Q.The steel cable of a crane or a suspension bridge is deliberately made both thick (large cross-sectional area) and relatively short rather than thin and long, and is made of a metal like steel rather than a much more ductile metal such as pure lead. Explain both design choices using the ideas of stress, strain, elastic limit, and Young's modulus.

Why thick (large cross-sectional area): For a given load $F$, the tensile stress developed in the cable is $\text{stress} = F/A$. A larger cross-sectional area $A$ directly reduces this stress for the same load, keeping the cable comfortably within its elastic (and ideally, well within its proportional) limit, with a wide safety margin against reaching the yield point or breaking.

Why short: For a given strain (which is kept small by choosing an adequately thick cable, as above), the actual elongation is $\Delta L = \text{strain} \times L$. A shorter cable produces a smaller absolute elongation $\Delta L$ for the same strain -- important for a bridge or crane, where even a small fractional strain, multiplied by a very long cable length, could otherwise add up to an unacceptably large sag or stretch in absolute terms. …

Apply stress $= F/A$ and $\Delta L = \text{strain}\times L$ to see how cross-sectional area and length each independently affect the cable's mechanical response, then compare steel's ela …

• Explaining only the "thick" choice via strength/stress and forgetting the separate, independent reason for keeping the cable short (limiting absolute elongation, not just strain). …