• In reality, the perfect rigid body can be stretched, compressed and bend. This means the solid body is not perfectly rigid.
  • Elasticity- It is a property of material to regain its original shape and size after removal of deforming force.
  • Elastic- A material that return to its original shape after the force is removed.
  • Plasticity- The property of material to permanently deform without breaking when a force is applied.
  • plastic- The material that does not return to its original shape after the force is removed.
  • The elastic behaviour of material plays very important role in engineering design.

ELASTIC BEHAVIOUR OF SOLIDS-

  • In solid, every atom or molecules bonded with other surrounded atom or molecule. It bonded with interatomic or intermolecular forces and live in equilibrium position. when solid object deform, then also atom or molecules are displaced form equilibrium state which causing change in intermolecular or interatomic distance. When the deforming or external force removed, all disturbance in microscopic level get back and solid regain its original size or shape.
  • Elastic behaviour of solid- It is a property of solid to return its original size and shape after removal all external force within its elastic limit.
  • Robert hooke(1635-1703), an English Physicist perform an experiment on spring and found that the elongation produced in body is proportional to applied external force.
  • Also he present a law of elasticity, called hooke ‘s law
  • Hooke ‘s Law- The force required to stretch or compress a spring is directly proportional to the amount of stretch or compression, as long as the material stays within its elastic limit.

STRESS-

  • It is a restoring force of a body which have equal in magnitude and opposite in direction to applied force. OR Stress is force applied per unit area on an object.
  • Stress= F/A, where F= force and A= area.
  • It unit is Nm-2 or pascal.
  • Its dimension is [M1L-1T-2].
  • There are many ways which solid change its dimension when any external force is applied. OR Types of stress-
    • Tensile Stress- Force that stretches an object, increasing its length.
    • Compressive Stress- Force that compresses or shortens an object.
    • Shear Stress or Tangential stress– Force that causes layers of an object to slide past each other.
    • Hydraulic Stress- It exerted on material by fluid pressure, typically in system involving liquid or gases.

STRAIN-

  • Strain- It is change in shape or size of a material when subjected to stress.
  • Types of strain-
    • Tensile strain- When force stretches an object, length is increase.
    • Compressive Strain- When force compress an object, length is decrease.
    • Shear Strain- When force applied on an object, shape is change.
    • Longitudinal Strain– It is change in length of a material divided by its original length when stretched or compressed along its length.
    • Volume Strain- It is change in volume of a material divided by its original volume when pressure are subjected.
  • Different between stress and strain are-
STRESSSTRAIN
Internal force per unit area.Change in shape/size.
Stress = Force/AreaStrain = Change on dimension/original dimension
Unit- Pascal(Pa)Unit- no unit
Types- Tensile, Compressive, etc.Types- Tensile, compressive, etc.

HOOKE ‘S LAW-

  • It state that, within the elastic limit, the stress applied to a material is directly proportional to strain it produces.
  • Stress= Elastic Constant * Strain
    • Constant is known as modulus of elasticity.

STRESS-STRAIN CURVE-

  • The stress-strain curve shows the relationship between stress (force per unit area) and strain (deformation) in a material.
    • Some important definitions of key points are-
      • Yield point(or elastic limit)- It is the stress level where a material starts to deform permanently, transitioning from elastic to plastic behavior.
      • Yield strength- It is the stress at which a material begins to deform plastically, marking the end of elastic behavior and the start of permanent deformation.
      • Permanent set- It is the deformation which remains in a material after removal of applied stress, provided the material was loaded beyond its elastic limit. It indicates the irreversible change in the material’s shape or size.
      • Plastic deformation- It is the permanent change in a material’s shape that occurs when it is stressed beyond its elastic limit. In this case, the material does not return to its original shape even after the stress is removed.
      • Ultimate tensile strength (UTS)- It is the maximum stress a material can withstand while being stretched or pulled before necking begins. It represents the highest point on the stress-strain curve.
      • Brittle- It is a material is one that breaks or fractures without significant deformation when stress is subjected. It has a small plastic region and low toughness (e.g., glass, ceramics).
      • Elastomers- It is a materials that can stretch significantly and return to their original shape after removing the force, like rubber.

