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A piano wire 0.90 m long and 0.85 mm in diameter is fixed on one end....

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Physics

A piano wire 0.90 m long and 0.85 mm in diameter is fixed on oneend. The other end is wrapped around a tuning peg 3.5 mm indiameter. Initially the wire, whose Young's modulus is2.4×1010N/m2,
has a tension of 30 N .

Part A

Find the tension in the wire after the tuning peg has beenturned through one complete revolution.

Express the tension in newtons to two significant figures.

T =

166.16

  N  

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Answer & Explanation Solved by verified expert
4.1 Ratings (503 Votes)

ans)

from above data that

given that

{Initial Length} = L0 = 0.90 m

we know that
{Initial Cross Section Area} = A0 = π*D2/4
         = π*(0.85e-3 m)2/4
          = 5.67 e-7m3

{Stretch Length} = ΔL = π*(3.5e-3m) = 1.09 e-2m

{ΔForce} = ΔF = E*A0*ΔL/L0 =                            (<--- E = Young's Modulus)
             = (2.24e+10 N/m2)*(5.67 e-7 m3 )*(1.09 e-2 m)/(0.90 m)
             = 153.8N

{New Wire Tension}

= Tnew = Told + ΔF
          = (30.0 N) +(153.8 N)
          = 183.8  N
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