Understanding Elastic Moduli
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Questions and Answers

What is the ratio of tensile (or compressive) stress to the longitudinal strain?

  • Change in Length/Length
  • Stress/Strain (correct)
  • Force/Area
  • Force × Length/Area × Change in Length

    • What unit is used to measure Young’s modulus?

  • Pascal (Pa) (correct)
  • Meter (m)
  • Newton (N)
  • Kilogram (kg)

    • What material requires the largest force to produce a small change in length?

  • Copper
  • Brass
  • Steel (correct)
  • Aluminium

    • What region of the stress-strain curve is of great importance for structural and manufacturing engineering designs?

    <p>Proportional region within the elastic limit</p> Signup and view all the answers

    What is the region within the stress-strain curve that is of great importance for structural and manufacturing engineering designs?

    <p>Proportional region</p> Signup and view all the answers

    What is the ratio of tensile (or compressive) stress to the longitudinal strain defined as?

    <p>Young’s modulus</p> Signup and view all the answers

    What is the unit of Young’s modulus?

    <p>Pascal (Pa)</p> Signup and view all the answers

    For a given material, the magnitude of the strain produced is same whether the stress is tensile or compressive. True or False?

    <p>True</p> Signup and view all the answers

    What is the symbol used to denote Young’s modulus?

    <p>Y</p> Signup and view all the answers

    What type of force is required to increase the length of a thin steel wire by 0.1%?

    <p>2000 N</p> Signup and view all the answers

    Which material is more elastic than copper, brass, and aluminium?

    <p>Steel</p> Signup and view all the answers

    What is the ratio of tensile (or compressive) stress to the longitudinal strain?

    <p>Y = σε</p> Signup and view all the answers

    What type of stress-strain curve region is of great importance for engineering designs?

    <p>Proportional region</p> Signup and view all the answers

    What is the force required to produce the same strain in aluminium, brass, and copper wires having the same cross-sectional area?

    <p>690 N, 900 N, 1100 N</p> Signup and view all the answers

    True or false: Young's modulus is a characteristic of the material and is denoted by the symbol Y?

    <p>True</p> Signup and view all the answers

    True or false: The ratio of stress and strain is known as Young's modulus?

    <p>False</p> Signup and view all the answers

    True or false: Young's modulus has the unit of N m–2 or Pascal (Pa)?

    <p>True</p> Signup and view all the answers

    True or false: Steel is less elastic than copper, brass, and aluminium?

    <p>False</p> Signup and view all the answers

    True or false: The force required to produce the same strain in aluminium, brass, and copper wires having the same cross-sectional area are 690 N, 900 N and 1100 N respectively?

    <p>True</p> Signup and view all the answers

    True or false: The proportional region within the elastic limit of the stress-strain curve is of great importance for structural and manufacturing engineering designs?

    <p>True</p> Signup and view all the answers

    True or false: Strain is a dimensionless quantity?

    <p>True</p> Signup and view all the answers

    True or false: For a given material, the magnitude of the strain produced is different whether the stress is tensile or compressive?

    <p>False</p> Signup and view all the answers

    True or false: To increase the length of a thin steel wire of 0.1 cm2 cross-sectional area by 0.1%, a force of 2000 N is required?

    <p>True</p> Signup and view all the answers

    True or false: The unit of Young's modulus is the same as that of strain?

    <p>False</p> Signup and view all the answers

    Table 8.1 gives the values of Young’s moduli and yield strengths of some ______

    <p>materials</p> Signup and view all the answers

    From the data given in Table 8.1, it is noticed that for metals Young’s moduli are ______

    <p>large</p> Signup and view all the answers

    To increase the length of a thin steel wire of 0.1 cm2 cross-sectional area by 0.1%, a force of 2000 N is ______

    <p>required</p> Signup and view all the answers

    The ratio of tensile (or compressive) stress (σ) to the longitudinal strain (ε) is defined as Young’s modulus and is denoted by the symbol ______

    <p>Y</p> Signup and view all the answers

    The unit of Young’s modulus is the same as that of ______

    <p>stress</p> Signup and view all the answers

    The force required to produce the same strain in aluminium, brass, and copper wires having the same cross-sectional area are 690 N, 900 N and 1100 N ______

    <p>respectively</p> Signup and view all the answers

    The proportional region within the elastic limit of the stress-strain curve (region OA in Fig. 8.2) is of great importance for structural and manufacturing engineering ______

    <p>designs</p> Signup and view all the answers

    The ratio of stress and strain, called modulus of elasticity, is found to be a characteristic of the ______

    <p>material</p> Signup and view all the answers

    The magnitude of the strain produced is same whether the stress is tensile or ______