ELASTIC MODULI-

  • Elastic moduli- It is measure a material’s ability to deform under stress and return to its original shape when the stress is removed.
  • Modulus of elasticity- It shows how stiff a material is. It tells how much a material stretches or compresses when a force is applied.
    • It is a ratio of stress and strain.
  • It has 3 types-
    • 1. Young ‘s modulus,
    • 2. Shear Modulus and
    • 3. Bulk Modulus.
  1. YOUNG ‘S MODULUD-
  • It is the ratio of stress (force per unit area) to strain (proportional deformation) in a material within its elastic limit.
  • Young’s modulus measures a material’s stiffness.
  • A higher value means the material is stiffer.
  • It is represented by E.
  • Young ‘s modulus of wire ‘s material-
    • E= Stress / Strain ​= F⋅L / A⋅ΔL​, where
      • F- Force applied (in Newtons, N),
      • L- Original length of the wire (in meters, m),
      • A = Cross-sectional area of the wire (in square meters ,m2) and
      • ΔL = Change in length (in meters, m)

2. SHEAR MODULUS-

  • Shear modulus measures a material’s resistance to shape change under a tangential (shear) force.
  • It is the ratio of shear stress to shear strain.
  • Shear modulus is represented by G.
  • G = Shearing stress / Shearing strain
  • Shearing Stress = G * θ
  • The SI unit of shear modulus is Pa or Nm-2

3. BULK MODULUS-

  • It is the ratio of volumetric stress and resulting volumetric strain.
  • It is represented by K.
  • K=Bulk Stress / Bulk Strain ​=ΔP / ΔV/V​​, where
    • ΔP = Change in pressure
    • V = Initial volume
    • ΔV = Change in volume
  • It shows how hard it is to compress a material without changing its shape.
  • A higher bulk modulus means the material is less compressible.
  • Gases have large compressibility, which varies with temperature and pressure.

POISSION ‘S RATIO-

  • Lateral Strain- It is perpendicular to the applied force.
  • Lateral strain is directly proportional to the longitudinal strain.
  • Poisson ‘s Ratio- It is the ratio of lateral strain and longitudinal strain.
  • Poisson ‘s ratio is the ratio of 2 strain; it is pure number and has no dimension or unit.
  • Its value depend on only nature of material.

ELASTIC POTENTIAL ENERGY IN A STRETCHED WIRE-

  • If the wire put under a tensile stress, then the work is done against the inter-atomic forces, this work is stored in the wire in a form of elastic potential energy.
  • Elastic potential energy in a stretched wire- It is the energy stored due to its deformation.
  • U= 1/2 * F ΔL and
  • U= 1/2 * F2*L / (A*E), where
    • F= Force applied,
    • ΔL= Extension of the wire,
    • L= Original length of the wire,
    • A= Cross-sectional area of the wire and
    • E= Young’s modulus of the material.

APPLICATIONS OF ELASTIC NATURE OF MATERIALS-

  • Springs- Used in mechanical systems like suspension systems in vehicles, where the material returns to its original shape after being stretched or compressed when force is applied.
  • Bridges and Buildings- Materials like steel are used in construction for their ability to withstand forces and return to their original shape without permanent deformation.
  • Elastic Bands- Used in everyday items like hair ties or as fasteners, utilizing the ability of rubber to stretch and return to its original shape.
  • Bungee Jumping- The elastic cord stretches under the weight of the jumper and then returns to its original shape, providing a safe landing.
  • Musical Instruments- Strings in instruments like guitars or pianos rely on elastic properties to vibrate and produce sound.
  • Eyeglass Frames- Made from materials like plastic or metal that bend but return to their original shape when adjusted.

