PHYSICS
CXC REVISION
SPEEDRUN
A base (or fundamental) quantity is one
that cannot be expressed as another
quantity, e.g. length, time.
A derived quantity is one that is a
combination of base quantities.
e.g. ‘speed’ is distance per unit time.
BASE QUANTITIES
• Length (L), unit = m
• Mass (m), unit = kg
• Time (t), unit = s
• Current (I), unit = A
• Temperature (T), unit = K
• Amount of a substance (n), unit = mol
• Luminous intensity (lv), unit = candela (cd)
DERIVED QUANTITIES
• Area (A), unit = m2 (m x m)
• Volume (V), unit = m3 (m x m x m)
• Pressure (P), unit = Pa (N/m2)
• Force (F), unit = N (kg m/s2)
• Charge (Q), unit = C (A x s)
Prefixes
• Micro (µ) = 10-6 (÷ 1,000,000)
• Milli (m) = 10-3 (÷ 1000)
• Centi (c) = 10-2 (÷ 100)
• Kilo (k) = 103 (x 1000)
• Mega(M) = 106 (x 1,000,000)
Prefixes (examples)
5600ms to s = 5600 ÷ 1000 = 5.6s
300cm to m = 300 ÷ 100 = 3m
2.5kW to W = 2.5 x 1000 = 2500 W
Scalar is a quantity that has magnitude but NO
direction.
e.g. distance, speed, area, volume, density
Vector is a quantity that has BOTH magnitude and
direction.
e.g. displacement, velocity, acceleration, force,
momentum
Sum of parallel and anti-parallel vectors:
Resolving non-parallel vectors
Mass (unit = kg)
The amount of matter contained in an object. It is
a measure of an object’s inertia or resistance to
change in motion.
Weight (unit = N)
The force exerted on a body’s mass by gravity.
w = mg
e.g. If an astronaut has a mass of 70kg on Earth,
what is her weight on the Moon if its gravitational
field strength is 1.6 N/kg?
70 x 1.6 = 112 N
The centre of gravity of an object can be defined
as the point at which the weight of a body acts.
Wide base (low centre of gravity) = higher stability
• Forces enable masses to overcome inertia, i.e.
they are able to cause a change in an object’s
acceleration, deceleration or direction (even
shape and size, but NOT mass)
• Forces are measured in Newtons (N) which can
be derived as 1N = 1 kg m/s2.
Type of Force
GRAVITY
WEIGHT
FRICTION
BUOYANCY / UPTHRUST
ELECTROSTATIC
Description
MAGNETIC
REACTION
An attraction or repulsion caused by north and south poles.
The force that always acts opposite to another, e.g. the forward
push from swimming while pushing the water backward.
TENSION
CENTRIPETAL
NUCLEAR
An upward force exerted on a string or rope attached to a load.
The pull towards a central point for an object moving in a circle.
The attraction holding the nucleus of an atom together.
Pulls objects towards the centre of the Earth.
The effect of gravity on an object’s mass.
The resistance an object experiences when rubbing a surface.
The upward force exerted by a fluid.
Attraction due to charged particles called electrons stored in an
object.
If a force is absent, there will be no change in
motion or direction.
In the car, two “resistant forces”
are equal to the applied forward
thrust of the car. This will give
an overall resultant or net force
of 0 Newtons.
The car is at equilibrium and will keep moving at a constant
velocity.
ACCELERATION
DUE TO GRAVITY
In a vacuum, objects
(whether it be a rock or
paper) will accelerate
and fall at the same rate.
In air, the force of air
resistance will affect
falling speeds.
GRAVITATIONAL CONSTANT (g)
The acceleration due to gravity on Earth is 10 m/s2.
This means that with each second under the force
of only gravity, the velocity increases by 10 m/s.
So, after 3s in freefall (with negligible air resistance), the
final velocity would be 30 m/s.
LEVERS are simple machines that have an input
and an output. The input force is usually referred
to as the EFFORT and the output as the LOAD.
Levers have a point of
rotation that these forces
will turn about.
This point of rotation is
referred to as the
PIVOT or FULCRUM.
The Principle of Moments states that:
THE SUM OF CLOCKWISE AND ANTICLOCKWISE MOMENTS
ABOUT THE SAME PIVOT IS EQUAL AT EQUILIBRIUM.
