Mechanical Properties of Solids Chapter 8
24 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the property of a body that tends to regain its original size and shape when the applied force is removed?

elasticity

What is the deformation caused by a body that does not tend to regain its previous shape?

plastic deformation

What is the property called when a body is pressed with a hand and pushed horizontally?

  • Tensile stress
  • Compressive stress
  • Shearing stress (correct)
  • Hydraulic stress

    • Hooke's Law states that stress is not proportional to strain for small deformations.

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

    What is the typical term for a material if the ultimate strength and fracture points are close?

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

    What is the term used to describe a material if the ultimate strength and fracture points are far apart?

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

    What is the ratio defined as Young's Modulus?

    <p>Stress to Strain</p> Signup and view all the answers

    What is the unit of Young's Modulus?

    <p>N m^-2 or Pascal (Pa)</p> Signup and view all the answers

    What is the name given to materials like rubber and tissue of aorta that exhibit large elastic regions?

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

    What is the ratio of hydraulic stress to the corresponding hydraulic strain called?

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

    What is the symbol used to denote Bulk Modulus?

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

    The negative sign in the bulk modulus formula B = - p/(∆V/V) indicates that with an increase in pressure, a decrease in _____ occurs.

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

    Which of the following materials has the highest bulk modulus?

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

    Bulk moduli for liquids are generally smaller than for solids.

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

    What is the formula for the amount a bar sags when loaded at the centre by a load? Write it in terms of the load (W), length (l), breadth (b), depth (d), and Young's modulus (Y).

    <p>$\delta = \frac{Wl^3}{4bd^3Y}$</p> Signup and view all the answers

    What is the elastic limit for a typical rock if the shear modulus is 30 x 10^7 N m^-2?

    <p>30 x 10^7 N m^-2</p> Signup and view all the answers

    What is the relationship between stress and strain under tension or compression based on Hooke's law?

    <p>$F/A = Y\Delta L/L$</p> Signup and view all the answers

    What are the three types of stresses mentioned in the text?

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

    Hooke's law is only valid in the linear part of the stress-strain curve.

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

    Calculate the bulk modulus of water given: Initial volume = 100.0 litre, Pressure increase = 100.0 atm, Final volume = 100.5 litre. Compare the bulk modulus of water with that of air at constant temperature. Explain why the ratio is so large.

    <p>Bulk modulus of water = $2.27 × 10^9$ Pa. The bulk modulus of water is much larger than air due to water being nearly incompressible compared to air.</p> Signup and view all the answers

    What is the density of water at a depth where the pressure is 80.0 atm, given that its density at the surface is 1.03 × 10^3 kg m^3?

    <p>Density of water at 80.0 atm pressure = $1.08 × 10^3$ kg m^3</p> Signup and view all the answers

    Calculate the fractional change in volume of a glass slab when subjected to a hydraulic pressure of 10 atm.

    <p>Fractional change in volume = 0.0194 or 1.94%</p> Signup and view all the answers

    Determine the volume contraction of a solid copper cube with 10 cm edges when subjected to a hydraulic pressure of 7.0 × 10^6 Pa.

    <p>Volume contraction = $7.0 × 10^{-8}$ m^3</p> Signup and view all the answers

    How much should the pressure on a litre of water be changed to compress it by 0.10%?

    <p>Pressure change required = 1.0 atm</p> Signup and view all the answers

    Study Notes

    Mechanical Properties of Solids

    • Mechanical properties of solids are important in engineering design and everyday life.
    • Solids can be stretched, compressed, and bent, and their properties can be changed by applying external forces.

    Stress and Strain

    • When a force is applied to a solid, it deforms, and the body develops a restoring force to counteract the applied force.
    • Stress is the restoring force per unit area, and its SI unit is N m-2 or Pascal (Pa).
    • Strain is the ratio of change in dimension to the original dimension, and it has no units or dimensional formula.

    Types of Stress and Strain

    • There are three types of stress: tensile, compressive, and shear stress.
    • Tensile stress occurs when a force is applied normal to the cross-sectional area of a body, causing it to elongate.
    • Compressive stress occurs when a force is applied parallel to the cross-sectional area of a body, causing it to compress.
    • Shear stress occurs when a force is applied tangentially to the surface of a body, causing it to deform by an angle.

    Hooke's Law

    • Hooke's law states that stress and strain are proportional to each other for small deformations.
    • The law is an empirical law and is valid for most materials.
    • The proportionality constant is known as the modulus of elasticity.

    Stress-Strain Curve

    • The stress-strain curve is a graph that shows the relationship between stress and strain for a given material.
    • The curve can be used to determine the elastic limit, yield strength, and ultimate tensile strength of a material.
    • The elastic region of the curve is where the stress and strain are proportional to each other.

    Elastic Moduli

    • Elastic moduli are measures of the stiffness of a material.
    • Young's modulus is a measure of the stiffness of a material under tensile or compressive stress.
    • Shear modulus is a measure of the stiffness of a material under shear stress.

    Applications of Elastic Behavior

    • The elastic behavior of materials is important in engineering design, such as in the design of buildings, bridges, and machines.
    • The elastic behavior of materials is also important in biological systems, such as in the structure of bones and tissues.

    Examples and Problems

    • A structural steel rod is stretched by a 100 kN force, and its elongation is calculated.
    • A copper wire and a steel wire are stretched by a load, and the net elongation is calculated.
    • The compression of a thighbone under an extra load is calculated.

