Unit 3 Aos 2: Electrical Energy
Unit 3 Aos 1: Fields
Elevator Physics: When an elevator is travelling upwards the apparent
weight is the force from gravity + the moving force. If it is travelling
downwards it’s the force from gravity - the moving force
E=W=Fs
E=Change in grav potential (J)
W=Work Done (J)
Force-Distance Graph Area under= Change in grav potential
energy=Work done. It may sometimes be represented as Newtons per
Kilo so to find change in grav pot it must be multiplied by the mass
Electric (E-Field)
direction + 🡪 –- [lines
never cross] Number of
field lines indicates
relative strength of
charges. Like charges repel & Unlike charges attract (+&−)
Electromagnetic Induction: The creation of an electric current or an
emf in a loop of wires as a result of changing the magnetic flux
through the loop.
Induced Emf: E=LvB
L=length of conductor
Emf vs Flux: The emf is equal
to the negative gradient of the
magnetic flux. When the
gradient of magnetic flux is zero
then the emf will be zero. When
the flux is at a maximum the emf
will be zero. When the flux is at
then the emf will be at a
maximum.
Speed of Satellite: v=2πr/T = √GM/R
3
2
Satellite Constant: R /T = GM/4π
2
VCE 2017 (d) In Fig 2a, ē’s are
introduced between parallel plates
& deflected by a uniform E-field,
& then by a uniform B-field (Fig
2b). Explain why paths of ē’s in the
two fields have different shapes.
A: In Fig 2a, strength of E-field is constant & acts ↓ on an ē. For an ē
injected into field from left, path is parabolic, exactly same as a stone thrown
from top of a cliff (ē accelerates towards + plate). In Fig 2b, B-field is
constant, but always acts in a direction at 90° to velocity of ē. Using RH slap
rule means that constant Force always perpendicular to velocity &
acceleration of ē = constant (& directed inwards), so its path is circular.
As the bar magnet is
moved toward a
stationary conducting
loop (or loop moves
toward the magnet,
motion must be relative) a current is induced in the
direction shown. B-field lines are due to the bar magnet. LL: use RHG rule
with thumb = North (since loop wants to repel incoming north end of
magnet), fingers curl in direction of I (anti-clockwise when viewed from left)
Diagram 🡪 is when a magnet approaches ring at a constant speed from a
long way off & passes thru to the other side.
VCE 2012 Qn asked (Vertical coil) Q7.
Describe how Φ thru rotating coil changes
as coil makes a complete rotation. May
include a sketch. A: Initially the flux thru
the coil is to the right & at a maximum
value. (1) Over the next 1/4-turn amount of flux reduces to zero. For
the next quarter turn, the flux enters from the other side of the coil,
starting at zero & building to a maximum value. For the third quarter
turn, the amount of flux reduces to zero & for the last 1/4-turn, the flux
passes through the coil from the original side increasing back to
starting value.
Special relativity
Newton's Laws:
● An object will remain at rest or travelling at a constant
velocity unless acted upon by an external unbalanced force
● Fnet = ma
● For every action force there is an equal and opposite
reaction force
Einstein’s First Postulate: Laws of physics must be the same in all
inertial (non-accelerating, constant speed (or relative speed of zero))
frames of reference . Note: Circular (constant speed) motion or
gravity ≠ inertial frame [i.e. it is an accelerating frame]
Design Speed: The speed at which a vehicle experiences no
sideways force as it travels around a track.
Tanθ= Fnet/Fg
θ=tan-1 (v2/rg) v= √rgtanθ
0
Lenz's Law: When a coil is placed in a region of changing magnetic
flux, a magnetic field will be induced that opposes the change in flux.
DC Generator: (2 time
periods shown on graph)
Direction of emf output
from loop is changed by
the SPLIT ring commutator every half turn & so output is always in the same
direction. This keeps Vout either + or -
Mono-pole- A single point of charge
Dipole- Two poles of opposite sign
Unit 3 Aos 3: Motion
Split Ring Commutator: A ring which every half turn of the coil will
reverse the connection in order for the coil to continue to turn. This
ensures the direction of current in the circuit is constant or the
direction of rotation is constant.
AC Generator: Uses solid (slip) rings
since I varries sinusoidally (+/−) as the
loop rotates. Slip rings connect the
rotating loop to an external circuit and
provide constant connection = AC emf.
