Second Semester Review Notes

Second Semester Review

Module 10: Work and Energy

• Concept of Work
• Kinetic Energy:
  • Definition and calculations.
• Potential Energy:
  • Definition.
• Relationship:
  • Potential energy and kinetic energy.
• Mechanical Energy
• Conservation of Energy:
  • Total Energy = KE + PE = Constant
  • $Total Energy = KE + PE = Constant$
  • Energy changes from potential to kinetic and back again.
• Examples:
  • Pendulum.
• Power:
  • Definition and calculations.
• Force vs. Distance Graphs:
  • Meaning of area under the curve.
• Using Force vs. Distance Graphs:
  • Calculate work.
• Calculating:
  • Work and change in types of energy.

Module 11: Heat and Thermodynamics

• Density ($\rho$)
• Temperature Scales:
  • Fahrenheit
  • Celsius
  • Kelvin
  • Notable temperatures on each scale:
    • Boiling Point of H2O: 212°F = 100°C = 373 K
    • Avg. Body Temp: 98°F = 37°C = 310 K
    • Freezing Point of H2O: 32°F = 0°C = 273 K
    • Absolute Zero: -460°F = -273°C = 0 K
• Thermal Energy vs. Temperature:
  • Thermal energy = The TOTAL amount of kinetic energy contained within the particles of an object.
  • Temperature = The AVERAGE amount of kinetic energy contained within the particles of an object.
• Specific Heat (C):
  • Different from one substance to the next. Amount of energy needed to raise the temperature of (1) kg of a substance by (1) degree Celsius/Kelvin.
  • High specific heat → “tough” to heat up
  • Low specific heat → “easy” to heat up
• Types of Heat Transfer:
  • Conduction
  • Convection
  • Radiation
• Heat Transfer (Q):
  • If $(T<em>F > T</em>i)$ → Q is positive
  • If $(T<em>F < T</em>i)$ → Q is negative
• Thermal Equilibrium:
  • Hot substance(s) combined with cold substance(s).
  • Thermal energy lost by hot substance(s) is equal to thermal energy gained by cold substance(s) assuming that substances equilibrate in a closed system.
• Changes of Phase:
  • Solid → Liquid = MELTING (increase entropy)
  • Liquid → Solid = FREEZING (decrease entropy)
  • Liquid → Gas = EVAPORATING (increase entropy)
  • Gas → Liquid = CONDENSING (decrease entropy)
  • Heat of Fusion ($H_f$) – [Different from one substance to the next]
    • Amount of heat transfer that occurs when $(m)$ kilograms of a substance goes from solid to liquid (or vice versa).
  • Heat of Vaporization ($H_v$) – [Different from one substance to the next]
    • Amount of heat transfer that occurs when $(m)$ kilograms of a substance goes from liquid to gas (or vice versa)
• Laws of Thermodynamics

Module 13/14: Vibrations and Waves

• Wave Properties:
  • Types of Waves
    • Transverse – Direction of wave travel is perpendicular to the direction of disturbance that creates the wave.
    • Longitudinal – Direction of wave travel is parallel to the direction of disturbance that creates the wave
  • Crests, Troughs, Amplitude, Wavelength $\lambda$, Frequency $(f)$
  • Velocity of a wave $(v)$
• Wave Behavior:
  • Constructive & Destructive Interference
    • Nodes – Points of minimum displacement (maximum pressure)
    • Antinodes – Points of maximum displacement (minimum pressure)
  • When waves encounter boundaries between media
    • Free end – wave returns un-inverted
    • Fixed end – wave returns inverted

Module 13/14: Sound

• Properties of Sound:
  • Sound is a longitudinal wave
  • Speed of sound in different materials
    • Fastest in solids, slowest in gases)
  • Loudness (The Decibel Scale)
    • Increase of 20 dB → Pressure amplitude is 10x larger
    • Increase of 10dB → Sound is “twice as loud”
    • Increase of 10dB → Intensity is 10x the intensity.
  • Pitch ≈ Frequency
    • Humans can hear sounds from 20 Hz – 16,000 Hz
  • Doppler Effect
    • Apparent change in the pitch of a sound caused by the relative motion between the sound source and the observer (e.g. ambulance siren)
• The Physics of Music:
  • Closed-Pipe Resonators
    • Resonance lengths, Ln are odd #s of quarter-wavelengths
      • $L<em>1 = (¼) \lambda, L</em>2 = (¾) \lambda$, etc.
    • Natural frequencies
      • $f<em>1 = v/4L</em>1$
      • $f<em>2 = 3 \cdot f</em>1 , f<em>3 = 5 \cdot f</em>1 , f<em>4 = 7 \cdot f</em>1$, etc.
  • Open-Pipe Resonators
    • Resonance Lengths, Ln are even #s of quarter-wavelengths
      • $L<em>1 = (2/4)\lambda , L</em>2 = (4/4)\lambda$, etc.
    • Natural Frequencies
      • $f_1 = v/2L$
      • $f<em>2 = 2 \cdot f</em>1 , f<em>3 = 3 \cdot f</em>1 , f<em>4 = 4 \cdot f</em>1$, etc.
  • Beat Frequency, $(f_{beat})$
    • Created when playing two notes together, $(f<em>A)$ and $(f</em>B)$, that have almost the same frequency