    Tables

    • Table 8.1 shows the values of Young's moduli and yield strengths of some materials.
    • Table 8.2 shows the values of shear moduli of some common materials.### Mechanical Properties of Solids
    • Stress and Strain:
      • Stress: the restoring force per unit area, measured in N m^-2 (Pa) or GPa.
      • Strain: the fractional change in dimension, a pure number with no dimensions or units.
    • Young's Modulus (Y):
      • The ratio of tensile stress to tensile strain, measured in N m^-2 (Pa) or GPa.
      • Symbol: Y, unit: N m^-2 (Pa) or GPa.
      • Young's modulus is a measure of the stiffness of a material.
    • Compression in Thighbone:
      • The weight of the body is supported by the legs, and the thighbone is compressed.
      • The compression in each thighbone (∆L) can be computed using the formula: ∆L = (F × L)/(Y × A).
      • The fractional decrease in the thighbone is ∆L/L = 0.000091 or 0.0091%.

    Shear Modulus

    • Shear Modulus (G):
      • The ratio of shearing stress to the corresponding shearing strain, measured in N m^-2 (Pa) or GPa.
      • Symbol: G, unit: N m^-2 (Pa) or GPa.
      • The shear modulus is a measure of the rigidity of a material.
      • The shear moduli of a few common materials are given in Table 9.2.

    Bulk Modulus

    • Bulk Modulus (B):
      • The ratio of hydraulic stress to the corresponding hydraulic strain, measured in N m^-2 (Pa) or GPa.
      • Symbol: B, unit: N m^-2 (Pa) or GPa.
      • The bulk modulus is a measure of the compressibility of a material.
      • The bulk moduli of a few common materials are given in Table 8.3.

    Elastic Potential Energy

    • Elastic Potential Energy in a Stretched Wire:
      • When a wire is put under a tensile stress, work is done against the inter-atomic forces.
      • The work is stored in the wire in the form of elastic potential energy.
      • The elastic potential energy per unit volume of the wire (u) is given by the formula: u = (1/2) × σ ε.

    Poisson's Ratio

    • Poisson's Ratio:
      • The ratio of the lateral strain to the longitudinal strain in a stretched wire.
      • A pure number with no dimensions or units.
      • Poisson's ratio is a measure of the lateral strain response to a longitudinal tensile strain.

    Applications of Elastic Behaviour of Materials

    • Crane Design:
      • The design of a crane requires knowledge of the elastic behaviour of materials.
      • The rope should be able to withstand the weight of the load without deforming permanently.
    • Beam Design:
      • The design of a beam requires knowledge of the elastic behaviour of materials.
      • The beam should be able to withstand the load without bending or breaking.
      • The formula for the sagging of a beam under a load is: δ = W l^3/(4bd^3Y).
    • Bridge Design:
      • The design of a bridge requires knowledge of the elastic behaviour of materials.
      • The beam should be able to withstand the load of the flowing traffic, the force of winds, and its own weight.
      • The cross-sectional shape of the beam is critical in reducing the bending.
    • Mountain Height:
      • The maximum height of a mountain on earth is limited by the elastic properties of rocks.
      • The stress due to the weight of the material on top should be less than the critical shearing stress at which the rocks flow.
      • The formula for the maximum height of a mountain is: h = 30 × 10^7 N m^-2/(3 × 10^3 kg m^-3 × 10 m s^-2) = 10 km.### Types of Stresses
    • There are three types of stresses: tensile stress, shearing stress, and hydraulic stress
    • Tensile stress is associated with stretching, while compressive stress is associated with compression
    • Shearing stress occurs when a pair of forces is applied parallel to the upper and lower faces of an object
    • Hydraulic stress occurs when an object undergoes compression due to a surrounding fluid

    Hooke's Law

    • Hooke's law states that for small deformations, stress is directly proportional to strain for many materials
    • The constant of proportionality is called the modulus of elasticity
    • There are three elastic moduli: Young's modulus, shear modulus, and bulk modulus
    • Young's modulus is used to describe the elastic behavior of objects under tension or compression
    • Shear modulus is used to describe the elastic behavior of objects under shearing stress
    • Bulk modulus is used to describe the elastic behavior of objects under hydraulic stress

    Young's Modulus

    • Young's modulus (Y) is used to calculate the stress and strain of an object under tension or compression
    • The formula for Young's modulus is F/A = Y∆L/L, where F is the applied force, A is the cross-sectional area, and ∆L/L is the tensile or compressive strain

    Shear Modulus

    • Shear modulus (G) is used to calculate the stress and strain of an object under shearing stress
    • The formula for shear modulus is F/A = G × ∆L/L, where F is the applied force, A is the cross-sectional area, and ∆L/L is the displacement of one end of the object in the direction of the applied force

    Bulk Modulus

    • Bulk modulus (B) is used to calculate the pressure and volume change of an object under hydraulic stress
    • The formula for bulk modulus is p = B (∆V/V), where p is the pressure, ∆V/V is the volume strain, and B is the bulk modulus

    Points to Ponder

    • Hooke's law is only valid in the linear part of the stress-strain curve
    • Young's modulus and shear modulus are only relevant for solids, as they have lengths and shapes
    • Bulk modulus is relevant for solids, liquids, and gases, and refers to the change in volume under uniform stress
    • Materials with larger values of Young's modulus require a larger force to produce small changes in length
    • Materials that stretch more are not necessarily more elastic; in fact, materials that stretch less are considered more elastic

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Mechanical Properties of Solids PDF

    Description

    This quiz covers the mechanical properties of solids, including stress and strain, and the motion of rigid bodies.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser