A material has stress \(60\,\mathrm{MPa}\) and strain \(3.0\times10^{-4}\). Find Young's modulus.

State the modulus used for a change in volume under pressure.

A wire has \(Y=1.6\times10^{11}\,\mathrm{Pa}\), \(L=2.0\,\mathrm{m}\), \(A=3.0\times10^{-6}\,\mathrm{m^2}\), and load \(480\,\mathrm{N}\). Find its extension.

A block has shear modulus \(G=8.0\times10^{9}\,\mathrm{Pa}\) and shear strain \(2.0\times10^{-5}\). Find the shear stress.

Pressure on a liquid increases by \(4.5\,\mathrm{MPa}\). Its bulk modulus is \(1.5\,\mathrm{GPa}\). Find \(\Delta V/V\).

A rod has \(Y=70\,\mathrm{GPa}\), area \(5.0\times10^{-5}\,\mathrm{m^2}\), and length \(0.80\,\mathrm{m}\). Find its axial stiffness \(k_{\mathrm{axial}}\).

Two wires have the same material and length. Wire A has twice the area of wire B. Compare their axial stiffnesses and extensions under the same load.

A \(1.0\,\mathrm{m}\) steel wire with \(Y=2.0\times10^{11}\,\mathrm{Pa}\) must extend by no more than \(1.0\,\mathrm{mm}\) under \(500\,\mathrm{N}\). Find the minimum area.

Two rods of equal length \(L\) are fixed between the same rigid plates and carry a total tensile load \(P\). Rod 1 has \(Y_1,A_1\); rod 2 has \(Y_2,A_2\). Derive each rod's load share and the common extension. State assumptions and interpret the stiffer-rod limit.

Two axial members are connected in series and carry the same tensile load \(P\). Member \(i\) has \(Y_i,A_i,L_i\). Derive the equivalent axial stiffness and a symbolic condition for total extension to stay below \(\delta_{\max}\). State assumptions and interpret which member dominates compliance.