A 200 -kg load is hung on a wire of length 4.00 m, cross-sectional area 0.200 ×10^-4 m^2 , and Y

step 1 We're told that we have 200 kilograms hanging from a wire, and that wire has a Young's modulus o

A 200 -kg load is hung on a wire of length 4.00 m,...

A 200 -kg load is hung on a wire of length $4.00 \mathrm{m},$ cross-sectional area $0.200 \times 10^{-4} \mathrm{m}^{2}$ , and Young's modulus $8.00 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} .$ What is its increase in length?

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Key Concepts

Strain

Strain is the measure of deformation representing the relative change in length or shape of a material when subjected to stress. It is a dimensionless quantity that indicates the extent to which a material stretches or compresses compared to its original dimensions.

Hooke's Law

Hooke's Law states that, within the elastic limit of a material, the strain experienced is directly proportional to the applied stress. This linear relationship allows for the calculation of material deformation using parameters such as Young's modulus and is essential for analyzing the elastic behavior of materials under load.

Stress

Stress is the measure of internal forces within a material that arise from externally applied loads. It is calculated by dividing the force applied by the cross-sectional area over which the force is distributed and is a key factor in determining how a material will react to a load.

Young's Modulus

Young's modulus is a material constant that quantifies the stiffness of a material when subjected to tensile or compressive forces. It is defined as the ratio of the stress (force per unit area) over strain (relative deformation) within the elastic limit, indicating how much a material will extend or compress under a given load.

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