Module 15/16: Light and Reflection

• Light fundamentals:
  • Illuminance – rate at which light falls on a surface
• Light and Matter:
  • Additive Primary Light Colors – Red, Green, Blue
  • Subtractive Primary Pigments – Yellow, Cyan, Magenta
• Polarization of light:
  • Only when two polarizing filters are at right angles to each other, no light comes through
• Law of Reflection:
  • Angle of Incidence = Angle of Reflection
• Mirrors:
  • Plane Mirrors (i.e. flat mirrors)
    • Create a right-side-up, undistorted, virtual image with a magnification of one
  • The Lens/Mirror Equations
    • $1/f = 1/p + 1/q$
    • $m = -q/p$
    • $f$ = focal length
    • $p$ = object position
    • $q$ = image position
    • $m$ = magnification
    • $q$ is positive for real images in mirrors
    • $q$ is negative for virtual images in mirrors
  • Images
    • Real image
      • Formed by converging rays of light
      • Up-side-down, relative to the object
    • Virtual Image
      • Formed by converging sight lines
      • Right-side-up
  • Concave Mirrors (Inside surface of a spoon)
    • $f$ is positive for concave mirrors
    • Real inverted images when outside the focal length and either enlarged or reduced
    • Virtual enlarged images when inside the focal length
  • Convex Mirrors (Back side of a spoon)
    • $f$ is negative for convex mirrors
    • Images are always virtual, regardless of object position

Module 16/17: Refraction and Lenses

• Refraction:
  • The bending of light caused when light moves from one medium to another.
• Index of Refraction ($\eta$)
  • $\eta = c/v$
    • $c$ = speed of light in a vacuum
    • $v$ = speed of light in the medium
• Snell’s Law of Refraction
  • $n<em>i sin(\theta</em>i) = n<em>r sin(\theta</em>r)$
    • $n_i$ = index of refraction of incident (initial) material
    • $n_r$ = index of refraction of refracting (final) material
    • $\theta_i$ = angle of incidence (from the normal)
    • $\theta_r$ = angle of refraction (from the normal)
• Going from low $n$ to higher $n$ (air to glass), light bends towards the normal
• Going from high $n$ to lower $n$ (glass to air), light bends away from normal
• Refraction does not change the frequency of the light
• Lenses
  • $1/f = 1/p + 1/q$
    • $f$ = focal length
    • $p$ = object position
    • $q$ = image position
    • $q$ is negative for virtual images
    • $q$ is positive for real images
  • Concave Lenses (“diverging lens”)
    • $f$ is negative for concave lenses
  • Convex Lenses (“converging lens”)
    • $f$ is positive for convex lenses
• Magnification, m
  • $m = -q/p$
  • If (m < 0) → image is inverted, otherwise it is upright
  • If |m| > 1 → image is larger than object
  • If |m| < 1 → image is smaller than object

Module 17: Interference and Diffraction

• Interference demonstrates that light has wave properties.
• Light passing through two closely spaced, narrow slits produces a pattern on a screen of dark and light bands called interference fringes.
• Interference patterns can be used to determine wavelength of light.
  • Young’s Double Slit Experiment – Constructive interference when waves are separated by a whole wavelength.
• Thin film interference causes a spectrum of colors as a result of the constructive and destructive interference of light waves due to reflection in a thin film.
• Light passing through narrow openings is diffracted and produces an interference pattern on a screen.
• The limits of resolution in a lens due to the diffraction and interference can be improved by using a larger lens or using shorter wavelength light.

