Read Stress, Strain and Modulus from the Wire Geometry

The slope of a stress-strain graph is Y, while the slope of a load-extension graph is Y A / l, so for wires of the same material and length a thinner wire has a smaller slope, and for wires of identical dimensions the one with the steeper load-extension line has the larger Y.

Two wires of the same material and length stretched by the same force with diameters in the ratio 1 : 2 have stresses in the ratio 4 : 1 (area goes as the square of diameter), so their energies per unit volume are in the ratio 16 : 1.

When a wire of fixed volume V is drawn to length l, its area is A = V/l, so Δl = F l / (A Y) = F l² / (V Y): extension is proportional to l², and the straight-line graph is Δl against l². For two wires of equal volume with areas A and 2A, the lengths are in the ratio 2 : 1; write the extension formula for each, then equate the extensions or ratios. Always write F l / (A Y) for each wire in the problem before comparing.

The moduli are linked by Y = 2η(1 + σ) = 3B(1 - 2σ), where η is the rigidity modulus and σ is Poisson's ratio: if Y = 2.4 η then 1 + σ = 1.2 and σ = 0.2. A wire hanging under its own weight breaks when the stress at the top, ρ g l, reaches the breaking stress, so the maximum length is l = (breaking stress) / (ρ g).

On a plot of potential energy U against the separation r of two atoms, the equilibrium separation is where U is a minimum, because the force F = -dU/dr is zero there. For r smaller than that value the force is repulsive, and for larger r it is attractive; the depth of the minimum below zero is the binding energy. Read statements about equilibrium separation, force and energy directly off the position of the minimum.