The figure shows the stress versus strain plot for an aluminum wire that is stre

Question

The figure shows the stress versus strain plot for an aluminum wire that is stretched by a machine pulling in opposite directions at the two ends of the wire. The scale of the stress axis is set by s = 7.0 in units of 107 N/m2. The wire has an initial length of 0.5 m and an initial cross-sectional area of 5.00E-6 m2. How much work does the force from the machine do on the wire to produce a strain of 1.0E-3?

The figure shows the stress versus strain plot for an aluminum wire that is stretched by a machine pulling in opposite directions at the two ends of the wire. The scale of the stress axis is set by s = 7.0 in units of 10^7 N/m^2. The wire has an initial length of 0.5 m and an initial cross-sectional area of 5.00E-6 m^2. How much work does the force from the machine do on the wire to produce a strain of 1.0E-3?

Explanation / Answer

from strain = e / L , elongation e = strain x L = 1.0 x10^-3 x 1.3 = 1.3 x10^-3
and sress = F / A, so that F = stress x A = 7 x10^7 x 5 x10^-6 = 350 N

and then stain energy in the wire Es = (1/2) F e = (1/2) x 350 x 1.3 x10^-3 J

ie., Es = 227.5 x10^-3 J = 227.5 m J.

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