Calculating the effort, E:
F1 x D1 (Effort)
= F2 x D2 (Load)
E x (0.40 + 0.80) = 600 x 0.80
1.20 E
= 480
E
= 480 / 0.12 = 400 N
If C is the centre of gravity of the plank, calculate the
weight of the plank.
F1D1
+ F2D2
= F3D3
(500 x 2.0) + (300 x 0.5) = F3 x 0.75
1000 + 150
= 0.75 F3
1150
= 0.75 F3
F3
F3
= 1150 / 0.75
= 1533.33 N
Hooke’s Law states that:
The extension of a spring is directly proportional to the
force acting on it, given it is within its elastic limit.
F = kx
F = Force (N)
x = extension (m)
k = spring constant (N/m)
The elastic limit of a spring is within the limit of
proportionality between force and extension. If too much
force is applied, the spring can experience permanent
deformation.
Hooke’s Law
(worked example)
A 200 N load is attached to
a spring with an initial
length of 100 cm.
If its spring constant (k) is
5 N/cm, calculate the final
length, L, of the spring.
F = kx
x=F÷k
= 200 ÷ 5
= 40 cm
L = 40 + 100
= 140cm
Density is defined as mass per unit volume.
The SI unit is kg/m3.
Relative density is a given ratio of the
density of a substance in reference to the
density of the medium.
e.g. Calculate the R.D. of oil in seawater, if oil has a density of
800 kg/m3 and seawater has a density of 1020 kg/m 3.
R.D. = Density of oil / Density of seawater
= 800 / 1020 = 0.78 (no unit)
Archimedes’ Principle states that:
The upward buoyant force that is exerted on an
object immersed in a fluid is equal to the weight of
fluid displaced.
Floating occurs if an object’s buoyant force is
greater than its weight, or if it is less dense
than its medium.
More surface area = more likely to float
Sinking occurs if an object’s weight is
greater than its buoyant force, or if it is
denser than its medium.
Distance is how much ground an object has
covered despite direction. It is a scalar.
Displacement is the overall change in position
of an object in a straight line between its
origin and destination. It is a vector.
In the displacement-time graph, the gradient
represents velocity.
Gradient of upward slope:
y2 – y1 = 25 - 0
x2 – x1
5– 0
= 5 m/s
(velocity)
Speed is distance per unit time. It is a scalar.
Velocity is the displacement per unit time. It
is a vector.
Speed = distance / time
Velocity = displacement / time
Unit = m/s
Acceleration is a change in velocity over time.
The unit is m/s2.
a = (v – u)
t
v = final velocity
u = initial velocity
Calculate a car’s acceleration after
braking for 4 seconds if the velocity
decreased from 24 m/s to 16 m/s.
a = (16 – 24) = -8
4
4
= -2 m/s2
In the velocity-time graph, the gradient
represents acceleration.
In the velocity-time graph, the displacement
travelled is represented as the area under the
graph. The unit is metres (m).
Newton’s 1st Law
An object at rest remains at rest, or an object
in motion remains in motion at a constant
velocity, unless an unbalanced force acts
upon it.
Newton’s 2nd Law (example)
A 2000 kg minibus increases its velocity from 8 m/s
to 14 m/s in half of a minute. Calculate the force
required to do this.
a = (v – u) / t
= (14 – 8) / 30s = 6 / 30 = 0.2 m/s2
F = ma
= 2000 x 0.2 = 400N
Newton’s 2nd Law
The force on a body is directly proportional to
its acceleration. (F = ma)
Newton’s 3rd Law
• Every action force has an equal and opposite reaction
force.
• If a Body A acts on Body B, then B exerts an equal and
opposite force on A.
Linear momentum (p) is the product of mass
and velocity for an object travelling in a
straight line.
Impulse is the force
that produces a
change in momentum.
Momentum = mass x velocity
p = mv
▲p = F x t
Unit = kg m/s or Ns
The law of conservation of
linear momentum states
that:
With no external forces,
the total momentum
before collision is equal to
the total momentum after
collision.
If the wreckage moves as a combined mass after collision, calculate
its net velocity and direction.
Energy is simply defined as the capacity for doing
work. The SI unit for energy is Joule (J).
A Joule is defined as the work needed to move 1N
by a 1m distance, so 1J = 1Nm.
The law of conservation of energy states that
Energy can neither be created nor destroyed. It can
only be converted from one form to another.
