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NEWTONIAN MECHANICS

NEWTONIAN MECHANICS. Kinematic equations. Frictional Force. μ = coefficient of friction. Centripetal acceleration: The acceleration of an object due to it’s changing direction as it moves at a constant speed in a circular path. Always directed toward the center of the circle. a. F.

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NEWTONIAN MECHANICS

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  1. NEWTONIAN MECHANICS

  2. Kinematic equations
  3. Frictional Force
  4. μ = coefficient of friction
  5. Centripetal acceleration: The acceleration of an object due to it’s changing direction as it moves at a constant speed in a circular path. Always directed toward the center of the circle
  6. a F
  7. Torque: A force applied at a distance from the pivot to produce a rotation.
  8. Units: Nm
  9. momentum: The product of the mass and velocity. impulse: The product of the average force applied and the time is equal to the change in momentum. Momentum is a vector so remember the negatives
  10. F (N) area = Δp t (s) Units: kgm/s or Ns
  11. kinetic energy – Energy of motion gravitational potential energy – Energy due to position in a gravitational field Elastic potential energy – energy due to a stretch or compression
  12. Units: Nm = J
  13. Work: A force applied through a distance that changes the energy of the system Power: The rate of doing work
  14. Work Units: Nm Power Units: J/s = Watts
  15. Hooke’s law: The force due to a stretch or compression.
  16. k = the spring constant. How hard or easy it is to stretch the spring units N/m
  17. Period of a pendulum Period of a mass on a spring The period is the inverse of the frequency
  18. Period of a pendulum only depends on length and gravitational field, independent of mass and amplitude
  19. Gravitational Force: The force between two masses Gravitational potential energy: The potential energy between two masses
  20. Notice the force is divided by r2 and the energy is divided by r

  21. ELECTRICITY

  22. Coulomb’s Law: The force between two point charges.
  23. k = Coulomb’s constant 9.0E9 q = charge (C) r = distance between charges Like charges repel Unlike charges attract Forces are always equal and opposite regardless of charge size. -6C +4C
  24. The Electric Field: The force per unit charge at a point in space due to a the distribution of charges.
  25. Units: N/C or V/m
  26. The electric potential energy between two point charges
  27. + + If the charges are released the electric potential energy will be transferred to kinetic energy
  28. The Electric Potential (Voltage): The electrical potential energy per unit charge at a position in an electric field.
  29. Conservation of energy Potential difference between two charged plates Potential at a point due to a collection of point charges.
  30. Capacitance: Charge stored on two parallel metal plates due to a potential difference between the plates. The capacitance is directly proportional to the Area of the plates and inversely proportional to the distance between the plates.
  31. C is the capacitance (units C/V = F) A = area (m2) d = distance between plates (m) V = potential difference between plates (J/C =V) Q = charged stored on plate (C)
  32. Energy Stored on a Capacitor
  33. units : J
  34. Current – The rate at which charge flows in a circuit
  35. I = Current measured in C/s = A ΔQ = change in charge (C) Δt = change in time (s)
  36. The resistance of a wire is directly proportional to the resistivity and length of the wire and inversely proportional to the cross sectional area.
  37. R = Resitance (Ω) ρ = resistivity property of the material A = cross sectional area of wire (m2) L = Length of wire (m)
  38. Ohm’s Law: The relationship between the voltage, current and resistance. Current is directly proportional to the voltage and inversely proportional to the resistance.
  39. V I I R 1/R I V R
  40. Power – The rate at which electrical energy is dissapated.
  41. Units: J/s = W
  42. As resistors are added in series the total resistance goes up. As resistors are added in parallel the total resistance goes down.
  43. Capacitors are just the opposite
  44. R2 24V R1 R3 I Series Circuit Current is the same. Voltage is split. When one bulb goes out, all go out Greatest resistance is the brightest. Rs=R1+R2+R3+...
  45. R2 R1 R3 12V I1 I2 I3 I Parallel Circuit Voltage is the same. Current is split. When one bulb goes out, others stay the same. Least resistance is the brightest 1/Rp=1/R1+1/R2+1/R3+ …