    <p>compressive</p> Signup and view all the answers

    Since strain is a dimensionless quantity, the unit of Young’s modulus is the same as that of stress i.e., N m–2 or ______

    <p>Pascal (Pa)</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Elastic limit = Maximum stress a material can withstand without permanent deformation Young's modulus = Ratio of tensile (or compressive) stress to the longitudinal strain Stress-strain curve = Graphical representation of the relationship between stress and strain Modulus of elasticity = Ratio of stress and strain</p> Signup and view all the answers

    Match the following materials with their Young's moduli:

    <p>Steel = Large Young's modulus Copper = Small Young's modulus Brass = Small Young's modulus Aluminium = Small Young's modulus</p> Signup and view all the answers

    Match the following forces with the materials they are applied to produce the same strain:

    <p>2000 N = Steel wire 690 N = Aluminium wire 900 N = Brass wire 1100 N = Copper wire</p> Signup and view all the answers

    What is the reciprocal of the bulk modulus called?

    <p>Compressibility</p> Signup and view all the answers

    Which type of material is the least compressible?

    <p>Solids</p> Signup and view all the answers

    What is the ratio of lateral strain to longitudinal strain in a stretched wire called?

    <p>Poisson's ratio</p> Signup and view all the answers

    What is the value of Poisson's ratio for steels?

    <p>0.28</p> Signup and view all the answers

    What is the primary reason for the incompressibility of solids?

    <p>Tight coupling between atoms</p> Signup and view all the answers

    What is the fractional change in volume per unit increase in pressure defined as?

    <p>Compressibility</p> Signup and view all the answers

    What region of the stress-strain curve is of great importance for engineering designs?

    <p>Proportional limit</p> Signup and view all the answers

    What is the ratio of the lateral strain to the longitudinal strain in a stretched wire?

    <p>Poisson's ratio</p> Signup and view all the answers

    What is the modulus of elasticity for liquids compared to solids?

    <p>Much smaller</p> Signup and view all the answers

    What is the compressibility of gases compared to solids?

    <p>Much larger</p> Signup and view all the answers

    What is the symbol used to denote shear modulus?

    <p>G</p> Signup and view all the answers

    What is the SI unit of bulk modulus?

    <p>Pascal (Pa)</p> Signup and view all the answers

    What is the relationship between shear modulus (G) and Young's modulus (Y) for most materials?

    <p>G ≈ Y</p> Signup and view all the answers

    What does the negative sign in the expression for bulk modulus indicate?

    <p>Increase in pressure with a decrease in volume</p> Signup and view all the answers

    What is the ratio of shearing stress to the corresponding shearing strain known as?

    <p>Shear modulus</p> Signup and view all the answers

    What is the ratio of hydraulic stress to the corresponding hydraulic strain known as?

    <p>Bulk modulus</p> Signup and view all the answers

    What is the other name for shear modulus?

    <p>Rigidity modulus</p> Signup and view all the answers

    What is the relationship between bulk modulus (B) and pressure (p) for a system in equilibrium?

    <p>B = p/∆V</p> Signup and view all the answers

    What does the shear stress (σs) equal to in terms of shear modulus (G) and shear strain (θ)?

    <p>σs = G × θ</p> Signup and view all the answers

    What is the ratio of shearing stress to the corresponding shearing strain used to determine?

    <p>Material's rigidity</p> Signup and view all the answers

    True or false: Solids are more compressible than gases?

    <p>False</p> Signup and view all the answers

    True or false: Poisson's ratio has dimensions or units?

    <p>False</p> Signup and view all the answers

    True or false: Gases have large compressibilities that do not vary with pressure and temperature?

    <p>False</p> Signup and view all the answers

    True or false: Poisson's ratio is a pure number that depends only on the nature of the material?

    <p>True</p> Signup and view all the answers

    True or false: The incompressibility of solids is primarily due to loosely coupled neighboring atoms?

    <p>False</p> Signup and view all the answers

    True or false: The molecules in liquids are not as strongly bound to their neighbors as in solids?

    <p>True</p> Signup and view all the answers

    True or false: Poisson's ratio for steels is about 0.33?

    <p>False</p> Signup and view all the answers

    True or false: Poisson's ratio is a ratio of two stresses?

    <p>False</p> Signup and view all the answers

    True or false: The reciprocal of the bulk modulus is called compressibility and is denoted by k?

    <p>True</p> Signup and view all the answers

    True or false: The lateral strain in a stretched wire is directly proportional to the longitudinal strain within the elastic limit?

    <p>True</p> Signup and view all the answers

    True or false: Shear modulus is also known as the modulus of elasticity?