Some types of energy:
- Chemical, e.g. batteries, fuel
- Kinetic, e.g. moving car, falling water
- Gravitational potential, e.g. boulder on cliff
- Elastic potential, e.g. compressed spring
- Thermal, e.g. fire
- Electromagnetic, e.g. sunlight
- Nuclear, e.g. fission reactors
Work is energy used to produce some type of
mechanical change. Measured in Joules (J).
Power is the rate of energy conversion. Measured
in Watts (W).
A 500 N package is lifted 20 m above the ground.
This takes 25s to occur. Calculate the work done
and power.
W = F x d = 500 x 20
= 10 000 J
P =W/t
= 10 000 / 25 = 400 W (or 400 J/s)
EFFICIENCY refers to the percentage or ratio of
useful output compared to total supplied input.
KINETIC ENERGY (KE)
is the energy possessed by an object in motion or
during collision.
GRAVITATIONAL POTENTIAL ENERGY (GPE)
is the energy possessed by an object by virtue of its
position or height.
KE and GPE Conversions
A coconut of mass 2 kg falls from a distance of 30m to
10m. Assuming negligible air resistance, calculate its
velocity as it falls. (g = 10 N/kg)
▲GPE = mg▲h = 2 x 10 x (30 – 10)
= 20 x 20 = 400 J
100% of GPE converts to KE
KE = ½ mv2
v2 = KE / (½m) = 400 / 1 = 400
v = √400 = 20 m/s
KE and GPE Conversions
•
•
•
•
•
1 – Maximum GPE, minimum KE
2 – GPE converting to KE
3 – Minimum GPE, maximum KE
4 – KE converting to GPE
5 – Maximum GPE, minimum KE
ALTERNATIVE ENERGY SOURCES
- Solar panels. Converts sunlight to electric.
- Hydroelectric dams. Converts KE from water to electric.
- Geothermal. Uses KE from steam wells below surface.
- Tidal. Uses natural ebb of ocean and waves.
- Biofuels. Uses methane or ethanol from harvests.
- Wind turbines. Uses KE from natural winds.
- Nuclear. Uranium fission yields high amounts of energy.
Reducing energy wastage
– Switching from incandescent to fluorescent lights
– Carpooling and public transport
– Turning off lights or A.C. unit when not in use
– Use more energy-efficient appliances
– Hybrid or electric vehicles
Pressure is force acting per unit area.
Pressure in a fluid increases with depth and
density of the fluid.
Calculate the total pressure at the base of a 20m deep
container of oil of density 800 kg/m 3 if the atmospheric
pressure is given as 101 kPa.
P = density x g x h = 800 x 10 x 20 = 160,000 Pa
Total pressure = 160,000 + 101,000 = 261,000 Pa
Manometers are used to find pressures of fluids of
interest. The difference in column height is used to
calculate pressure.
Pascal’s Law states:
The pressure applied to a point in an
incompressible fluid is evenly distributed to all
points in that fluid.
Wider area = Larger force
The pressure exerted by
the fluid is equal at
all points.
HEAT is a form of energy that is transferred from
areas of higher temperature to lower temperature
until the objects and their surroundings are at
equilibrium, the same temperature.
HEAT energy is converted from mechanical energy.
The scientist, James Joule, proved this with the
experiment set-up below.
THE KINETIC THEORY OF MATTER indicates that
molecules in a gas move freely and rapidly along
straight lines. In a liquid and solid, intermolecular
bonds form, which reduce movement in the
medium.
COMPARING SOLIDS, LIQUIDS, GASES
Temperature represents the average kinetic energy
per molecule in a substance.
Its SI unit is Kelvin (K).
To convert to Kelvin, add 273 to the Celsius value,
e.g. 100oC = 100 + 273 = 373 K
Lower fixed point is the temperature of pure
melting ice at 1 atmosphere.
Its value is 0oC or 273 K.
Upper fixed point is the temperature of pure dry
steam at 1 atmosphere.
Its value is 100oC or 373 K.
Absolute zero is the temperature at which there is
heat or internal energy in the molecules.
Its value is -273oC or 0 K. At this point, the pressure
is zero.
A thermometer has a physical property that
changes steadily with temperature e.g. when
mercury is heated, it expands proportionately and
moves along the bore of the thermometer.
A clinical thermometer has a thinner, larger bulb
(faster conduction), a narrower bore (more
sensitive readings) and a constriction (prevents
liquid from immediately returning to bulb).
