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When the mass is removed, the length of the cable is found to be l0 = 4.66 m. After the mass is added, the length is remeasured and found to be l1 = 5.31 m. Determine Young's Modulus Y in N/m2 for the steel cable if the weight has a mass m = 55 kg and the cable has a radius r = 0.045 m.

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Answer:

[tex]\gamma=6.07*10^5\frac{N}{m^2}[/tex]

Explanation:

For a linear elastic material Young's modulus is a constant that is given by:

[tex]\gamma=\frac{F/A}{\Delta L/L_0}[/tex]

Here, F is the force exerted on an object under tensio, A is the area of the cross-section perpendicular to the applied force, [tex]\Delta L[/tex] is the amount by which the length of the object changes and  [tex]L_0[/tex] is the original length of the object. In this case the force is the weight of the mass:

[tex]F=mg\\F=55kg(9.8\frac{m}{s^2})\\F=539N[/tex]

Replacing the given values in Young's modulus formula:

[tex]\gamma=\frac{F/\pi r^2}{(L_1-L_0)/L_0}\\\gamma=\frac{539N/\pi(0.045m)^2}{(5.31m-4.66m)/4.66m}\\\gamma=6.07*10^5\frac{N}{m^2}[/tex]

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