■ 🡩 Rotation (🡫 Δt or 🡩 f) or B or A
increases Vout.= emf
■ Lower rotation speed 🡫 emf & 🡩 period
■ If ↑ N loops &/or ↑ A (radius) of loop gives 🡩 emf
■ Blue line is half speed of rotation (freq) of black line = 2 × period but ½
emf voltage produced
RMS: The rms values are the values of a DC supply that would be
needed to provide the same average power as an AC supply
Transformer: A device that transfers an alternating current from one
circuit to one or more other circuits. The iron core inside them ensures
that all the flux generated in the primary coil passes onto the
secondary coil. A Generator converts mechanical energy into
electrical energy whereas a Motor converts electrical into mechanical
Ways to Increase Current in Resistor:
● Use a stronger Magnet
● Increase number of coils
● Weaker resistance wire
2017 VCE Sample Loop starts face-on to B-field (0.50 T), N = 20 turns, A
of loop = 0.020 m^2 & rate of rotation is 10 Hz. a. Calc magnitude of
EMF(average) induced as the loop
turns face-on to a point one-quarter of
a period later. A: Average induced
EMF = N ΔΦ/Δt. f = 10 Hz, so a
quarter period = ¼×1/10 = 1/40 sec.,
and ΔΦ = 0.50×0.020 🡪 emf = 20×0.50×0.020 ÷ (1/40) = 8.0 Volts
b. AC alternator gradually slows to a stop. Sketch voltage output expected.
Scale values are not required. A: AC voltage is a sine wave, but as rotation
slows down, period of the voltage will 🡩 & peak voltage will also 🡫. Draw
at least 3×cycles of a weakening & lengthening sine wave.
Einstein’s Second Postulate: The speed of light has a constant
value for all observers regardless of their motion or the motion of the
source.
Inertial Frame of reference: A frame of reference that is either
moving with a constant velocity or is stationary. It is not accelerating
Min Speed at top of point: v= √rg
Travelling through dips: To get the normal force add the centripetal
force to the gravitational force. The normal force is greater than the
grav force so they will feel heavier.
Travelling over humps: To get the normal force subtract the
centripetal force from the grav force. The rider will feel lighter.
Impulse= Change in momentum = m △v = F△t
Force vs Time Graph:The impulse= Area under the force time graph
Work: W=Fnet x s = △KE
Strain Potential Energy: The work done = SPE. Therefore the area
under a force - displacement graph is equal to the strain potential E.
Mass-Energy Relationship
Relativistic Momentum and Mass: Relativistic momentum includes
the Lorentz factor hence as more impuls is added, the mass seems
to increase towards infinity as the speed gets closer to C. Po and Mo
refer to the normal momentum and rest mass.
P=ƔPo m=ƔMo
Nuclear Fission/Fusion: The reactions result in a mass defect
(change). It is this difference in mass that is converted to the energy
released in nuclear reactions. △E= △mc2
Only light travels at ‘c’
(Shape is also SAME for mass, KE) As
object approaches the speed of light, the KE
(speed) of the particle increases slightly
while its relativistic mass, m, increases
substantially. As v ↑ relativistic mass
approaches ∞. Classical KE is a parabola
only Calc speed given rest mass or energy
& work done (KE in J)
2019 NHT Q17 A spaceship is travelling (at
0.85c, γ = 1.90) from Earth to a star system
(10.5 light-years from Earth’ FoR).
Determine duration of flight as measured
by the astronauts on the spaceship.
1 light-year = 9.46E15 m. A: from earth
FoR time (dilated) = distance ÷ speed =
10.5 ÷ 0.85 = 12.35 years. For spaceship
time, t = 12.35 ÷ 1.9 = 6.5 years. Q18. A
spaceship passes Bob (see fig left), who is on a space station, at
speed v = 0.990c (γ = 7.09). Spaceship = cube, x/y/z-axis length =
3.2E3 m in spaceship’s frame of reference (FoR). Determine
dimensions of the cube-shaped spaceship as measured from Bob’s
FoR A: Since cube’s direction or travel is not changing along y or
z-axis there is no change to those dimensions. However along x-axis
there is a change, Bob would measure a length (contraction) of L =
Lo÷γ = 3200 ÷ 7.09 = 451 m (3 sig fig)
Proper Time: The proper time is the time measured by a clock in the
same frame of reference as the event.
● t = the time that is observed in the stationary frame
● to = Time observed in the moving frame (Proper time)
Time Dilation: When the effects of time dilation can be seen, the
time will appear to travel more slowly on a moving object compared
to a stationary object.
