GEMP 2023 PHYSICS

Outline

  • Physics Reference Materials
  • GEMP Physics Topics
    • Mechanics
    • Properties of matter
    • Elastic & plastic
    • Viscosity
    • Vibrational motion
    • Circular motion
    • Oscillations
    • Resonance
    • Thermodynamics
    • Kinetic theory
    • Real and ideal gases
    • Laws of thermodynamics
    • Electromagnetic Properties of matter
    • Magnetic materials
    • Dielectrics
    • Semiconductors
    • Selected Topics in Modern Physics
    • The photon
    • Heisenberg Uncertainty Principle
    • Particle in a box
    • Selected Measuring instruments
    • Spectrometers

Physics Reference Materials

  • University Physics
  • Fundamentals of Physics
  • Physics: Principles with Applications
  • Sears & Zemansky's University Physics with Modern Physics (Fifteenth Edition, Global Edition)
  • Physics Principles with Applications by Douglas C. Giancoli
  • Fundamentals of Physics by Jearl Walker
  • Halliday & Resnick
  • Previously sold as the 10th Edition
  • Extended

Mechanics

Elastic Properties of Bodies

  • Real bodies deform when stressed.
  • For small deformations, stress is proportional to strain.
    • Stress: ext{Stress} = rac{F}{A}
    • Strain: ext{Strain} = rac{ riangle L}{L0} = rac{L - L0}{L_0}
    • Young’s Modulus: E = rac{ ext{Stress}}{ ext{Strain}} = rac{ rac{F}{A}}{ rac{ riangle L}{L_0}}
Bulk Properties
  • Bulk stress: ext{Bulk stress} = rac{F}{A}
  • Bulk strain: ext{Bulk strain} = rac{ riangle V}{V_0}
  • Bulk modulus: K = - rac{ riangle P}{ rac{ riangle V}{V_0}}
  • Compressibility: eta = rac{1}{K} = - rac{1}{V_0} rac{ riangle V}{ riangle P}
Shear Properties
  • Shear stress: ext{Shear stress} = rac{F}{A}
  • Shear strain: ext{Shear strain} = an{ heta}
  • Shear modulus: G = rac{ ext{Shear stress}}{ ext{Shear strain}}
Poisson’s Ratio
  • u = - rac{ ext{transverse strain}}{ ext{longitudinal strain}} = - rac{ rac{ riangle D}{D0}}{ rac{ riangle L}{L0}}
    • Alternative expressions:
      u = rac{3(1-2
      u)}{2(1+
      u)}

Plastic Properties

  • Typical stress-strain diagrams exhibit the following:
    • Elastic limit or yield point: The maximum stress that can be subjected before permanent deformation.
    • Proportional limit: The region of elastic behavior where stress is proportional to strain.
    • Plastic deformation: Permanent deformation occurring after the yield point.
    • Fracture point: The stress where the material finally breaks.
    • Elastic hysteresis: The difference in stress-strain behavior under increasing vs. decreasing stress.

Example: Stress and Strain of an Elongated Rod

  • A steel rod with:
    • Radius: R = 9.5 ext{ mm}
    • Length: L = 81 ext{ cm}
    • Force applied: F = 62 ext{ kN}
  • Key ideas:
    1. Stress calculation: ext{Stress} = rac{F}{A} where A = rac{ ext{π}R^2}.
    2. Elongation related to stress and Young's Modulus: riangle L = rac{F L}{AE} where E is Young's modulus.
    3. Strain is the ratio of elongation to the initial length: ext{Strain} = rac{ riangle L}{L}.

Calculations

  1. Compute stress:
    ext{Stress} = rac{62 imes 10^3 N}{ ext{π}(9.5 imes 10^{-3 m})^2} = 2.2 imes 10^8 N/m^2

    • The yield strength for structural steel is approximately 2.5 imes 10^8 N/m^2, indicating the rod is near its yield strength.

