Question

A piano wire 0.70 m long and 0.70 mm in diameter is fixed on one end. The other end is wrapped around a tuning peg 4.5 mm in diameter. Initially the wire, whose Young's modulus is 2.4× 10 10 N/ m 2 , has a tension of 20 N . Find the tension in the wire after the tuning peg has been turned through one complete revolution.

Answer 1

Cross - sectional area of wire A = 172 - (0.35 x 10-3) : A = 3.85 x 10-7 m2 In one revolution, change in length of the wire AL = circumference of, the peg - 20r = id = 3.14 4.5 x163 . AL : 14:13 x 10-3 m Young's modulus Y = 2.4 x 10 Initial length of wire - 0.70 m We have the relation Āx AL Lo : F. AYAL Lo 3.85 x 10-7 x 2.4 x 100 x 14.13 x 10-3 0.70 .. F = 186.52 N