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Calculate the tensile stress in a rod with a diameter of 80 mm subjected to a tensile force of 900 N. Express the answer in MPa.

Physics

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Answer

0.179 MPa\text{0.179 MPa}

Step-by-step solution

3 steps
  1. Calculate the cross-sectional area of the rod.

    The diameter of the rod is D=80 mmD = 80 \text{ mm}.
    First, convert the diameter to meters: D=80×10−3 m=0.08 mD = 80 \times 10^{-3} \text{ m} = 0.08 \text{ m}.
    The radius of the rod is r=D/2=0.08 m/2=0.04 mr = D/2 = 0.08 \text{ m} / 2 = 0.04 \text{ m}.
    The cross-sectional area AA of a circular rod is given by the formula A=πr2A = \pi r^2.

    A=π(0.04 m)2=π×0.0016 m2≈0.0050265 m2A = \pi (0.04 \text{ m})^2 = \pi \times 0.0016 \text{ m}^2 \approx 0.0050265 \text{ m}^2
  2. Calculate the tensile stress.

    Tensile stress (σ\sigma) is defined as the tensile force (FF) divided by the cross-sectional area (AA).
    The tensile force is given as F=900 NF = 900 \text{ N}.

    σ=FA=900 N0.0050265 m2\sigma = \frac{F}{A} = \frac{900 \text{ N}}{0.0050265 \text{ m}^2} σ≈179047.6 Pa\sigma \approx 179047.6 \text{ Pa}
  3. Convert the stress to megapascals (MPa).

    Since 1 MPa=106 Pa1 \text{ MPa} = 10^6 \text{ Pa}, we divide the stress in Pascals by 10610^6.

    σ≈179047.6106 MPa≈0.179 MPa\sigma \approx \frac{179047.6}{10^6} \text{ MPa} \approx 0.179 \text{ MPa}

    The tensile stress is 0.179 MPa\text{0.179 MPa}.

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