need to use the formulas related to stress, strain, and Young's modulus. Let's go step by step:
a.) Stress on the wire:
Stress (𝜎) is defined as the force applied per unit area. It can be calculated using the formula:
𝜎 = F / A
where 𝜎 is the stress, F is the force applied, and A is the cross-sectional area of the wire.
To find the stress, we need to calculate the cross-sectional area of the wire first. The cross-sectional area (𝐴) of a wire is given by the formula:
A = πr^2
where r is the radius of the wire.
Given that the diameter of the wire is 2.0mm, we can calculate the radius (𝑟) by dividing the diameter by 2:
r = 2.0mm / 2 = 1.0mm = 0.001m
Now, we can calculate the stress:
𝜎 = F / A
𝜎 = 50N / (π * (0.001m^2))
𝜎 ≈ 50N / (3.14 * 0.001m^2)
Therefore, the stress on the wire is approximately equal to 50N / (3.14 * 0.001m^2).
b.) Strain on the wire:
Strain (𝜀) is defined as the deformation per unit length of an object compared to its original length. It can be calculated using the formula:
𝜀 = ΔL / L
where 𝜀 is the strain, ΔL is the change in length, and L is the original length.
Given that the wire extended by 0.025mm, we know ΔL = 0.025mm = 0.025 * 10^-3m. The original length (L) of the wire is given as 5.0m.
Now, we can calculate the strain:
𝜀 = ΔL / L
𝜀 = (0.025 * 10^-3m) / 5.0m
Therefore, the strain on the wire is approximately equal to (0.025 * 10^-3m) / 5.0m.
c.) Young's Modulus:
Young's modulus (𝐸) is a measure of the stiffness of a material. It quantifies the relationship between stress and strain. Young's modulus can be calculated using the formula:
𝐸 = 𝜎 / 𝜀
where 𝐸 is Young's modulus, 𝜎 is stress, and 𝜀 is strain.
Using the previously calculated values for stress and strain, we can find Young's modulus:
𝐸 = 𝜎 / 𝜀
𝐸 ≈ (50N / (3.14 * 0.001m^2)) / ((0.025 * 10^-3m) / 5.0m)
Therefore, Young's modulus is approximately equal to (50N / (3.14 * 0.001m^2)) / ((0.025 * 10^-3m) / 5.0m).