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Where necessary, use pi = 3,142 throughout this activity

Physics

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2 parts
a

265.22 MPa\text{265.22 MPa}

b
0.125

Step-by-step solution

5 steps

Here's the solution for question 5:

Part a· 3 steps

The stress.

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

    The diameter (DD) is 12 mm12 \text{ mm}, which is 12×10−3 m12 \times 10^{-3} \text{ m}. The area (AA) of a circular cross-section is given by π(D2)2\pi \left(\frac{D}{2}\right)^2. Use π=3.142\pi = 3.142.

    A=π(D2)2A = \pi \left(\frac{D}{2}\right)^2 A=3.142×(12×10−3 m2)2A = 3.142 \times \left(\frac{12 \times 10^{-3} \text{ m}}{2}\right)^2 A=3.142×(6×10−3 m)2A = 3.142 \times (6 \times 10^{-3} \text{ m})^2 A=3.142×(36×10−6 m2)A = 3.142 \times (36 \times 10^{-6} \text{ m}^2) A=1.13112×10−4 m2A = 1.13112 \times 10^{-4} \text{ m}^2
  2. Convert the force to Newtons.

    The force (FF) is 30 kN30 \text{ kN}, which is 30×103 N30 \times 10^3 \text{ N}.

  3. Calculate the stress in the rod.

    Stress (σ\sigma) is force per unit area.

    σ=FA\sigma = \frac{F}{A} σ=30×103 N1.13112×10−4 m2\sigma = \frac{30 \times 10^3 \text{ N}}{1.13112 \times 10^{-4} \text{ m}^2} σ=265221000.7 Pa\sigma = 265221000.7 \text{ Pa} σ=265.22×106 Pa\sigma = 265.22 \times 10^6 \text{ Pa} σ=265.22 MPa\sigma = \boxed{\text{265.22 MPa}}

Part b0.125

The strain.

  1. Identify the change in length and original length.

    The change in length (ΔL\Delta L) is 0.3 m0.3 \text{ m}. The original length (LL) is 2.4 m2.4 \text{ m}.

  2. Calculate the strain.

    Strain (ϵ\epsilon) is the ratio of the change in length to the original length.

    ϵ=ΔLL\epsilon = \frac{\Delta L}{L} ϵ=0.3 m2.4 m\epsilon = \frac{0.3 \text{ m}}{2.4 \text{ m}} ϵ=0.125\epsilon = 0.125 ϵ=0.125\epsilon = \boxed{0.125}
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