Chapter 10, Problem 62 GO One end of a piano wire is wrapped around a cylindrica

Question

Chapter 10, Problem 62 GO One end of a piano wire is wrapped around a cylindrical tuning peg and the other end is fixed in place. The tuning peg is turned so as to stretch the wire. The piano wire is made from steel 2.0x10 N/m2). It has a radius of 0.59 mm and an unstrained length tuning peg is 1.2 mm. Initially, there is no tension in the wire, but when the tuning peg is turned, tension develops. Find the tension in the wire when the tuning peg is turned through two of 0.50 m. The radius of the revolutions. 7.4v/0.2 m

Explanation / Answer

elongation of wire = 2*2*pi*1.2=15.08 mm

strain in wire=15.08/500=0.03

tensile stress in wire=2*1011*0.03=6.03*109 N/m2

area of cross section of wire=pi*(0.59*10-3)2 =1.09*10-6 m2

tension in wire =6.03*109 *1.09*10-6 =6594.3 N =6.59 kN

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