A copper wire of diameter 2 mm is 10 m long and stretched out between two posts. The normal stre

step 1 Here in this question as f is equals to AS which is equals to A, E, delta, L divided by L0, and

A copper wire of diameter 2 mm is 10 m long and stretched...

A copper wire of diameter $2 \mathrm{mm}$ is $10 \mathrm{m}$ long and stretched out between two posts. The normal stress (pressure) $\sigma=E\left(L-L_{0}\right) / L_{0},$ depends on the length $L$ versus the unstretched length $L_{0}$ and Young's modulus $E=1.1 \times 10^{6} \mathrm{kPa}$. The force is $F=A \sigma$ and measured to be $110 \mathrm{N}$. How much longer is the wire and how much work was put in?

Key Concepts

Cross-sectional Area Calculation

Calculating the cross-sectional area is necessary for converting stress into force, especially for cylindrical objects. For a circular cross-section, the area is determined by geometric formulas involving the diameter, and it directly influences the magnitude of internal forces in the material.

Work Done in Elastic Deformation

The work done in elastic deformation is the energy required to stretch or compress a material. It is typically computed by integrating the force over the displacement and reflects the energy stored as potential energy within the material, analogous to the energy stored in a spring.

Strain

Strain measures the deformation of a material as a result of stress, described as the ratio of the change in length to the original length. It is a critical, dimensionless parameter that, together with stress, defines the elastic response of materials.

Young's Modulus

Young's modulus is a material constant that relates stress (force per unit area) to strain (relative deformation) in the linear, elastic regime. It quantifies the stiffness of a material, indicating how much it will extend or compress under a given load and is central to understanding the elastic behavior of materials.

Stress

Stress is defined as the force applied per unit area within a material. It represents the internal pressures that arise in response to external loads, and its calculation is fundamental in determining how materials react under tension or compression.

Hooke's Law

Hooke's Law states that, for small deformations within the elastic limit, the strain in a material is directly proportional to the applied stress. This linear relationship is essential for predicting how much an object like a wire will stretch when subjected to a tensile force.

Transcript

Please give Ace some feedback