A thermocouple uses difference in voltage
between hot and cold junctions for rapid, accurate
readings in temperature.
CONDUCTION is the transfer of heat through the
vibrations of molecules to adjacent molecules in a
medium.
CONVECTION is the transfer of heat through bulk
movement of the medium itself.
RADIATION is the transfer of heat through the
propagation of electromagnetic waves. It can occur
through a vacuum.
Conductors are materials with free electrons (such
as metals), which allow the efficient transfer of
heat.
Insulators do not have many free electrons and
may have structural gaps or air spaces that do not
efficiently transfer heat, such as cloth or
polystyrene. Air is a POOR CONDUCTOR of heat.
Vacuum flasks keep liquids at constant
temperatures by limiting heat transfer.
Good absorbers (and good emitters) of heat are usually:
- Black in colour
- Rough in texture
- Small in area
- Dull in nature
Good reflectors of heat are usually:
- White in colour
- Smooth in texture
- Large in area
- Shiny in nature
Specific Heat Capacity of a material is defined as
the amount of heat energy required to change the
temperature of 1kg of the material by 1 Kelvin.
e.g. Water has a specific heat
capacity of 4200 J/kg K.
Specific heat capacity
is a constant.
If the temperature of 1kg of water
is to be raised from 10oC to 11oC, it
would require 4200 J.
To raise it from 10oC to 12oC, it
would require 8400 J.
Example question:
A 1.2 kW heater was used to heat a 2 kg mass of water for 5
minutes. The initial temperature of the water is 20oC. If the specific
heat capacity of water is 4200 J/kg K, calculate the final
temperature of the water.
E = mc▲T
P=E÷t
▲T = E ÷ (mc)
E = P x t = 1200 W x (5 x 60s)
= 360,000 ÷ (2 x 4200)
= 360,000 J
= 42.86oC
T (final) = 20 + 42.86
= 62.86oC
Heat capacity of a body is defined as the amount
of heat energy required to change the
temperature of the body by 1 Kelvin.
e.g. Water has a specific heat
capacity of 4200 J/kg K. And a large
container of water has 10 kg.
It would require 42000 J (4200 x 10)
to change the raise the temperature
of the 10 kg container of water by 1
Kelvin.
Heat capacity of a body is defined as the amount
of heat energy required to change the
temperature of the body by 1 Kelvin.
e.g. Water has a specific heat
capacity of 4200 J/kg K. And a large
container of water has 10 kg.
It would require 42000 J (4200 x 10)
to change the raise the temperature
of the 10 kg container of water by 1
Kelvin.
Testing for specific heat capacity
The metal aluminum block is heated for 3
minutes with a 5A current, 10V supply. If
the initial and final temperatures of the
2kg block are 30oC and 35oC respectively,
calculate its specific heat capacity.
E = IVt = 5 x 10 x (3 x 60)
= 9000 J
E = mcΔT
c = E ÷ (mΔT) = 9000 ÷ (2 x (35 – 30))
= 9000 ÷ 10 = 900 J/kg oC
Method of Mixtures
A 50g block is placed in 200g of water. The
block was heated to 100oC. The temperature of
the block dropped to 30oC and the water rose
from 30oC to 35oC.
Using 4.2J/g K as the specific heat capacity of
water, calculate the specific heat capacity of
the block, in J/g K.
Heat gained by water = Heat lost by metal
mcΔT (water) = mcΔT (substance)
mcΔT (water) = mcΔT (block)
200 x 4.2 x 5 = 50 x c x (100 – 30)
4200
= 3500 c
c
= 4200 ÷ 3500 = 1.2 J/g K
Specific latent heat of fusion is the energy required to change 1 kg
of a solid to a liquid without a temperature change.
Specific latent heat of vapourization is the energy required to
change 1 kg of a liquid to a gas without a temperature change.
The unit for each
is J/kg.
When latent heat is being released or absorbed, there is
no temperature change. State of matter changes as
molecular bonds are broken or reformed.
EXAMPLE QUESTION
A student heats 200g of ice
at 0oC until it turns to
steam at 100oC. How much
energy was needed to do
this?
•
•
•
[specific heat capacity of
water = 4200 J/(kg K)]
E = mLf
= 0.2 x (3.36 x 105)
= 67200 J
E = mcΔT
= 0.2 x 4200 x 100
= 84000 J
[specific latent heat of
fusion of ice =
3.36 x 105 J/kg]
[specific latent heat of
vapourization of water =
2.25 x 106 J/kg]
E = mLv
= 0.2 x (2.25 x 106) = 450 000 J
E (total) = mLf + mcΔT + mLv = 601 200 J
Air pressure is the result of collisions of gas
molecules with the walls of the container the gas
is held within. The higher the frequency of
collisions with the walls, the higher the pressure.
