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SPH4U · Ontario — vectors, momentum, energy, orbits, fields and light

Grade 12 Physics

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Rearranging
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Setup & units
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Answers
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Forces in Two Dimensions

  • L1
    Breaking the vector
    resolve a force · cos along, sin across
    ★★★★★
    Start
  • L2
    Building the resultant
    components in, one net force out
    ★★★★★
    Start
  • L3
    Friction on the flat
    f = μN · the normal force from the weight
    ★★★★★
    Start
  • L4
    Static or kinetic?
    the breakaway ceiling and the angle of repose
    ★★★★★
    Start
  • L5
    The tilted world
    N = mg cos θ and mg sin θ · the incline's two shadows
    ★★★★★
    Start
  • L6
    Sliding down
    a = g sin θ, and what friction takes off it
    ★★★★★
    Start
  • L7
    Around the bend
    flat curves, banked curves, and the v² demand
    ★★★★★
    Start
  • ★
    The Loading Ramp
    the boss · no calculator · weight to normal to friction to speed
    ★★★★★
    Start

Momentum & Collisions

  • L9
    Momentum itself
    p = mv, asked every way
    ★★★★★
    Start
  • L10
    The impulse
    J = FΔt · a force held for a time
    ★★★★★
    Start
  • L11
    Impulse meets momentum
    FΔt = Δp · the bridge between the two
    ★★★★★
    Start
  • L12
    Nothing is lost
    conservation of momentum for two bodies
    ★★★★★
    Start
  • L13
    Sticking together
    the perfectly inelastic collision · one lump, one speed
    ★★★★★
    Start
  • L14
    The bounce
    elastic collisions and the coefficient of restitution
    ★★★★★
    Start
  • ★
    The Crash Investigation
    the boss · no calculator · momenta before, one lump after
    ★★★★★
    Start

Energy, All the Way Down

  • L16
    Work at an angle
    W = Fd cos θ · only the along-the-path part counts
    ★★★★★
    Start
  • L17
    Energy of motion
    Eₖ = ½mv² · the square does the damage
    ★★★★★
    Start
  • L18
    Work becomes speed
    the work–energy theorem · net work is the KE ledger
    ★★★★★
    Start
  • L19
    Energy of height
    U = mgh · position as a bank account
    ★★★★★
    Start
  • L20
    The spring
    F = kx and U = ½kx² · the half and the square
    ★★★★★
    Start
  • L21
    The great exchange
    conservation · height, speed and spring trade one currency
    ★★★★★
    Start
  • L22
    The rate of doing work
    P = W/t and P = Fv · a speedometer for energy
    ★★★★★
    Start
  • ★
    The Coaster Car
    the boss · no calculator · hilltop to valley to spring stop
    ★★★★★
    Start

Gravitation & Orbits

  • L24
    The inverse square
    F = Gm₁m₂/r² · double r, quarter F
    ★★★★★
    Start
  • L25
    Little g from big G
    g = GM/r² · weight is a field reading
    ★★★★★
    Start
  • L26
    Falling around the Earth
    v = √(GM/r) · r runs from the centre
    ★★★★★
    Start
  • L27
    The year of a satellite
    T = 2πr/v and T = 2π√(r³/GM) · two roads
    ★★★★★
    Start
  • L28
    Kepler's bargain
    T² over r³ · one ratio rules every moon
    ★★★★★
    Start
  • L29
    Leaving for good
    escape velocity · and the negative well
    ★★★★★
    Start
  • ★
    Mission Control
    the boss · no calculator · field, speed, period, escape
    ★★★★★
    Start

Electric & Magnetic Fields

  • L31
    Coulomb's count
    the electric inverse square · microcoulombs and the constant
    ★★★★★
    Start
  • L32
    The charge reservoir
    C = Q/V and the energy a capacitor banks
    ★★★★★
    Start
  • L33
    The sideways push
    F = qvB sin θ · the force that only notices motion
    ★★★★★
    Start
  • L34
    Wires in the field
    F = BIL · the motor effect · and wires pushing each other
    ★★★★★
    Start
  • L35
    The flux through the loop
    solenoid fields · Φ = BA cos θ · and the weber
    ★★★★★
    Start
  • L36
    The changing flux
    Faraday's law and motional EMF · change is what induces
    ★★★★★
    Start
  • ★
    The Mass Spectrometer
    the boss · no calculator · qvB supplies mv²/r
    ★★★★★
    Start

The Wave Nature of Light

  • L38
    The wave equation
    v = fλ and T = 1/f · nanometres, terahertz, and the speed limit
    ★★★★★
    Start
  • L39
    Slower in glass
    n = c/v · light's speed tax, and what survives the crossing
    ★★★★★
    Start
  • L40
    The bending rule
    Snell's law · sines, not angles · measured from the normal
    ★★★★★
    Start
  • L41
    Trapped light
    the critical angle and apparent depth · refraction's two tricks
    ★★★★★
    Start
  • L42
    Two slits, one pattern
    Δy = λL/d · measuring light with a ruler · the unit gauntlet
    ★★★★★
    Start
  • L43
    The grating
    mλ = d sin θ · orders, line counts, and the ceiling on sin θ
    ★★★★★
    Start
  • L44
    The polarizing angle
    Brewster's angle · the one formula in the chapter with a tangent
    ★★★★★
    Start
  • L45
    Colours in the film
    thin-film interference · why soap bubbles wear rainbows
    ★★★★★
    Start
  • ★
    The Optics Bench
    the boss · no calculator · one laser, four instruments
    ★★★★★
    Start

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