These all are the notes of chapter 1 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊

Important Questions And Answers Which Strong Your Concept Are-

Answer- Brittle materials are used where strength and hardness are required, even though they fracture without much deformation.

  1. What is elasticity ?
    • Answer- Elasticity is the property of a material to regain its original shape and size after the removal of a deforming force.
  2. What is a perfectly rigid body ?
    • Answer- A perfectly rigid body is an ideal object that cannot be stretched, compressed, or bent. However, in reality, no solid is perfectly rigid.
  3. What is an elastic material ?
    • Answer- An elastic material returns to its original shape after the force causing deformation is removed.
  4. What is plasticity ?
    • Answer- Plasticity is the property of a material to undergo permanent deformation without breaking when a force is applied.
  5. What is a plastic material ?
    • Answer- A plastic material does not return to its original shape after the deforming force is removed.
  6. Define stress.
    • Answer-
      • Stress is the force applied per unit area on an object. It is a restoring force that acts opposite to the applied force.
      • Formula: Stress = F/A
      • Unit: Pascal (Pa)
  7. What are the types of stress ?
    • Answer-
      • Tensile Stress: Stretches the object, increasing its length.
      • Compressive Stress: Compresses or shortens the object.
      • Shear Stress: Causes layers to slide past each other.
      • Hydraulic Stress: Exerted by fluids under pressure.
  8. Define strain.
    • Answer- Strain is the change in shape or size of a material when subjected to stress. It has no unit.
  9. What are the types of strain ?
    • Answer-
      • Tensile Strain: Increase in length.
      • Compressive Strain: Decrease in length.
      • Shear Strain: Change in shape.
      • Longitudinal Strain: Ratio of change in length to original length.
      • Volume Strain: Ratio of change in volume to original volume.
  10. State Hooke’s Law.
    • Answer- Hooke’s Law states that within the elastic limit, stress is directly proportional to strain.
      • Formula: Stress = Elastic Constant × Strain
  11. What are the types of elastic moduli ?
    • Answer-
      • Young’s Modulus (E): Stiffness of a material under stretching or compression.
      • Shear Modulus (G): Resistance to shape change under shear force.
      • Bulk Modulus (K): Resistance to compression under pressure.
  12. Write the formula for Young’s Modulus.
    • Answer- E= Stress/Strain = ​=F*L​/A*ΔL, where
      • F: Force applied,
      • L: Original length,
      • A: Cross-sectional area,
      • ΔL: Change in length.
  13. What happens to molecules when a solid is deformed ?
    • Answer- When a solid is deformed, its atoms or molecules are displaced from their equilibrium position, causing changes in interatomic distances. Upon removal of force, these return to their equilibrium state.
  14. Why is the elastic behavior of materials important in engineering ?
    • Answer- Elastic behavior helps in designing structures and materials that can withstand forces without permanent deformation, ensuring safety and durability.
  15. What is the stress-strain curve ?
    • Answer- he stress-strain curve shows the relationship between stress and strain in a material.
  16. Define yield point.
    • Answer- The yield point is the stress level where a material starts to deform permanently, transitioning from elastic to plastic behavior.
  17. What is ultimate tensile strength (UTS) ?
    • Answer- UTS is the maximum stress a material can withstand before necking occurs during stretching.
  18. Name some applications of elastic materials.
    • Answer-
      • Springs in vehicle suspension systems.
      • Steel in bridges and buildings.
      • Rubber bands for everyday use.
      • Elastic cords for bungee jumping.
      • Guitar strings for sound production.
  19. What is elastic potential energy ?
    • Answer- Elastic potential energy is the energy stored in a material due to its deformation.
      • U= ½ FΔL
  20. What is Poisson’s Ratio ?
    • Answer- Poisson’s Ratio is the ratio of lateral strain to longitudinal strain. It is a dimensionless number.
  21. Why are brittle materials like glass used ?
    • Answer- Brittle materials are used where strength and hardness are required, even though they fracture without much deformation.