Cross-sectional refers to the shape or area obtained by cutting through an object perpendicular to its longest dimension. It provides insights into the internal structure and characteristics of the material. In engineering and physics cross-sectional analysis is crucial for understanding stress distribution and material behavior under various forces and loads.
Class 11 Physics Chapter 8 examines the mechanical properties of solids including stress strain and elasticity. It covers how materials deform when subjected to forces and the conditions under which they return to their original shape. Key concepts include Hooke’s law types of stress and strain and their significance in engineering applications and material selection.
To calculate the work done W by stretching a wire of length L and cross-sectional area A through an amount x, we could use the following relationship between stress strain and Young’s modulus:
The stress in the wire, σ, can be found by the relation as follows:
σ = F/A
where F represents the applied force. The strain ε is described by:
ε = x/L
As related by Young’s modulus Y,
Y = σ/ε = (F/A)/(x/L)
From this we can write the force F:
F = (YAx)/L
The work done W when the wire is stretched by an amount x is given by the area under the stress-strain curve which is the integral of force over displacement:
W = ∫ F dx = ∫ (YAx/L) dx
Evaluating the integral we get:
W = (Y A/L) ∫ x dx = (Y A/L) * [x²/2] from 0 to x = (Y A/L) * (x²/2)
Work done is hence,
W = (Y A x²)/(2 L)
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