you tighten the guitar strings that are made of steel (young\'s modulus = 2.0 X1

Question

you tighten the guitar strings that are made of steel (young's modulus = 2.0 X10^11 N/m^2). One end of the steel string is wrapped around a tuning peg that is a cylinder of radius 5.0 mm. when you turn the peg using a knob on the side of the guitar, you are applying a force on the string because of which the length of the string increases. Before you turn the knob, the guitar string has an original length of 0.75 m and a radius of .2m, find the tension force acting on the guitar string when you turn the tuning peg through two revolutions.

Explanation / Answer

Apply Y = FLo/A(delta L)

delta L = 2(2pi)(.005) = .0628 m

Then (2 X 1011) = F(.75)/(pi)(.005)2(.0628)

F = 1.32 X 106 N

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