    <p>False</p> Signup and view all the answers

    True or false: The shear modulus of a material is generally greater than Young’s modulus?

    <p>False</p> Signup and view all the answers

    True or false: The SI unit of bulk modulus is N m–2 or Pa?

    <p>True</p> Signup and view all the answers

    True or false: The negative sign in the expression for bulk modulus indicates an increase in volume with an increase in pressure?

    <p>False</p> Signup and view all the answers

    True or false: The shearing stress can be expressed as σs = G × θ?

    <p>True</p> Signup and view all the answers

    True or false: The ratio of shearing stress to the corresponding shearing strain is known as Poisson's ratio?

    <p>False</p> Signup and view all the answers

    True or false: For most materials, the relationship between shear modulus (G) and Young's modulus (Y) is G ≈ Y/3?

    <p>False</p> Signup and view all the answers

    True or false: The bulk modulus of a material is generally less than Young’s modulus?

    <p>True</p> Signup and view all the answers

    True or false: The ratio of hydraulic stress to the corresponding hydraulic strain is known as bulk modulus?

    <p>True</p> Signup and view all the answers

    True or false: The ratio of shearing stress to the corresponding shearing strain is known as shear modulus?

    <p>True</p> Signup and view all the answers

    ______ = shearing stress (σs )/shearing strain

    <p>Shear Modulus</p> Signup and view all the answers

    SI unit of shear modulus is N m–2 or ______

    <p>Pascal (Pa)</p> Signup and view all the answers

    The ratio of hydraulic stress to the corresponding hydraulic strain is called bulk ______

    <p>modulus</p> Signup and view all the answers

    The negative sign in the expression for bulk modulus indicates a decrease in volume with an increase in ______

    <p>pressure</p> Signup and view all the answers

    The bulk moduli of a few common materials are given in ______ 8.3

    <p>Table</p> Signup and view all the answers

    The ratio of shearing stress to the corresponding shearing strain is called the shear modulus of the material and is represented by ______

    <p>G</p> Signup and view all the answers

    The unit of Young’s modulus is the same as that of stress i.e., N m–2 or ______

    <p>Pascal (Pa)</p> Signup and view all the answers

    The proportional region within the elastic limit of the stress-strain curve (region OA in Fig. 8.2) is of great importance for structural and manufacturing engineering ______

    <p>designs</p> Signup and view all the answers

    Solids are the ______ compressible, whereas, gases are the most compressible

    <p>least</p> Signup and view all the answers

    Simon Poisson pointed out that within the elastic limit, lateral strain is directly proportional to the longitudinal ______

    <p>strain</p> Signup and view all the answers

    Poisson’s ratio is a ratio of two ______; it is a pure number and has no dimensions or units

    <p>strains</p> Signup and view all the answers

    The molecules in gases are very poorly coupled to their ______

    <p>neighbours</p> Signup and view all the answers

    For ______ the value is between 0.28 and 0.30, and for aluminium alloys it is about 0.33

    <p>steels</p> Signup and view all the answers

    The reciprocal of the bulk modulus is called ______ and is denoted by k

    <p>compressibility</p> Signup and view all the answers

    The strain perpendicular to the applied force is called lateral ______

    <p>strain</p> Signup and view all the answers

    The ratio of the lateral strain to the longitudinal strain in a stretched wire is called Poisson’s ______

    <p>ratio</p> Signup and view all the answers

    For a given material, the magnitude of the strain produced is same whether the stress is tensile or ______

    <p>compressive</p> Signup and view all the answers

    The incompressibility of the solids is primarily due to the tight coupling between the neighbouring ______

    <p>atoms</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Bulk modulus = Reciprocal of the compressibility Compressibility = Fractional change in volume per unit increase in pressure Poisson’s ratio = Ratio of the lateral strain to the longitudinal strain Young’s modulus = Measure of the stiffness of a solid material</p> Signup and view all the answers

    Match the following materials with their compressibility:

    <p>Solids = Least compressible Liquids = Moderately compressible Gases = Most compressible Air = Highly compressible</p> Signup and view all the answers

    Match the following stress-strain curve regions with their importance:

    <p>Proportional region within the elastic limit = Great importance for engineering designs Elastic limit = Defines the limit for linear elastic behavior Plastic region = Indicates permanent deformation Ultimate strength = Maximum stress a material can withstand</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Lateral strain = Strain perpendicular to the applied force Longitudinal strain = Strain parallel to the applied force Elastic limit = Maximum stress a material can withstand without permanent deformation Poisson’s ratio = Ratio of the lateral strain to the longitudinal strain</p> Signup and view all the answers

