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Brass cross

How much does it stretch?
A brass wire with Young's modulus of 9.2 x 10^10 Pa is 2.1 m long and has a cross-sectional area of 4.5 mm^2. If a weight of 5.5 kN is hung from the wire, by how much does it stretch?
? cm
4.5 mm^2 = 4.5 * 10^-6 m^2
5.5 kN = 5500 N
The tensile stress in the wire is:
Stress = F / A
Stress = 5500 N / (4.5 * 10^-6 m^2)
Stress = 1.2222 * 10^9 Pa
If this is still in the elastic regime of the brass's stress-strain curve, then the fractional increase in the wire's length is:
ΔL / L = (1.2222 * 10^9 Pa) / (9.2 * 10^10 Pa)
ΔL / L = 0.013285
The absolute change in length is:
ΔL = (ΔL / L) * L
ΔL = (0.013285) * (2.1 m)
ΔL = 0.0278986 m
The wire increases in length by 0.0279 meters, or 27.9 millimeters.
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The Cross of Honour - Darwen Brass




















































