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COMEDK2024PhysicsMechanical Properties of Solids

An elevator cable is to have a maximum stress of 7 10^7 ~N / m ^2 to allow for appropriate safety factors. Its maximum upward acceleration is 1.5 ~m / s ^2 . If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be

Options

  1. A3.22 ~cm ^2
  2. B2.38 ~cm ^2
  3. C0.32 ~cm ^2
  4. D8.23 ~cm ^2

Correct answer

A. 3.22 ~cm ^2

Step-by-step solution

aligned & T_ =m(g+a)=(2000)(9.8+1.5)=22600 ~N & Maximum stress = T_ Area aligned aligned Area & = T_ Maximum stress = 22600 7 10^7 & =3.22 10⁻⁴ ~m ^2=3.22 ~cm ^2 aligned

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