Section 2 review
The design process consists of a cycle of creation, analysis, and revision, in which a human need is to be satisfied with real-world materials. The design process makes use of physics while also accounting for cost and ensuring safety in unusual circumstances. A bridge or building will include a safety factor so that its critical components can withstand 10–20 times the forces expected in regular use; this provides some protection against rare but dangerous events. Extremely flexible structural elements such as ropes and chains only bear tension (pulling forces). Stiffer materials (such as beams) can withstand stress and shear (caused by pushing) as well as tension. Read the text aloud
safety factor, stress, tensile strength

F =0
τ=0

Review problems and questions

  1. A 35 kg lighting fixture hangs from a chain in a restaurant dining room. The builder chose a 4-mm-gauge chain with a breaking strength of 5,000 N, for this application. What safety factor does this imply? Read the text aloud Show
  1. A steel cable is used to lift a 24,000 kg container from a cargo ship. The tensile strength of steel is 2.50×108 N/m2.
    1. What is the minimum cross-sectional area of the cable that can support this load? (Do not include a safety factor.)
    2. What is the diameter of this cable? Read the text aloud Show
Acrobat standing on beam held by two chains
  1. A 60 kg acrobat stands upon a 3-m-long, 20 kg beam that is hanging from two chains. He stands a distance dp from the right-hand chain. When computing torques, consider the right-hand end of the beam to be the center of rotation.
    1. Calculate the tension in each of the two chains when dp = 1.5 m (that is, when the acrobat is standing on the center of the beam).
    2. The acrobat moves a half-meter toward the right-hand chain (that is, to dp = 1.0 m). Calculate the tension in each of the two chains.
    3. How did TL and TR each change?
    4. Predict the values of TL and TR if the acrobat were to slide another 0.5 m to the right.
    5. Test your predictions by performing the necessary calculations.
    6. Suppose that a safety factor of 20 were required, no matter where the acrobat stood upon the beam. What minimum breaking strength (in newtons) would be required for each chain? Read the text aloud Show

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