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: $ext{Stress} = \frac{F}{A}$
  • Strain: $ext{Strain} = \frac{ riangle L}{L<em>0} = \frac{L - L</em>0}{L_0}$
  • Young’s Modulus: $E = \frac{ ext{Stress}}{ ext{Strain}} = \frac{\frac{F}{A}}{\frac{ riangle L}{L_0}}$

Bulk Properties

• Bulk stress: $ext{Bulk stress} = \frac{F}{A}$
• Bulk strain: $ext{Bulk strain} = \frac{ riangle V}{V_0}$
• Bulk modulus: $K = -\frac{ riangle P}{\frac{ riangle V}{V_0}}$
• Compressibility: $\beta = \frac{1}{K} = -\frac{1}{V_0} \frac{ riangle V}{ riangle P}$

Shear Properties

• Shear stress: $ext{Shear stress} = \frac{F}{A}$
• Shear strain: $ext{Shear strain} = an{ heta}$
• Shear modulus: $G = \frac{ ext{Shear stress}}{ ext{Shear strain}}$

Poisson’s Ratio

• $\nu = -\frac{ ext{transverse strain}}{ ext{longitudinal strain}} = -\frac{\frac{ riangle D}{D<em>0}}{\frac{ riangle L}{L</em>0}}$
  • Alternative expressions: $<br />\nu = \frac{3(1-2<br />\nu)}{2(1+<br />\nu)}$

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: $ext{Stress} = \frac{F}{A}$ where A = rac{ ext{π}R^2}.
  2. Elongation related to stress and Young's Modulus: $riangle L = \frac{F L}{AE}$ where $E$ is Young's modulus.
  3. Strain is the ratio of elongation to the initial length: $ext{Strain} = \frac{ riangle L}{L}$.

Calculations

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

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

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: $<br />\nu = \frac{2}{5}$.
• Find:
  • Bulk modulus: $K = \frac{3(1-2<br />\nu)}{2(1+<br />\nu)} = 70 ext{ GPa}$
  • Shear modulus: $G = \frac{E}{2(1+<br />\nu)} = 15 ext{ GPa}$

Example: Ideal Gas Law

• State: $PV = nRT$
• Isothermal bulk modulus: $K = -\frac{PV}{nR}$,
  • 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:
  $a_c = \frac{v^2}{r}$
• 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:
  $KE = \frac{mv^2}{2} = \frac{20m imes 800N}{2}=8000 J$

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:
  $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0$

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: $ext{Efficiency} = 1-\frac{T<em>c}{T</em>h}$

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 $riangle S = \frac{1kg imes 3.34 imes 10^5 J}{273.15 K}$.

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.