Proper Length: The length of an object as measured by an observer
who is stationary relative to that object or they are stationary in the
inertial frame of reference of that object.
● L = Length in moving frame, measured by an observer
● Lo = Proper length ( Length by observer in moving frame)
Length Contraction: Objects that are moving faster relative to an
observer will appear to be contracted. An object that is moving at the
speed of light would appear to have a length of 0. the contraction will
only appear in the direction of the motion.
RELATIVITY 2017 VCE Sample Q15 Muons are elementary
particles, unstable & decay with half-life of 2.2 μs (2.2E–6 s) when
measured at rest. This means in reference frame of muons, half
decay in each time interval of 2.2 μs. Muons with v = 0.995c (γ = 10)
were observed to pass a top of a mountain (h= 2627 m). Scientists
measured number of muons reaching ground level. a) Calc half-life of
the muons as measured by a stationary observer on ground. A: Time
dilation, so measured half life = t0 γ = 2.2E−6×10 = 2.2E−5 s b. From
their FoR, the muons see ground rushing upwards at a speed of
0.995c. Find the height of the mountain as measured by the muons.
A: Speed of muons = 0.995c, so length contraction = Lo ÷ γ = 2627 ÷
10.0 🡪 measured length = 263 m c. Explain why many more muons
reached ground than would be expected according to classical
physics. A: c = same value in all inertial frames. Consequence is that
'moving clocks' are observed to be running slower. In muons' FoR,
half-life is 2.2μs, but from ground's FoR observe time dilation of
muons & effect of this is that muons take longer to decay. ∴ there are
more of them yet to decay by the time they reach ground.
2017 VCE particle travelling at 0.99875c (γ = 20). Scientists measure travel
of 9.14E−5 m before decays. (a) Lifetime in scientists frame = 9.14E−5 ÷
(0.99875 × 3E8) = 3.05E−13 s. (b) distance in particle’s frame = contracted
L = 9.14E−5÷20 = 4.6E−6 m
A proton’s rest energy (m0c2 = 938.26 MeV) & if a proton has a total energy
of 100.00 GeV, what speed, as a % of c, is proton moving at? Express result
to 6 sig fig. A:𝑣 = 𝑐
𝐸
2
1 − ( 𝐸 𝑅𝑒𝑠𝑡 ) = 𝑐
𝑇𝑜𝑡𝑎𝑙
1 −
(
0.93826 2
100
)
= 0.99996×100
= 99.9996c [1 GeV = 1000 MeV]
2018 NHT Q14 A planet is 1.0E18 m from Earth. Spaceship travels at 0.99c
(γ = 7.1) Estimate time in years as measured on spaceship. A: At that speed
the distance is contracted by 1.0E18 / 7.1 = 1.4085 E17 m (1). At a speed of
0.99c, time to travel this contracted distance is 1.4085E17 ÷ (0.99 × 3E8) =
4.7 E8 seconds ÷ 3.1536E7 seconds per year ≈ 15 yrs.
range of KE’s of ē’s as indicated by ↑ in Vo. Actual observation: ↑
intensity ↑ µA but has no effect on Vo.
Unit 4 AOS 1: How can waves explain light?
Graph of Photocurrent
(I) vs Voltage (V) Higher
intensity means horizontal
line goes up as I 🡩 with
light intensity. If light of a
higher frequency is used
the stopping voltage will be higher. RED LINE same f as original but
lower intensity.GREEN LINE has lower intensity but higher frequency
Amplitude:The max displacement of a particle from the average or
rest position.That is the distance from the middle of the wave to peak
Fixed End: When the end of the wave has a hard boundary. The
wave pulse that is rebounded will be inverted and a peak will now be
a trough.
Non-Fixed End: The end of the wave is free to move up or down.
The wave will be reflected in the same form as the original with no
inversion.
Resonance: When an object is exposed to vibrations at a frequency
equal to its natural resonant frequency. When the natural resonant
frequency is matched by the forcing frequency:
● The amp of the oscillations will increase
● The max possible energy of the source is transferred to the
resonating object.
Harmonics: The frequencies produced in the complex vibration of
standing waves in a string. The simplest mode has one antinode and
is called the fundamental. Higher level harmonics are called
overtones.
VCE 2017 Q15. f = 680 Hz & v (sound) =
340 m/s (a) λ = 340 ÷ 650 = 0.5 m
(b) Elli predicts that students will hear a
similar sound of double intensity. Sam,
disagrees. He says intensity of sound
depends on each student’s relative distance
from each speaker. Evaluate Elli’s & Sam’s
responses. A: • Sam is correct.
