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Engineering and Tech / Mechanics of Materials 7 / Chapter 2 / Problem 2.29

Mechanics of Materials | 7th Edition | ISBN: 9780073398235 | Authors: Ferdinand P. Beer; E. Russell Johnston Jr.; John T. DeWolf; David F. Mazurek

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A homogenous cable of length L and uniform cross section

Chapter 2, Problem 2.29

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QUESTION:

A homogenous cable of length L and uniform cross section is suspended from one end. (a) Denoting by \(\rho\) the density (mass per unit volume) of the cable and by E its modulus of elasticity, determine the elongation of the cable due to its own weight. (b) Show that the same elongation would be obtained if the cable were horizontal and if a force equal to half of its weight were applied at each end.

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QUESTION:

A homogenous cable of length L and uniform cross section is suspended from one end. (a) Denoting by \(\rho\) the density (mass per unit volume) of the cable and by E its modulus of elasticity, determine the elongation of the cable due to its own weight. (b) Show that the same elongation would be obtained if the cable were horizontal and if a force equal to half of its weight were applied at each end.

ANSWER:

Step 1 of 3

(a) For element at point identified by coordinate y,Refer to figure below.

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