A steel cable has breaking stress σ(breaking) and is required to carry a maximum working load W with factor of safety n. Neglect the weight of the cable. What is the minimum cross-sectional area required?
Options

Question

A steel cable has breaking stress σ(breaking) and is required to carry a maximum working load W with factor of safety n. Neglect the weight of the cable. What is the minimum cross-sectional area required?

Options

G1 Physics · Accepted Answer

Factor of safety is defined by factor of safety = breaking stress / allowable working stress. Therefore, σ(working) = σ(breaking) / n. For the minimum required area, W/A(min) = σ(working). Hence, W/A(min) = σ(breaking)/n. Therefore, A(min) = nW / σ(breaking). Correct option: B.