An aluminum cable with cross-sectional area 1.50 times 10^-6 m^2 is suspended fr

Question

An aluminum cable with cross-sectional area 1.50 times 10^-6 m^2 is suspended from the ceiling. A mass is suspended from the free end of the cable to keep the cable straight and at a certain length. If the temperature of the cable is reduced by 10 C degree, by how much should the suspended mass be increased so that the length of the cable remains the same? The coefficient of linear expansion for aluminum is alpha = 23 times 10^-6 /C degree; Young's modulus for aluminum is E = 70 times 10^9 N/m^2. Ignore changes in the cross-sectional area of the cable.

Explanation / Answer

the Young's modulus is expressed as,

E = FL/AdL

F = [AE]dL/L

mg =  [AE][alpha*dT]

the mass is,

m =  [AE][alpha*dT] /g

= 1.5x10-6*70x109*23x10-6*10 / 9.8

= 2.46 kg

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