Each solution should contain: Data, Find, Diagram, Formulas, Algebraic manipulat

Question

Each solution should contain: Data, Find, Diagram, Formulas, Algebraic manipulations, Unit conversions, Numerical evaluations, Unit calculations/cancellations.

Problem #6 A circular steel wire 5.00 m long must stretch no more than 5.00 mm when a tensile force of 500 Nis applied at each end of the wire. What is the minimum diameter required for the wire? TABLE 12.1 Typical Values for Elastic Modulus Young's Modulus Shear Modulus Bulk Modulus (N/m2) (N/m2) (N/m2) Substance 14 x 1010 35 x 1010 20 x 10 Tungsten 20 x 10 8.4 x 10 6 x 10 Steel 11 x 1010 4.2 x 10 14 x 10 Copper 3.5 x 1010 9.1 x 10 6.1 x 10 7.0 x 1010 2.5 x 1010 7.0 X 10 Aluminum 65-7.8 x 1010 2.6-3.2 x 101 5.0-5.5 X 100 Glass 5.6 x 1010 2.6 x 1010 2.7 x 10 Quartz Water 0.21 X 10 2.8 x 10 Mercury

Explanation / Answer

L = 5 m , DL = 5 mm, F = 500 N,

young modulus of steel wire Y = 20*10^10 N/m^2

Y = tensile stress/tensile strain

Y = (F/A)/(DL/L)

20*10^10 = (100*4/(3.14*d^2))(5/0.005)

d = 0.798 mm

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