Module 18: Electric Force and Fields / Electric Energy and Capacitance

• Electrical Charge:
  • Opposite charges attract, similar charges repel
  • Conductors – materials thru which charges move easily
  • Insulators – materials thru which charges do not move easily
• Methods of charging an object:
  • Conduction:
    • Physically touching an object to a charged object, causing the charged particles to flow until an equilibrium is reached.
    • Rubbing two objects together can transfer electrons from one to the other
    • Example: VanderGraf Generator – charges move out to the outer edge of the sphere and move into any object brought close enough to it
  • Conductor is a substance in which charged particles can move easily. Insulator is a substance in which they do not move easily
  • Induction:
    • Bringing an object near a charged object to induce the charges to move
• Measuring electrical charge (q):
  • The Coulomb is the base unit of electrical charge. It is not derived from any other units – it is one of the 7 basic SI units (meter, kilogram, second, etc.)
• Electric Force:
  • Coulombs Law – Electric Force $(F<em>E)$ between to charges $(q</em>A$ and $q_B)$ separated by some distance $(d)$.
    • $F<em>E = K \cdot (q</em>A \cdot q_B) / d^2$
    • $K = (9 \times 10^9) N \cdot m^2/C^2$
    • Only calculates the magnitude of the force, so don’t keep up with +/- signs of charges
  • Proton charge = $(1.6 \times 10^{-19}) C$, electron charge = $-(1.6 \times 10^{-19}) C$
• The energy added to a charged particle, $(q)$ by a voltage source, $(V)$:
  • $E = qV$
• Charge on a hollow metal sphere is distributed on the outside of the sphere. The electric field and charge inside the sphere is zero.
• Capacitance
  • $C = Q/V$
  • measured in Farads (F), 1 Farad = 1 Coulomb / Volt

Module 19: Circuits and Circuit Elements

• Currents and Circuits:
  • Electric Current, $I$ is the amount of charge that goes past a given point per second.
    • 1 Ampere = 1 Coulomb/sec
  • In an alternating current, the current is constantly changing direction. In a direct current, it always goes in the same direction.
  • Power = Voltage × Current
    • $P = V \cdot I$
  • Resistance & Ohm’s Law
    • $V=I \cdot R$
    • Resistance depends upon material, temperature, length and thickness
• Simple Circuits:
  • Series Circuits
    • Current is the same at any point in a series circuit
    • The voltage dropped across each resistor depends upon the size of the resistor – bigger resistor, bigger voltage drop
    • The total voltage drop of all resistors is equal to the source voltage – the amount of voltage lost by the resistors is equal to the voltage added by the battery
    • Equivalent Resistance for n series resistors:
      • $R<em>{eq} = R</em>1 + R<em>2 + … + R</em>n$
  • Parallel Circuits
    • The voltage drop across each resistor in parallel is the same, equal to the source voltage.
    • The current in a parallel circuit is distributed among the resistors/branches of the circuit. The amount of current going through a given resistor/branch depends upon the size of the resistor. Bigger resistor, smaller current
    • The sum of the currents going into each branch adds up to the total current, which is the current that comes straight from the source voltage.
    • Equivalent Resistance for n parallel resistors:
      • $1/R<em>{eq} = 1/R</em>1 + 1/R<em>2 + … + 1/R</em>n$

Module 20: Magnetism

• Magnets:
  • Regions of clustered neighboring atoms are called domains. In non-magnetic objects, the domains are randomly oriented. In magnets, they are lined up in the same direction.
  • Magnetized objects have a magnetic field all around them, which is the strongest at the poles (North and South).
• Magnetic Fields (MF’s) and Right-Hand Rules (RHR’s):
  • 1st RHR: MF around a straight current-carrrying wire
    • Thumb points in direction of current
    • MF is in direction of curled fingers
  • 2nd RHR: Location of Poles in an Electromagnet
    • Index finger follows incoming current around first loop.
    • Thumb points towards the North pole of the electromagnet created
    • Increasing the number of loops of wire increases the MF strength of the electromagnet created
  • 3rd RHR: Force on a current carrying wire in a magnetic field
    • Straight fingers point with MF (North-to-South)
    • Thumb points in direction of current in the wire
    • Palm faces in the direction of the force
    • Force, current and magnetic field are all perpendicular to one another
    • Two parallel wires with current in same direction attract each other
    • Two parallel wires with current in opposite direction repel each other
  • $F = BI l$
    • $F$ = Force on a current carrying wire in a magnetic field
    • $B$ = magnetic field strength
    • $I$ = current
    • $l$ = length of wire
  • $F = Bqv$
    • $F$ = Force on a moving charge in a magnetic field
    • $B$ = magnetic field strength
    • $q$ = charge
    • $v$ = velocity

