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A piano wire 0.82 m long and 0.93 mm in diameter is fixed
Chapter 17, Problem 45P(choose chapter or problem)
Problem 45P
A piano wire 0.82 m long and 0.93 mm in diameter is fixed on one end. The other end is wrapped around a timing peg 3.5 mm in diameter. Initially the* wire, whose Young’s modulus is 2.4 × 1010 N/m2, has a tension of 14 N. Find the tension in the wire after the tuning peg has been turned through one complete revolution.
Questions & Answers
QUESTION:
Problem 45P
A piano wire 0.82 m long and 0.93 mm in diameter is fixed on one end. The other end is wrapped around a timing peg 3.5 mm in diameter. Initially the* wire, whose Young’s modulus is 2.4 × 1010 N/m2, has a tension of 14 N. Find the tension in the wire after the tuning peg has been turned through one complete revolution.
ANSWER:
Step 1 of 3
A piano wire is fixed at one end and wrapped around a tuning peg on the other end. Rotating the tuning peg by a full revolution stretches the wire and increases the tension in the wire.
The equation that gives the relation between the stretch in the wire and the tension in the wire is
Now, turning the tuning peg through one complete revolution is equivalent to acting on the wire by a force (tension) that increases the length of the wire by an amount equal to the circumference of the tuning peg. Hence, the change in the length of the wire is
