A steel cable with a radius of 1.5 cm supports a chairlift...

A steel cable with a radius of $1.5 \mathrm{~cm}$ supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} \mathrm{~N} \mathrm{~m}^{-2}$, what is the maximum load the cable can support?

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Key Concepts

Stress

Stress is defined as the force per unit area and is a fundamental concept in material science and mechanical engineering. It measures how internal forces are distributed within a material when external loads are applied, and understanding stress is essential to ensure that the material's limits, such as its maximum stress tolerance, are not exceeded.

Cross-sectional Area

The cross-sectional area of an object, especially one with a circular cross section, determines how much load the object can handle. It is calculated using the formula A = ?r², where r is the radius. This concept is crucial because the area directly influences the distribution of stress across the structure when a load is applied.

Load (Force) Calculation

Calculating the maximum load that a structure can support involves multiplying the cross-sectional area by the material’s maximum allowable stress. This approach helps determine the tensile load capacity and ensures that the applied force does not exceed the material's strength, preserving the structural integrity under expected loads.

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