Question

A piano wire 0.90 m long and 0.85 mm in diameter is fixed on one end. The other end is wrapped around a tuning peg 3.5 mm in diameter. Initially the wire, whose Young's modulus is 2.4×1010N/m2, has a tension of 30 N .

Part A Find the tension in the wire after the tuning peg has been turned through one complete revolution. Express the tension in newtons to two significant figures. T = 166.16   N   SubmitPrevious AnswersRequest Answer Incorrect; Try Again; 2 attempts remaining

Answer 1

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}

= T_new = T_old + ΔF
          = (30.0 N) +(153.8 N)
          = 183.8  N