Let's begin with a very simple application of Y$=$StressStrain. A small elevator with a mass of $550$ kg hangs from a steel cable that is $3\mathrm{.}0$ m long when not loaded. The wires making up the cable have a total cross$-$sectional area of $0\mathrm{.}20$ cm$2,$ and with a $550$ kg load, the cable stretches $0\mathrm{.}40$ cm beyond its unloaded length. Determine the cable's stress and strain. Assuming that the cable is equivalent to a rod with the same cross$-$sectional area, determine the value of Young's modulus for the cable's steel. If the elevator were suspended from a cable made of tungsten, with a Young's modulus of $3\mathrm{.}61011$Pa$,$ how far would the cable stretch under the $550$ kg load?

Express your answer in centimeters.