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A force of 20 N is applied to a material with a cross-sectional area of 5 cm2. Calculate the stress.

Physics

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Answer

4×104 Pa\mathbf{4 \times 10^4\, Pa}

Step-by-step solution

3 steps

Here's the solution to the problem:

  1. Identify the given values and the formula for stress.

    The force applied, F=20 NF = 20\, \text{N}.
    The cross-sectional area, A=5 cm2A = 5\, \text{cm}^2.
    The formula for stress (σ\sigma) is:

    σ=FA\sigma = \frac{F}{A}
  2. Convert the cross-sectional area from cm2\text{cm}^2 to m2\text{m}^2.

    Since 1 m=100 cm1\, \text{m} = 100\, \text{cm}, then 1 m2=(100 cm)2=10000 cm21\, \text{m}^2 = (100\, \text{cm})^2 = 10000\, \text{cm}^2.
    Therefore, to convert cm2\text{cm}^2 to m2\text{m}^2, we divide by 10000.

    A=5 cm2×1 m210000 cm2=5×10−4 m2A = 5\, \text{cm}^2 \times \frac{1\, \text{m}^2}{10000\, \text{cm}^2} = 5 \times 10^{-4}\, \text{m}^2
  3. Calculate the stress using the formula.

    Substitute the force and the converted area into the stress formula:

    σ=20 N5×10−4 m2\sigma = \frac{20\, \text{N}}{5 \times 10^{-4}\, \text{m}^2} σ=205×104 N/m2\sigma = \frac{20}{5} \times 10^4\, \text{N/m}^2 σ=4×104 Pa\sigma = 4 \times 10^4\, \text{Pa}

    The stress is 4×104 Pa\mathbf{4 \times 10^4\, Pa}.

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