Problem 9.8

จาก \(Y = \frac{σ}{ε}\)

\(Y =\frac{FL}{A\Delta L}\)

\(F = (\frac{YA}{L})\Delta L\)

\(\Delta L =\frac{FL}{YA}\)

พิจารณาในส่วนของเหล็ก

จะได้ \(ΔL = \frac{FL}{YA}=\frac{(10,000 N )L}{(2.0\times 10^{11} N/m^{2})(0.25\times 10^{-4} m^{2})}= 2\times 10^{-3}L\)

พิจารณาบริเวณรอยต่อระหว่างเหล็กกับทองแดง

จาก \(F_{1} = F_{2}\)

\(\frac{Y_{1}A\Delta L_{1}}{L_{1}}=\frac{Y_{2}A\Delta L_{2}}{L_{2}}\)

\(\frac{Y_{1}\Delta L}{L}=\frac{Y_{2}(0.0080 - \Delta L)}{3.0 - L}\)

\(\frac{(2.0\times 10^{11} N/m^{2})\Delta L}{L}=\frac{(1.2\times 10^{11} N/m^{2})(0.0080 - \Delta L)}{3.0 - L}\)

\(2\Delta L(3.0 - L) = 1.2L(0.0080 - \Delta L)\)

\(2(2\times 10^{-3}L)(3.0 - L) = 1.2L(0.0080 - (2\times 10^{-3}L))\)

\(12 - 4L = 9.6 - 2.4L\)

\(L = 1.5 m \;\blacksquare\)