A copper alloy wire of length 2.0 m, cross sectional area 7.1 × 10−6 m2, and Young's modulus 11 × 1010 N/m2, has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)Select one:a.0.50 mmb.5.0 mmc.2.5 mmd.1.0 mm
Question
A copper alloy wire of length 2.0 m, cross sectional area 7.1 × 10−6 m2, and Young's modulus 11 × 1010 N/m2, has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)Select one:a.0.50 mmb.5.0 mmc.2.5 mmd.1.0 mm
Solution
To solve this problem, we need to use the formula for stress and strain in a material.
Stress (σ) is defined as the force (F) divided by the area (A) it is applied over. Strain (ε) is defined as the change in length (ΔL) divided by the original length (L).
The Young's modulus (Y) of a material is the ratio of stress to strain, so we can write this as:
Y = σ/ε
Rearranging this gives us:
ε = σ/Y
We can substitute the formulas for stress and strain into this equation to get:
ΔL/L = F/(AY)
We can now substitute the given values into this equation:
F = 200 kg * 9.8 m/s^2 = 1960 N (this is the weight of the load, which is the force due to gravity)
A = 7.1 × 10^-6 m^2
Y = 11 × 10^10 N/m^2
L = 2.0 m
So,
ΔL = (F * L) / (A * Y) = (1960 N * 2.0 m) / (7.1 × 10^-6 m^2 * 11 × 10^10 N/m^2)
Calculating this gives:
ΔL = 0.0005 m, or 0.5 mm
So, the increase in length of the wire is 0.5 mm. Therefore, the correct answer is a. 0.50 mm.
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