The number of gas
molecules in the container
will also increase the
frequency of collisions and
increase the pressure.
Gas molecules in high temperature have more
kinetic energy and thus, move faster, have more
momentum and collide more often with the walls.
Temperature and pressure have a directly
proportional relationship.
There are THREE GAS LAWS:
1. Boyle’s Law
2. Charles’ Law
3. Pressure Law
And a combination of the three:
The General (or Combined) Gas Law
BOYLE’S LAW:
For a fixed mass of gas at constant temperature, pressure
and volume are inversely proportional.
Basically:
Low volume = high pressure
High volume = low pressure
BOYLE’S LAW (example)
A syringe at a fixed temperature has a gas at an initial volume of
50ml at 4 kPa. At what volume would the pressure be 10 kPa?
50 x 4 = 10 x V2
200 = 10 V2
V2 = 200 / 10
V2 = 20ml
CHARLES’ LAW:
For a fixed mass of gas at constant pressure, volume and
temperature are directly proportional.
Basically:
High temperature = high volume
Low temperature = low volume
CHARLES’ LAW (example)
When filled with 24m3 of helium at a temperature of 32oC,
a hot air balloon is able to float. What is the volume of the
balloon at 75oC?
PRESSURE LAW:
For a fixed mass of gas at constant volume, pressure and
temperature are directly proportional.
Basically:
High temperature = high pressure
Low temperature = low pressure
PRESSURE LAW (example)
A car tyre is pumped to a pressure of 2 x 105 Nm-2 when the
temperature is 23oC. Later in the day, the temp. rises to 34oC.
Calculate the new pressure in the tyre if the volume was constant.
COMBINED GAS LAW:
In this scenario, no factor except the mass of the gas is
constant.
You can always start with this law for any gas law
problem. Just eliminate the quantity that is constant, e.g.
eliminate T1 and T2 for Boyle’s Law.
COMBINED GAS LAW
(example)
An ideal gas has a volume of
150 cm3 at a temperature of
300 K and a pressure
equivalent to 76 cm Hg.
What will its volume be if the
temperature goes up to 320 K
and the pressure drops to
70 cm Hg?
What is a WAVE?
A wave is a propagation of energy from one location to
another.
ANATOMY OF A WAVE:
The wavelength (λ) is the distance between any two
successive points in phase.
The amplitude (A) is the height of the wave, or the
maximum displacement of the oscillation.
ANATOMY OF A WAVE:
The period (T) is the time taken for one complete
oscillation. In the graph, it is 0.6 seconds.
The frequency (f) is number of oscillations passing a point
per second.
f=1÷T
= 1 ÷ 0.6
= 1.67 Hz
or 1.67 waves per second
PERIOD (worked example)
The maximum audible range of a human is 20,000 Hz.
Calculate the period of the sound wave.
T=1÷f
= 1 ÷ 20 000
= 0.00005 seconds
ANATOMY OF A WAVE:
High frequency waves have more oscillations per second.
High amplitude waves are ‘taller’, have greater
displacements.
VELOCITY OF A WAVE (example):
If a sound wave has a frequency of 15 Hz and a wavelength
of 22 m, calculate its velocity.
v=fλ
= 15 x 22
= 330 m/s
TRANSVERSE WAVES
Are waves with crests and troughs; and the displacement
of particles is perpendicular to its propagation.
Examples are: light, radio waves, gamma rays, X-rays.
LONGITUDINAL WAVES
Are waves with compressions and rarefactions; and the
displacement of particles is parallel to its propagation.
An example is sound.
SOUND WAVES
They are longitudinal and mechanical in nature.
Mechanical means that they require a medium to
propagate. It cannot propagate through a vacuum.
The denser the medium,
the higher the velocity.
Sound travels fastest in
a solid and slowest in a gas.
PITCH AND LOUDNESS
Pitch correlates with
frequency.
Loudness correlates with
amplitude.
The human audible range
Is 20 Hz – 20 kHz. A sound
that exceeds this is called
ultrasound.
ECHOES
An echo is a reflection of sound.
