A mineshaft has an ore elevator hung from a single braided...

A mineshaft has an ore elevator hung from a single braided cable of diameter $2.5 \mathrm{cm} .$ Young's modulus of the cable is $10 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} .$ When the cable is fully extended, the end of the cable is $800 \mathrm{m}$ below the support. How much does the fully extended cable stretch when $1000 \mathrm{kg}$ of ore is loaded?

Key Concepts

Elastic Deformation

Elastic deformation refers to the reversible change in shape that occurs when a force is applied to a material within its elastic limit. Understanding this concept helps predict how materials respond to loads and return to their original shape once the load is removed.

Young's Modulus

A measure of a material's stiffness, Young's modulus defines the linear relationship between stress (force per unit area) and strain (relative deformation) within the elastic limit of a material. It is essential in predicting how much a material will stretch or compress under a given load.

Stress and Strain

Stress is the applied force divided by the cross-sectional area, and strain is the deformation (change in length) divided by the original length. Understanding these concepts is crucial for analyzing how materials deform under load.

Hooke's Law for Elastic Materials

Hooke's Law states that within the elastic limit of a material, the deformation produced is directly proportional to the applied load. This principle is the foundation for calculating extensions or compressions in elastic materials.

Cross-Sectional Area Calculation

The cross-sectional area of a material, especially for objects with circular cross-sections, is calculated using the formula A = ?(d/2)^2. This area is used to determine the stress experienced by the material when a force is applied.

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