  46. MAGNETISM

  47. Magnetic field lines go out of the north and into the south
  48. The magnetic force on a moving charge in a magnetic field
  49. q = charge (C) v = velocity (m/s) B = magnetic field (T) θ = angle between the velocity and the field, usually 90 degrees
  50. Right Hand Rule Force out of palm for positive charges, out of back of hand for negative charges.
  51. Motion of a charged particle in a magnetic field
  52. The magnetic force on a current carrying wire in a magnetic field
  53. I = current (A) L = length of wire (m) B = magnetic field (T) θ = angle between the velocity and the field, usually 90 degrees
  54. The magnetic field around a current carrying wire
  55. μo = constant 4πx 10-7 (C) I = current (A) B = magnetic field (T) r = distance from wire
  56. Magnetic Flux: The strength of a magnetic field passing through a loop of wire.
  57. φm = magnetic flux (Tm2= Wb) A = Area of loop B = magnetic field (T) θ = angle between field and the normal to the area.
  58. The induced EMF (voltage) is the rate of change of the flux with respect to time.
  59. ε = emf or induced voltage (J/C = V) Δφ = the change in flux Δt = the change in time N = number of loops.
  60. Motional EMF: The EMF induced in a wire as it cuts across a magnetic field.
  61. ε = emf or voltage measure in volts B = magnetic field (T) L = Length of cross cutting wire v = velocity

  62. FLUIDS

  63. Density: The mass per unit volume
  64. Units: kg/m3
  65. The pressure in a fluid is the sum of the absolute pressure and the atmospheric pressure.
  66. gauge pressure atmospheric pressure Pressure (N/m2 = Pa) h = depth (m) g = gravitational field ρ = density (kg/m3)
  67. Buoyancy Force: The buoyant force depends on the density of the fluid, the submerged volume and the gravitational field.
  68. Flow continuity: If the volume of fluid flowing through a pipe is the same then the product of the fluid velocity and cross sectional area of the pipe must be constant.
  69. Like your thumb over the hose. Less area greater speed.
  70. Bernoulli’s principle: Fast moving fluids result in low pressure.
  71. Conservation of Energy.

  72. THERMODYNAMICS

  73. Pressure is the Force per unit area measured in N/m2 = Pa
  74. Ideal gas law: Assumes all the internal energy is kinetic energy. Forces between particles are negligible.
  75. Temperature must be in Kelvin
  76. 1st Law of thermodynamics: Heat added to a system (gas) is equal to the work done by the gas plus its change in internal energy Work is done by the gas when the volume increases. Work is done on the gas when the volume decreases.
  77. Q = heat added (+) or removed (-) from gas (J) ΔU = change in internal energy. Temp increase (+) temp decrease (-) W = Work done by the gas If volume increase +work, if volume decrease -work Work is the area under the PV graph
  78. Efficiency – The ratio of the work done to the input heat (energy) The maximum efficiency of a heat engine is given by the Carnot equation.
  79. ATOMIC AND NUCLEAR
  80. The Energy of a photon. A photon is a light “particle”
  81. E = Energy of a photon (J or eV) h = planck’s constant (Js) or (eVm) c = speed of light (m/s) λ = wavelength (m or nm) p = momentum (kgm/s or Ns)
  82. Kmax = maximum kinetic energy of the emitted photo electrons (J or eV) f = frequency of incoming photon (1/s) φ = work function, the amount of energy needed to just remove an electron from the metal. (J or eV)
  83. The DeBroglie equation gives the wavelength of a particle like an electron. h = planck’s constant (Js) λ = wavelength (m) p = momentum (Ns or kgm/s)
  84. Δm = mass defect (u or kg or MeVc-2) c = speed of light The mass energy equivalence equation
  85. Atomic energy level diagrams
  86. Waves, Light and Optics
  87. The wave equation
  88. v = speed of the wave (m/s) λ = wavelength (m) f = frequency (1/s = Hz)
  89. The speed of a wave is different in different mediums. The ration of the wave speed in a vacuum to the speed in the medium is the index of refraction of the medium
  90. Refraction – The bending of light due to the different speeds of a wave in the mediums. The law of refraction is the relationship between the angle of incidence and the angle of refraction.
  91. Total Internal Reflection n1>n2 water to air glass to air glass to water өc = critical angle ө1 < өc Reflection and refraction ө1 ≥ өcONLY Reflection
  92. Lens/Mirror equation. Relationship between the image distance, object distance and focal length for converging and diverging devices.
  93. do object distance di image distance f = focal length M = Magnification converging devices (convex lens and concave mirror) have a positive focal length Diverging devices ( concave lens and convex mirror) have a negative focal length.
  94. Constructive interference occurs when the path difference is a full wavelength. Destructive interference occurs when the path difference is in intervals of λ/2
  95. Double Slit Interference – Evidence that light has wave characteristics
  96. 2nd order bright x2 θ θ d Central Bright dsinθ Path difference = dsinθ =2λ L
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