    Match the following materials with their Poisson's ratio values:

    <p>Steels = Between 0.28 and 0.30 Aluminium alloys = About 0.33 Brass = Specific value not provided Copper = Specific value not provided</p> Signup and view all the answers

    Match the following moduli with their definitions:

    <p>Shear Modulus (G) = Ratio of shearing stress to the corresponding shearing strain Bulk Modulus (B) = Ratio of hydraulic stress to the corresponding hydraulic strain Young's Modulus (Y) = Ratio of tensile (or compressive) stress to the longitudinal strain Poisson's Ratio = Ratio of the lateral strain to the longitudinal strain in a stretched wire</p> Signup and view all the answers

    Match the following symbols with their corresponding moduli:

    <p>G = Shear Modulus B = Bulk Modulus Y = Young's Modulus θ = Poisson's Ratio</p> Signup and view all the answers

    Match the following materials with their moduli:

    <p>Shear Modulus (G) = Modulus of rigidity Bulk Modulus (B) = Incompressibility of solids Young's Modulus (Y) = Elasticity of solids Poisson's Ratio = Lateral strain in stretched wire</p> Signup and view all the answers

    Match the following equations with their moduli:

    <p>G = (F/A)/(∆x/L) = Shear Modulus (G) B = – p/(∆V/V) = Bulk Modulus (B) σs = G × θ = Shearing stress in terms of Shear Modulus (G) G ≈ Y/3.8 = Relationship between Shear Modulus (G) and Young's Modulus (Y)</p> Signup and view all the answers

    Match the following statements with their moduli:

    <p>Shear modulus (or modulus of rigidity) is generally less than Young’s modulus = Shear Modulus (G) SI unit of bulk modulus is the same as that of pressure = Bulk Modulus (B) Reciprocal of the bulk modulus is called compressibility and is denoted by k = Bulk Modulus (B) For most materials G ≈ Y/3.8 = Shear Modulus (G)</p> Signup and view all the answers

    Study Notes

    Young's Modulus and Stress-Strain Relationships

    • Young's modulus is the ratio of tensile (or compressive) stress to longitudinal strain.
    • The unit of Young's modulus is the Pascal (Pa), equivalent to N m⁻².
    • It characterizes a material's stiffness; higher values indicate greater resistance to deformation.

    Force and Material Properties

    • Steel typically requires a significant force to produce a small change in length, demonstrating high tensile strength.
    • Among common metals, steel is generally less elastic than copper, brass, and aluminium, which exhibit higher elasticity.
    • To stretch a thin steel wire with a 0.1 cm² cross-sectional area by 0.1%, a force of approximately 2000 N is necessary.

    Importance of the Stress-Strain Curve

    • The proportional region within the elastic limit (linear region) of the stress-strain curve is crucial for engineering designs, ensuring safety and functionality.
    • This region is characterized by a linear relationship between stress and strain.
    • The ratio of lateral strain to longitudinal strain in a stretched wire is known as Poisson's ratio, a value that typically ranges from 0.28 to 0.30 for most materials, with aluminium alloys around 0.33.

    Properties and Characteristics of Materials

    • Young's modulus is indicative of the stiffness of a material and is denoted by the symbol Y.
    • The relationship between shear modulus (G) and Young's modulus (Y) for most materials ranges approximately as G ≈ Y/3.
    • Lateral strain in a stretched wire is directly proportional to the longitudinal strain within the elastic limit, reflecting the material's response to stress.

    Bulk Modulus and Compressibility

    • The bulk modulus measures a material's resistance to uniform compression, with the reciprocal known as compressibility (k).
    • Solids are the least compressible materials, while gases exhibit high compressibility.
    • The negative sign in bulk modulus indicates that an increase in pressure leads to a decrease in volume.

    True or False Statements

    • True: Young's modulus is a characteristic of the material denoted by Y.
    • True: The SI unit of bulk modulus is N m⁻² or Pa.
    • True: The shearing stress is expressed as σs = G × θ, linking shear modulus and strain.
    • False: Solids are more compressible than gases; the opposite is true.
    • False: Poisson's ratio is a ratio of two strains, not stresses, and is dimensionless.

    Summary of Key Concepts

    • Poisson's ratio quantifies the relationship between lateral strain and longitudinal strain.
    • The shear modulus indicates how a material deforms under shear stress, and is a fundamental property of the material's elasticity.
    • The stress-strain curve and associated models are vital in many engineering applications, influencing design and material selection.

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    Test your knowledge of elastic moduli with this quiz. Explore concepts such as the proportional region within the stress-strain curve, modulus of elasticity, and Young's Modulus. Perfect for engineering and material science enthusiasts.

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