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Mechanical Properties of Solids - Physics with Calculus

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Terms in this set (20)

  • What is elasticity in solids?
    Elasticity is the property of a body to regain its original size and shape when the applied force is removed.
  • Define stress and its SI unit.
    Stress is the restoring force per unit area within a body. Its SI unit is pascal (Pa) or N/m².
  • What is strain in the context of solids?
    Strain is the fractional change in dimension of a body due to applied stress; it is dimensionless.
  • State Hooke's law for small deformations.
    For small deformations, stress is directly proportional to strain: stress = modulus of elasticity × strain.
  • What is Young's modulus?
    Young's modulus (Y) is the ratio of tensile or compressive stress to longitudinal strain: Y = (F/A) / (ΔL/L).
  • How is shearing strain defined?
    Shearing strain is the ratio of relative displacement between faces (Δx) to the length (L) of the body: shearing strain = Δx / L ≈ tan θ.
  • What is the shear modulus (modulus of rigidity)?
    Shear modulus (G) is the ratio of shearing stress to shearing strain: G = (F/A) / (Δx/L).
  • Define bulk modulus and its significance.
    Bulk modulus (B) is the ratio of hydraulic stress (pressure) to volume strain: B = -p / (ΔV/V), indicating resistance to uniform compression.
  • What is Poisson's ratio?
    Poisson's ratio is the ratio of lateral strain to longitudinal strain in a stretched wire; it is dimensionless.
  • Explain the stress-strain curve for a metal.
    The curve shows an initial linear elastic region obeying Hooke's law, followed by a yield point, plastic deformation, ultimate tensile strength, and fracture.
  • What is the yield strength of a material?
    Yield strength is the stress at the elastic limit beyond which permanent (plastic) deformation occurs.
  • How is elastic potential energy stored in a stretched wire calculated?
    Elastic potential energy per unit volume u = 1/2 × stress × strain = 1/2 × σ × ε.
  • Why are steel ropes made of many thin wires braided together?
    Braiding thin wires provides flexibility, strength, and ease of manufacture while preventing permanent deformation under load.
  • What is the formula for elongation δ of a beam loaded at the center?
    δ = (W × l³) / (4 × b × d³ × Y), where W is load, l length, b breadth, d depth, and Y Young's modulus.
  • Why do beams often have an I-shaped cross-section?
    The I-shape provides large load-bearing surface and depth to prevent bending and buckling while reducing weight.
  • What is the typical range of Poisson's ratio for steel?
    Poisson's ratio for steel is typically between 0.28 and 0.30.
  • How does the bulk modulus of solids compare to that of gases?
    Solids have much larger bulk moduli and are far less compressible than gases, which have very small bulk moduli.
  • What is the significance of the elastic limit in materials?
    The elastic limit is the maximum stress a material can withstand without permanent deformation.
  • How is tensile stress calculated for a wire under load?
    Tensile stress = Force applied (F) divided by cross-sectional area (A): σ = F/A.
  • What causes buckling in beams and how is it prevented?
    Buckling occurs when a beam bends under load; it is prevented by using cross-sections with sufficient depth and shape, like the I-section.