Physics Units and Dimensions Quiz

Units and Dimensions

• Physics relies on experiments, which involve measuring physical properties like length, mass, time, etc.
• Physical quantities can be categorized as fundamental (independent) and derived (dependent on others).
• Fundamental quantities include:
  • Mass
  • Length
  • Time
  • Temperature
• The International System of Units (SI) is the standard for measurement.
• Derived quantities are derived from fundamental ones.
  • Examples: Area, Volume, Speed, Force
• SI units are crucial for consistent and accurate measurements in science.
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
  • Kelvin (K) for temperature
• There are other systems of units: CGS (centimeter, gram, second), FPS (feet, pound, second)

Stress and Strain

• Stress is the force applied per unit area.
• Strain is the fractional change in length, geometry, or volume caused by stress.
• Stress-Strain Relationship:
  • Stress = Elastic Modulus × Strain
• The elastic modulus describes a material's resistance to deformation.
• Hooke's Law: Relates stress and strain linearly within the elastic limit.
  • The restoring force is proportional to displacement.
• Types of stress:
  • Tensile Stress: Stretching or pulling force
  • Compressive Stress: Force causing compression
• Young's Modulus (E): Measures a material's resistance to stretching or compression.
  • It's the ratio of tensile stress to tensile strain.
• Brittle Materials: Can withstand high stress but break suddenly.
• Ductile Materials: Stretch more before breaking, have a larger elastic region.
• Plastic Materials: Stretch significantly but aren't very strong.
• Poisson's Ratio: Describes the change in dimensions perpendicular to the direction of stress.

Bulk Modulus

• Bulk Modulus (K): Measures a substance's resistance to uniform compression.
• It's the pressure change needed to cause a given relative volume change.
• Compressibility: The inverse of the bulk modulus.

Shear Stress and Strain

• Shear Stress: Force applied parallel to a surface.
• Shear Strain: Change in the shape of an object due to shear stress.
• Shear Modulus (S): Measures a material's resistance to shear deformation.
• Shear Stress - Shear Strain Relationship: Stress = Shear Modulus × Strain

Force in a Bar Due to Expansion or Contraction

• Temperature changes can cause expansion or contraction in materials.
• When a material is prevented from changing length, a force develops at the ends.
• Formula for Force:
  • F = Y * A * 𝛼 * ΔT
  • Where:
    • F: Force
    • Y: Young's modulus
    • A: Cross-sectional area
    • 𝛼: Linear coefficient of expansion
    • ΔT: Change in temperature

Energy Stored in a Wire

• Energy stored in a stretched wire:
  • W = (1/2) * F * ΔL (Joule/erg)
  • Where:
    • W: Work done or energy stored
    • F: Force applied
    • ΔL: Change in length
• Energy stored per unit volume:
  • Energy/Volume = (1/2) * stress * strain

Examples

• Example 1: Young's Modulus calculation
  • Calculate Young's modulus for a metal wire under tension.
• Example 2: Bulk Modulus and Volume Change
  • Calculate the change in volume of a lead sphere submerged under pressure.
• Example 3: Work Done in Stretching a Wire
  • Calculate the work done to elongate a wire and the energy stored per unit volume.

Test your understanding of fundamental and derived physical quantities along with the International System of Units (SI) in this quiz. Explore concepts related to stress and strain, and their relationships in materials. Perfect for students studying introductory physics topics.