What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Distinguish elasticity from plasticity.

An elastic body regains its original shape on removal of the force; a plastic body retains the deformed shape, like putty.

Define stress and strain.

Stress is the restoring force per unit area; strain is the fractional change in dimension, with no units.

Name the three types of stress.

Tensile or compressive (longitudinal) stress, shearing (tangential) stress and hydraulic (volume) stress.

Within the elastic limit, stress is directly proportional to strain, the proportionality constant being the modulus of elasticity.

What is the yield point on a stress-strain curve?

The point (elastic limit) beyond which the material no longer returns to its original dimensions and undergoes permanent (plastic) deformation.

Define Young's modulus.

The ratio of longitudinal stress to longitudinal strain, \(Y=(F/A)/(\Delta L/L)\), with SI unit pascal.

Why is steel preferred over copper in heavy structures?

Steel has a larger Young's modulus, so it requires a much greater force to produce the same elongation — it is more elastic.

Define bulk modulus and compressibility.

Bulk modulus \(B=-p/(\Delta V/V)\) measures resistance to volume change; compressibility \(k=1/B\) is the fractional volume change per unit pressure.

Define Poisson's ratio.

The ratio of lateral strain to longitudinal strain in a stretched wire; it is a dimensionless number depending only on the material.

Mechanical Properties of Solids

Q: Write the elastic potential energy per unit volume of a stretched wire.

\(u=\tfrac12\times\text{stress}\times\text{strain}=\tfrac12\sigma\varepsilon\).

Class 11 Physics · Physics Part II · Chapter 1

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CBSE Class 11 · Physics

Ch 8–14 formulas and table values, by page

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CBSE Class 11 · Physics

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Summary

Real solids are not perfectly rigid: a deforming force changes their shape or size, and elasticity is the property by which a body regains its original form when the force is removed, while plasticity is the opposite tendency to retain the deformed shape. Stress is the internal restoring force per unit area (SI unit pascal), and strain is the fractional change in dimension; there are three kinds — tensile or compressive (longitudinal), shearing, and hydraulic (volume). Hooke's law states that within the elastic limit stress is proportional to strain, the constant being a modulus of elasticity. The stress-strain curve shows a proportional region up to the yield point, then plastic deformation up to the ultimate tensile strength and fracture; materials are brittle or ductile, and elastomers like rubber do not obey Hooke's law. Young's modulus \(Y=\) stress/longitudinal strain, shear modulus \(G\) (modulus of rigidity), and bulk modulus \(B=-p/(\Delta V/V)\) describe the three deformations; compressibility is the reciprocal of \(B\). Poisson's ratio is the lateral to longitudinal strain. Elastic potential energy per unit volume of a stretched wire is \(\tfrac12\times\text{stress}\times\text{strain}\). These ideas guide the design of beams, columns, bridges and cranes, and explain the limit on mountain height.

Stress and strainHooke's lawStress-strain curveElastic moduli: Young's, shear and bulkPoisson's ratioElastic potential energy in a stretched wireApplications of elastic behaviour of materials

Key terms

Elasticity

The property by which a body regains its original shape and size when the deforming force is removed.

Stress

The internal restoring force developed per unit area in a deformed body; SI unit pascal (Pa).

Strain

The fractional change in dimension of a body produced by stress; a dimensionless ratio.

Hooke's law

Within the elastic limit, stress is directly proportional to strain, the constant being a modulus of elasticity.

Young's modulus

The ratio of tensile (or compressive) stress to longitudinal strain, \(Y=\sigma/\varepsilon\).

Bulk modulus

The ratio of hydraulic stress to the volume strain it produces, \(B=-p/(\Delta V/V)\); its reciprocal is compressibility.

Extra questions & answers

Try one from this chapter

The property by which a body regains its original shape after the deforming force is removed is called:

Flashcards & interactive practice