Mechanical Properties of Solids — Practice

Question 1

A 3 m steel wire (Y = 2e11 Pa, area 2 mm^2) carries a 100 kg load. Find the elongation (g = 10 m/s^2).

Accepted Answer

F = mg = 1000 N. delta-L = FL/(AY) = (1000 x 3)/(2e-6 x 2e11) = 3000/4e5 = 7.5e-3 m = 7.5 mm.

Question 2

Water is compressed by 1%. Find the pressure increase (B = 2.2e9 Pa).

Accepted Answer

B = -delta-P/(delta-V/V), so delta-P = B x |delta-V/V| = 2.2e9 x 0.01 = 2.2e7 Pa = 22 MPa.

Question 3

A steel wire (L = 2 m, area 1 mm^2, Y = 2e11 Pa) is stretched by 1 mm. Find the energy stored.

Accepted Answer

U = (1/2)(YA/L)(delta-L)^2 = (1/2)(2e11 x 1e-6 / 2)(0.001)^2 = (1/2)(1e5)(1e-6) = 0.05 J.

Question 4

Which has the higher Young's modulus, rubber or steel?

Accepted Answer

Steel (about 2e11 Pa). Rubber's Young's modulus is far lower (about 1e6 Pa), so it stretches much more for the same stress.

Question 5

Why does a wire become thinner when stretched?

Accepted Answer

Because of the Poisson effect: longitudinal extension is accompanied by lateral contraction. The ratio of lateral to longitudinal strain is Poisson's ratio.

Practice — Mechanical Properties of Solids

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