Elasticity and Hooke's Law

Elasticity

Hooke's Law

• States that within the proportional limit, stress is directly proportional to strain
• Mathematically represented as: σ = Eε
• Where σ is stress, E is the modulus of elasticity, and ε is strain
• Applies to materials that obey Hooke's Law, such as most metals and alloys

Elastic Modulus (E)

• Measures the stiffness of a material
• Defined as the ratio of stress to strain within the proportional limit
• Units: Pa (Pascals) or psi (pounds per square inch)
• Higher elastic modulus indicates a stiffer material

Plastic Deformation

• Permanent deformation of a material under stress, beyond its elastic limit
• Occurs when a material is loaded beyond its yield point
• Characterized by a permanent change in shape or size
• Can be desirable (e.g., in metal forming) or undesirable (e.g., in structural failure)

Stress-Strain Curve

• Graphical representation of a material's behavior under tension or compression
• Plots stress (σ) against strain (ε)
• Typical curve features:
  • Proportional limit: linear region where stress is proportional to strain
  • Yield point: point at which the material begins to deform plastically
  • Ultimate strength: maximum stress a material can withstand
  • Fracture point: point at which the material breaks or fractures

Young's Modulus (E)

• A type of elastic modulus that relates to longitudinal stress and strain
• Defined as the ratio of longitudinal stress to longitudinal strain within the proportional limit
• Units: Pa (Pascals) or psi (pounds per square inch)
• Provides a measure of a material's stiffness in the longitudinal direction

Elasticity

• Stress is directly proportional to strain within the proportional limit, as stated by Hooke's Law
• Hooke's Law is mathematically represented as σ = Eε, where σ is stress, E is the modulus of elasticity, and ε is strain
• The law applies to materials that obey Hooke's Law, such as most metals and alloys

Elastic Modulus (E)

• Measures the stiffness of a material
• Defined as the ratio of stress to strain within the proportional limit
• Units are Pa (Pascals) or psi (pounds per square inch)
• A higher elastic modulus indicates a stiffer material

Plastic Deformation

• Permanent deformation of a material under stress, beyond its elastic limit
• Occurs when a material is loaded beyond its yield point
• Characterized by a permanent change in shape or size
• Can be desirable (e.g., in metal forming) or undesirable (e.g., in structural failure)

Stress-Strain Curve

• Graphical representation of a material's behavior under tension or compression
• Plots stress (σ) against strain (ε)
• Typical curve features include:
  • Proportional limit: linear region where stress is proportional to strain
  • Yield point: point at which the material begins to deform plastically
  • Ultimate strength: maximum stress a material can withstand
  • Fracture point: point at which the material breaks or fractures

Young's Modulus (E)

• A type of elastic modulus that relates to longitudinal stress and strain
• Defined as the ratio of longitudinal stress to longitudinal strain within the proportional limit
• Units are Pa (Pascals) or psi (pounds per square inch)
• Provides a measure of a material's stiffness in the longitudinal direction

Atmospheric Pressure

• Atmospheric pressure is the pressure exerted by the weight of the air in the atmosphere.
• It is measured in units of pascals (Pa) or atmospheres (atm).

Factors Affecting Atmospheric Pressure

• Atmospheric pressure decreases with increasing altitude.
• It increases with increasing temperature.
• It increases with increasing humidity.
• Changes in weather patterns can affect atmospheric pressure.

Scales Used to Measure Atmospheric Pressure

• Barometric scale measures pressure in inches of mercury (inHg).
• Millibars (mbar) are commonly used in meteorology.
• Pascals (Pa) are the SI unit of pressure.

Atmospheric Pressure and Weather

• High pressure is associated with fair weather, clear skies, and light winds.
• Low pressure is associated with poor weather, precipitation, and strong winds.
• Pressure gradients drive wind patterns and weather systems.

Importance of Atmospheric Pressure

• Understanding atmospheric pressure is crucial for predicting weather patterns.
• Pilots need to consider atmospheric pressure for safe flight operations.
• Atmospheric pressure affects the weather we experience daily.