• Addition of 2nd speaker will produce an interference pattern. • The
intensity that a student hears will depend on path difference between
2 speakers. (whole λ = constructive interference = louder) (½ λ =
destructive interference = softer sound) (c) Will students 2 & 5 hear
similar or different sound intensities?
A: Student 2 will hear a louder sound than #5. Using ∆x = λL/d,
where ∆x is spacing between maxima, ∆x = 0.500 × 24 / 4.0 = 3.0 m.
Student 4 is at central maximum. Student 2 is 3.0 m away so is also
at a maximum, while #5 is 1.5 m away & so is at a minimum.
VCE 2017 Sample Q6. Juan conducts an
experiment using a shallow tray of water in which
waves can be observed. He first produces straight
waves at a freq of 5 Hz. Measures λ = 10 cm. (a)
Calc speed of waves. A: Use v=f×λ, v = 5×10 = 50
cm/s, 5E1 cm/s. (expressed to one sig fig). Juan
now uses 2 point sources producing waves at same λ (10 cm) to investigate
two-point source interference patterns, (see Fig with Y, X & P). He observes
lines of maxima & minima in resultant pattern. Lines on diagram represent
wave crests. Point P is on a line of minima (nodal line). Juan measures
distance from source X to point P as 16.0 cm. Calc distance from source Y to
point P. A: P is on second nodal line, so path diff = 1.5λ which = 1.5×10 = 15
cm, distance from P to Y must be 15 + 16.0 = 31 cm.
UNIT 4 AOS 2: How are Light & Matter Similar?
String Fixed at Both Ends: It can have any number of harmonics
ƛ= 2L/n F=nv/2L
String Fixed at One End: It can only be odd harmonics
ƛ= 4L/n F=nv/4L
Wave model: Huygen’s principle states that
each point on a wave front can be considered
as a source of secondary waves.
Diffraction: Diffraction
pattern occurs because
each point on the wave
front moving through
the slit acts like a light
source
Diffraction Ratio: Wavelengths comparable to or larger than the
diameter of the obstacle or gap will produce significant diffraction.
this can be show by the ratio ƛ/w ≥ 1
Double Slit Experiment:Young passed light through a pair of
narrowly spaced double slits to produce an interference pattern,
evidence of constructive & destructive interference – this is wave-like
behavior. The 2 competing models of light were particle models,
initially proposed by Newton & the wave model favored by Huygens.
Wave model (correctly) predicts that if light behaved as a wave it
should show the wave-like properties of diffraction (spreading
through a narrow gap) & interference (points of reinforcement &
cancellation on the other side of a double slit). Particle model for light
would (incorrectly) predict that two bright bands would appear on the
screen.
Photoelectric Effect: Ejection
of ē (AKA photoelectrons) from
a metal surface exposed to light
(get a photocurrent on
ammeter). Light filter selects
frequency of light incident
(shining) on metal.
Findings: (1) Max KE of ē was independent of intensity. (2) Instantaneous
emission of photo-ē (Nano-seconds) (3) Existence of a cut-off frequency (f0)
below which no ē’s are emitted regardless of light intensity
2017 VCE PEE Q7 (c) Results of PEE experiments in general
provide strong evidence for particle-like nature of light.
Outline three aspects of these results that provide strong evidence
that is not explained by wave model of light & explain why. (i)
Negligible time delay 🡪 wave model predicts that if intensity (Io) of
light is low enough then = a measurable delay between initiating
illumination of metal & observation of a photocurrent (µA). Actual
observation is that regardless of Io of illumination, the µA is
observed to flow as soon as metal is illuminated. (ii) Existence of a
threshold frequency fo; wave model predicts that all light (regardless
of freq) should produce a µA since measure of its energy is its
amplitude. Actual observation: if fphoton < fo it won’t produce a µA
regardless of intensity (amplitude) of wave. (iii) Independence of
stopping voltage (Vo) from intensity – wave model predicts that ↑
intensity of light source will ↑ amount of energy delivered to metal per
unit of time. Should result in more ē’s being released with a greater
KE (of ejected photoelectrons) vs
Frequency (photon energy) FYI ϕ
(sodium) ≈ 2.36 eV
x-intercept: f0 = threshold freq
y-axis:=Work Function if below 0
However if it is above 0 from that
frequency this can be used to find
the stopping voltage
Production of light: spectra suggest an internal structure to atoms.
