(a) A steel wire of mass μ per unit length with a circular cross-section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs
from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find
the extension in the length of the wire. The density of steel is 7860 kg/m3.
(b) If the yield strength of steel is 2.5 × 108 N/m2, what is the maximum weight that can be hung at the lower end of the wire?
Let dx be the small element
Let dm be the mass
Let L be the length of the wire
Let x be the distance from the end where it is hung
Let μ be the mass per unit length
Therefore,
dm = μ.dx
r = 0.1 cm
A = π(10)-3
M = 25 kg
L = 10 m
a) The downward force is used for calculating the mass, m = 0.25 kg
b) The maximum weight that can be hung at the lower end of the wire is calculated using the tension in the wire which is the maximum at x = L
Therefore, the mass is = 78.25 kg
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