Dynamics: Motion, Velocity and Acceleration

• Dynamics is a branch of mechanics studying the motion of bodies under forces
• Motion is caused by force

Fundamental Definitions

• Length: Interval between two points on an object, measured in meters (m)
• Distance: Total length between initial and final points along the path taken, a scalar quantity in meters (m)
• Displacement: Length between initial and final points along the direct path, a vector quantity in meters (m)
• Speed: Change in distance per unit time, a scalar quantity in meters per second (m/s)
• Velocity: Change in displacement per unit time, a vector quantity in meters per second (m/s)
• Acceleration: Change in velocity per unit time, a vector quantity in meters per second squared (m/s²)

Equations of Motion

• For a body with mass m moving with velocity v from initial velocity u after a displacement s:
• v = u + at
• s = ut + (1/2)at²
• v² = u² + 2as
• Under gravity, acceleration a is replaced by g (9.81 m/s²), and initial velocity is zero for free-falling objects

Newton's Laws of Motion

• First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion unless acted on by an external force
• Inertia: Property of matter resisting changes in motion
• Mass: Measure of inertia, measured in kilograms (kg)
• Force: A push or pull, measured in Newtons (N)
• Second Law (Force and Acceleration): Acceleration is directly proportional to net force and inversely proportional to mass. F = ma
• Weight is a force: W = mg
• Third Law (Action-Reaction Law): Every action has an equal and opposite reaction

Reference Frames

• Inertial Frame: A frame where Newton's first law holds
• Non-inertial Frame: A frame undergoing acceleration where Newton's laws don't hold without introducing pseudo forces

Stress and Strain

• Stress: Internal resistance of a material to an external force
• Tensile stress: Force pulling materials apart
• Compressive stress: Force squeezing a material
• Shear stress: Force causing one part to slide over another
• Strain: Deformation of a material due to stress
• Tensile strain: Elongation from tensile stress
• Compressive strain: Reduction in size from compressive stress
• Shear strain: Distortion from shear stress

Stress-Strain Diagram

• Elastic limit: Maximum stress before permanent deformation
• Yield point: Stress level when plastic deformation starts
• Ultimate strength: Maximum stress before failure
• Fracture point: Stress at material breakage

Principal Mechanical Properties of Materials

• Strength: A material's ability to withstand external loads without failure
• Types of strength: Tensile, compressive, shear, and torsional
• Elasticity: A material's ability to return to its original shape after deformation
• Elastic limit: Maximum stress before permanent deformation
• Stiffness: Resistance to deflection or deformation, measured by Young's modulus (E); higher E indicates a stiffer material
• Plasticity: Ability to permanently deform without breaking, useful in shaping
• Ductility: Ability to be stretched into a wire without breaking, measured by elongation percentage
• Malleability: Ability to be compressed into thin sheets without cracking, important in food processing
• Brittleness: Tendency to break without significant deformation
• Toughness: Ability to absorb energy before failure, important in food packaging design
• Hardness: Resistance to indentation or scratching, measured using Brinell, Rockwell, and Vickers tests
• Impact strength: Resistance to fracture under sudden force, tested using IZOD and CHARPY tests
• Resilience: Capacity to absorb and release energy elastically, relevant in food materials like gels
• Fatigue: Failure due to repeated cyclic loading
• Creep: Slow deformation under constant stress, significant in stored food materials

Applications in Food Science

• Mechanical properties aid in designing food processing equipment
• Texture analysis: crispiness, chewiness, hardness
• Enhancing food packaging: matching material properties to requirements

Introduction to Rheology

• Rheology: Study of flow and deformation of matter relative to force, deformation, and time
• Essential for understanding textural properties and processing in food science

Importance of Rheology in Food Systems

• Aids in mixing and blending, flow control in pipes and containers, pumping liquids and semi-solids, texture analysis, quality assessment, new product development

Viscosity and Flow Behavior

• Newtonian fluids: Constant viscosity regardless of shear stress
• Linear relationship between shear stress and shear rate
• Examples: Milk, juices, sucrose solutions, honey
• Non-Newtonian fluids: Viscosity varies with shear rate
• Shear-thinning (pseudoplastic) fluids: Viscosity decreases with increasing shear rate (e.g., fruit purees, melted chocolates)
• Shear-thickening (dilatant) fluids: Viscosity increases with increasing shear rate (e.g., starch pastes, candy compounds)
• Thixotropic fluids: Viscosity decreases over time under constant shear (e.g., ketchup, mayonnaise)
• Rheopectic fluids: Viscosity increases over time under constant shear (rare in food systems)
• Plastic fluids: Requires minimum yield stress before flow (e.g., ketchup, yogurt)

Deformation and Mechanical Properties

• Elastic solids: Return to original shape after stress removal (e.g., fresh cheese, bread)
• Viscoelastic materials: Exhibit both solid-like and liquid-like behavior (e.g., dough, gelatin gels)

Rheological Models

• Kelvin Model: Used for viscoelastic solids
• Maxwell Model: Describes stress relaxation in viscoelastic materials
• Burgers Model: Predicts creep behavior in food systems
• Generalized Maxwell and Kelvin Models: Better representation of food rheology
• Bingham Model: Used for plastic flow behavior

Applications in Food Science and Engineering

• Meat products: Tenderness evaluation and quality grading
• Dairy products: Texture analysis of cheese, cream, and yogurt
• Bakery: Dough consistency, shelf-life prediction
• Confectionery: Thickness, chewiness, elasticity assessment
• Jams and jellies: Gel integrity and consistency measurement
• Snack foods: Crispiness, hardness, and packaging needs
• Beverages: Viscosity control for improved mouthfeel and stability