A line Emission spectrum is produced by energised atoms (ē’s jump
to an excited energy level & drop back down they emit specific
energy (λ) photons). Absorption spectrum is created when white
light passes through a cold gas. (see below right)
(6) Quantised states of an atom = wave & particle-like nature of
matter
Experimental Stuff
(1) Hypothesis Is a possible explanation that needs to be rigorously
tested by experiment
(2) Theory: Is a well-tested, substantiated, and unifying explanation.
Result of testing a hypothesis many times.
Systematic Error which always occurs, with the same value, when
we use the instrument in the same way and in the same case, Eg’s
are incorrectly calibrated instruments, consistent parallax error or
poor quality instruments. SE can often be ↓ or detected by improving
procedures or doing experiments in a different way. They CANT be
reduced with repeated readings
Random Error which may vary from observation to another.RE is
due to factors which can’t/won’t be controlled.RE can be reduced by
repeated results & averaging & plotting a graph with a line of best fit.
Accuracy is defined as the difference between the mean & actual
value
Precision is the range between measurements
Validity refers to whether or not the results are valid, and not
influenced by any untoward biases
Reliability refers to whether or not another researcher could repeat
your investigation by following your method
and get similar results.
Uncertainty: On a measuring device the uncertainty will be half of
the smallest increment. If a digital measuring device is being used
then the uncertainty is one of the smallest increments.
De Broglie Wave-Particle Theory: His theory was that since light
sometimes demonstrated particle-like properties that matter might
sometimes demonstrate wave-like properties. In order for an
everyday object to produce a noticeable diffraction pattern it would
need to pass through a gap much smaller than a fraction of a proton
diameter.
Bohr model: ē’s in atoms have circular orbits around nucleus of
defined energy levels (i.e. radii). No radiation is emitted or absorbed
in these orbits unless ē can jump from its current orbit (energy) level
to another by either emitting or absorbing a photon of a certain
energy. Hence, electron energies within the atom are quantised,
since only certain values are allowed.
2017 NHT Q 21 De Broglie suggested that the quantised
energy states of atoms could be explained in terms of
electrons forming standing waves. Describe how the
concept of standing waves can help explain the quantised
energy states of an atom. You should include a diagram.
A: (1) ē’s exhibit a wave behaviour. (2) ē’s form standing waves in
orbits where the circumference is a whole multiple of the electron
wavelength. i.e 2 π r = n λ (3) This means that only certain discrete
energy states can exist.
VCE 2017: Q19 Roger & Mary are discussing diffraction. Mary says
ē’s produce a diffraction pattern. Roger says this is impossible as
diffraction is a wave phenomenon & ē’s are particles; diffraction can
only be observed with waves, such as X-rays (electromagnetic
waves). Evaluate Mary’s & Roger’s statements in light of the current
understanding of light & matter. Describe 2 experiments that show
difference between Mary’s & Roger’s views. A: • Mary is correct • ē’s
do possess wave properties & their λ = dBW. Refer to 2 of following:
(i) If ē’s are passed thru a crystal 🡪 produces a diffraction pattern,
just as if X-rays were passed thru crystal. (ii) If ē’s are passed thru a
1x slit 🡪 also produce a diffraction pattern. or (iii) if ē’s are passed
thru two closely spaced slits 🡪 get diffraction pattern.
SUMMARY: MAIN LIGHT & MATTER EXPERIMENTS:
(1) Young’s double-slit = wave-like nature of light
(2) Interference & Diffraction Patterns = wave-like nature of light &
matter
(3) Photoelectric Effect = particle-like nature of light
(4) de Broglie λ (dBW) = wave-like nature of matter
(5) Absorption & Emission Spectra of atoms/photons = particle-like
nature of light & matter
Percentage Uncertainty:
Percentage Error (sometimes referred to as fractional difference)
Measures the accuracy of a measurement by the difference between
a measured or experimental value E and a true
or accepted value A. This can only be used if you know the accepted
value! The percent error is calculated from the
following equation:
VCE 2018 NHT Q18 MC A student measures a very small current in
a circuit and obtains the result 0.000670 A. Number of significant
figures in the measurement is = 3 (A: convert to scientific notation =
6.70E−4) Q19 An independent variable is best described as one that
is: A: set by the researcher.Q20 The main reason for repeating an
experiment is to A: reduce random error.