Electromagnetic Induction

• Energy converters:
  • Generators – mechanical energy → electrical energy
  • Motors – electrical energy → mechanical energy
• Induced emf:
  • $emf = -N (ΔΦ/Δt)$
    • $N$ = number of loops
    • $Φ$ = magnetic field
    • $t$ = time
• Transformers:
  • Power = I·V. Overall power is conserved in a transformer, but voltage and current are changed.
    • $(V<em>p \cdot I</em>p) = (V<em>s \cdot I</em>s)$
      • $V_p$ = primary voltage
      • $I_p$ = primary current
      • $V_s$ = secondary voltage
      • $I_s$ = secondary current
  • Transformer Equation
    • $V<em>p / V</em>s = N<em>p / N</em>s$
      • $(p)$ primary , $(s)$ secondary
      • $N_p$ = number of primary loops
      • $N_s$ = number of secondary loops
  • Step-up Transformer
    • Low $(V<em>p)$ gets “stepped-up” to a higher $(V</em>s)$
    • $N<em>p < N</em>s$
  • Step-Down Transformer
    • High $(V<em>p)$ gets “stepped-up” to a lower $(V</em>s)$
    • $N<em>p > N</em>s$
• Electromagnetic waves are generated by varying electric fields and magnetic fields that are perpendicular to each other and travel through space at the speed of lights.

Module 21-23: Atomic Physics

• Planck’s constant, $h = (6.63 \times 10^{-34}) J/Hz$
• Energy of a photon, $E = hf$
  • Speed of a photon = $c$ = speed of light = $(3 \times 10^8)m/s$
  • $E = hc / \lambda$
  • 1 Electron-Volt (eV) = $(1.6 \times 10^{-19}) Joules$
• Photoelectric Effect:
  • Radiation will eject electrons from a given material if the frequency of the radiation is above the threshold frequency, $f_0$ for that material.
  • $KE_{max} = hf - W$
    • $KE_{max}$ = Maximum Kinetic Energy
    • $W$ = Work function
• Momentum of a photon
  • $p = h / \lambda$
• deBroglie wavelength
  • $\lambda = h / p$
• Heisenberg Uncertainty Principle
  • It is impossible to accurately measure both the momentum and position of a particle. Whenever you measure one, you disrupt the other.
  • $(Δx)(Δp) ≥ h/2π$
• Rutherford Model – based on gold foil experiment, positive charge is concentrated in the nucleus
• The nucleus:
  • The nucleus is located at the center of the atom
  • It makes up 99.999% of the mass of the atom
  • It contains protons and neutrons, which have approximately equal masses of 1 atomic mass unit (1u)
• Bohr Model of atom
  • energy levels
  • emission spectrum

Module 21-23: Subatomic Physics

• Radioactivity:
  • Isotopes – more neutrons that protons
    • $Z$ = # protons (i.e. atomic #)
    • $A$ = #(protons + neutrons)
    • Example: “Uranium-238”
      • 92 Protons
      • +146 Neutrons
      • 238 Total particles in the nucleus
  • Alpha Decay
    • Reduces the mass number by 4 and the atomic number by 2
  • Beta Decay
    • A neutron decays into a proton, an electron, and an antineutrino
  • Gamma Decay
    • Highly penetrating, high-energy photons
• Half-Life (H)
  • $N(t) = N_0 (1/2)^{t/H}$
    • $N(t)$ = amount remaining after time t
    • $N_0$ = original amount
    • $H$ = half life
  • After each half-life, half of the sample is gone
  • @ $2 \cdot H$ → 1/4
  • @ $3 \cdot H$ → 1/8
  • @ $4 \cdot H$ → 1/16
• Activity – number of decays per unit time. Measured in Becquerels or Curies
• Fundamental Particles:
  • Leptons
  • Quarks
• Standard Model – Big Bang theory

Formulas for Honors Physics Spring Exam

• Energy
• Thermodynamics
• Waves/Harmonics
  • Open Pipe
    • $f_n = n \cdot (v/2L)$
  • Closed Pipe
    • $f_n = n \cdot (v/4L)$
• Light/reflection
  • $c = 3 \times 10^8 m/s$
• Refraction
  • $n = c/v$
  • $n<em>1sinθ</em>1 = n<em>2sinθ</em>2$
• Interference/diffraction
  • $dsinθ = mλ$

Static Electricity

• $K= 9.0 \times 10^9 Nm^2/C^2$

Current Electricity

• $V = IR$
• $P = IV$
• Series: $R<em>{eq} = R</em>1 + R_2 + …$
• Parallel: $1/R<em>{eq} = 1/R</em>1 + 1/R_2 + …$

Magnetism

• $F = BI l$
• $F = Bq v$

Electromagnetism

• $ε = -N(ΔΦ/Δt)$
• $(V<em>p)(I</em>p) = (V<em>s)(I</em>s)$
• $V<em>p/V</em>s = N<em>p/N</em>s$

Atomic Physics

• $h= 6.626 \times 10^{-34} J/Hz = 4.14 \times 10^{-15} eV/Hz$
• $E = hf$
• $c = 3 \times 10^8m/s$
• 1 u => 931.49 MeV