  2. Young's modulus from table: E_{steel} = 2.0 imes 10^{11} N/m^2

    • Elongation:
      riangle L = rac{ST}{E} = rac{(2.2 imes 10^8 N/m^2)(0.81 m)}{(2.0 imes 10^{11} N/m^2)} = 0.00089 m = 0.89 mm

  3. Strain:
    ext{Strain} = rac{0.00089 m}{0.81 m} = 0.0011 = 0.11 ext{%}

Example: Young's Modulus Calculation

  • Given:
    • Young's modulus = 42 GPa, Poisson ratio:
      u = rac{2}{5}.
  • Find:
    • Bulk modulus: K = rac{3(1-2
      u)}{2(1+
      u)} = 70 ext{ GPa}
    • Shear modulus: G = rac{E}{2(1+
      u)} = 15 ext{ GPa}

Example: Ideal Gas Law

  • State: PV = nRT
  • Isothermal bulk modulus: K = - rac{PV}{nR},
    • Evaluation under pressure: P = 100 kPa
      ightarrow compressibility = 1/(K) ext{ at temperature T}

Common Problems

  • Biceps Muscle Example:
    • When relaxed requires 25.0 N for elongation of 3.0 cm.
    • Maximum tension requires 500 N for same elongation.
    • Determine Young's modulus for both conditions assuming uniform cylinder properties.

Viscosity

  • Defined as the internal friction in a fluid.
  • Influences and relates flow rate to pressure gradient through the Poiseuille equation.
  • Volume flow rate:
    Q = ext{velocity} imes ext{Area}

Example: Water Flow in Capillary Tube

  • Given:
    • Pressure differential: 1.5 mm
    • Viscosity: 0.801 cP.
  • Calculation of water flow in 30 seconds across stated tube diameter:
    Q = 5.17 imes 10^{-6} m^3 s^{-1}

Vibrational Motion

  • Discussed in context of circular motion with critical acceleration related computations.
  • Centripetal acceleration defined:
    a_c = rac{v^2}{r}
  • Uniform circular motion is characterized by constant speed and periodic motion.

Example: Kinetic Energy in Circular Motion

  • Object of mass 2kg moving in a circle of radius 20m under centripetal force of 800 N:
    KE = rac{mv^2}{2} = rac{20m imes 800N}{2}=8000 J

Resonance

  • Occurs when the driving frequency matches the system's natural frequency.
  • Characterized by motion equations of damped driven oscillators
  • Damping behaviors detail amplitude decay related to system design frequency:
    m rac{d^2x}{dt^2} + b rac{dx}{dt} + kx = 0

Laws of Thermodynamics

  • Zeroth Law: If system A is in equilibrium with system B, and B is in equilibrium with system C, then A and C are in equilibrium.
  • First Law: riangle U = Q - W (energy conservation)
  • Second Law: States that all heat cannot be converted into mechanical work without losses.
  • Carnot Efficiency Equation: ext{Efficiency} = 1- rac{Tc}{Th}

Real Gases

  • Discuss Van der Waals equation of state and deviations from ideal gas behavior at high pressures or low temperatures.

Example: Ice Melting

  • Determine the energy efficiency when 1 kg of ice melts at 0°C, specific latent heat of ice is 3.34 imes 10^5 J kg^{-1} resulting in riangle S = rac{1kg imes 3.34 imes 10^5 J}{273.15 K}.

Electromagnetic Properties of Materials

  • Discuss magnetic materials, dielectrics, and semiconductors.
Magnetic Properties
  • Diamagnetism: Overall negative magnetization, weakly repelled by external fields.
  • Paramagnetism: Material with unpaired electrons, characterized by a positive weak magnetic susceptibility of about 10^{-4}.
  • Ferromagnetism: Materials like iron, cobalt, and nickel: strong interactions exist between magnetic dipoles.
    • Magnetization is also dependent on temperature and exhibits hysteresis behaviors.

Semiconductor Properties

  • Discuss intrinsic and extrinsic semiconductors, their band structures, and charge carrier behavior.

Example: Transistor Applications

  • Bipolar junction transistors (BJTs) demonstrate critical current amplification characteristics in circuits.

Selected Topics in Modern Physics

  • The photon is a quantum of the electromagnetic field.
  • Heisenberg Uncertainty Principle: Constraints on precision measurements of conjugate variables.
  • Solve examples related to motion of particles in quantum systems described by the Schrödinger equation.

Example: Mass Spectrometry

  • Explanation of ionized particle dynamics in magnetic fields to quantify masses in atomic units, with specific calculations indicated.