It can be used in SONAR to detect sea depths.
An ultrasound signal is sent via a transducer,
reflects off a dense surface and is picked back
up by a detector. The speed is calculated by:
ECHOES (example problem)
In an experiment, Ravi stands 60m away from a wall and
claps two blocks together 20 times. Chantal records the
time for the 20 echoes as 7.2 seconds. Calculate the speed
of sound from this data.
Time for 1 echo = 7.2 ÷ 20 = 0.36s
Speed = 2d ÷ t
= (60 x 2) ÷ 0.36
= 333.33 m/s
ELECTROMAGNETIC SPECTRUM
From lowest frequency to highest frequency
(or longest wavelength to shortest)
ACRONYM
RICH MEN IN VEGAS USE
XPENSIVE GADGETS:
RADIO – broadcasting, RADAR
MICROWAVES – cellular communications
INFRA-RED – heat emission, night vision
VISIBLE LIGHT – optical fibres, human eye vision
ULTRAVIOLET – sterilization of equipment, tanning beds
X-RAYS – radiographs of bones (due to electron bombardment)
GAMMA RAYS – killing of cancer cells, radioactive decay
DIFFRACTION
Occurs when a wave passes through a narrow aperture
(opening) and thus spreads out over a large area as it
continues to progress. All waves can undergo diffraction.
INTERFERENCE
Occurs when two waves superpose with each other to
form a resultant wave that might either raise or lower the
amplitude.
Constructive interference
means that the waves are
exactly superposed.
Destructive interference means
that the waves are out of
phase by ½ of a wavelength.
THEORIES OF LIGHT
Newton – “Light is a stream of particles or corpuscles.”
Huygens – “Light is a transverse wave.”
Young – “Light is a wave that can undergo interference.”
Einstein – “Light can behave as both a wave and a particle.”
(Quantum Theory)
YOUNG’S DOUBLE SLIT EXPERIMENT
Where the waves are in phase
(CONSTRUCTIVE interference), the crests
and troughs are aligned and result in
bright fringes (called MAXIMAS).
Where the waves are out of phase
(DESTRUCTIVE interference), they result in
dark fringes (called MINIMAS). Troughs of
one wave ‘cancel’ out the crests of
another.
REFLECTION OF LIGHT
Occurs when an incident light ray bounces off a surface.
A normal is an imaginary
line perpendicular (or 90o)
to a boundary or surface.
All relevant angles are
measured from the normal
to the ray.
REFLECTED IMAGES are:
1. The same height as the
object
2. The same distance from
the mirror as the object
3. Laterally inverted
(flipped sideways)
4. Virtual (cannot be
projected)
LAWS OF REFLECTION
1. The incident ray,
reflected ray and
normal all lie on the
same plane.
2. The angle of incidence is
equal to the angle of
reflection.
REFRACTION OF LIGHT
In the glass block, the
emergent ray is parallel
to the incident ray.
Lateral displacement is the
perpendicular distance the
ray shifted from its initial
path. The denser the medium,
the greater the lateral
displacement.
If a wave moves into a denser medium, its:
- Wavelength decreases
- Speed decreases
- Frequency remains unchanged.
DISPERSION OF LIGHT
Occurs when light comprised of various wavelengths passes through
a prism. The light splits into different colours.
Red has the longest
wavelength and is
refracted the least.
Violet has the shortest
wavelength and is
refracted the most.
REFRACTIVE INDEX
The refractive index (n) is the ratio of the sines of the
angles of incidence and refraction of a ray passing from
one medium to another.
REFRACTIVE INDEX (worked examples)
Calculate the refractive index from air to glass.
REFRACTIVE INDEX (worked examples)
Calculate the angle of refraction
if n = 1.50.
LAWS OF REFRACTION
1. The incident ray, refracted
ray and normal all lie on the
same plane.
2. The refractive index is the
ratio of the sines of the angles
of incidence and refraction for a
wave moving from one medium
to the next.
(also called Snell’s Law)
CRITICAL ANGLE
Is the angle of incidence that produces an angle of
refraction equal to 90o.
It can be calculated with:
n = sin 90 / sin c
= 1 / sin 42
= 1 / 0.67
= 1.49
TOTAL INTERNAL REFLECTION
If the angle of incidence surpasses the critical angle, the
ray is reflected instead of refracted. This is total internal
reflection.
TOTAL INTERNAL REFLECTION
Optical fibres, periscopes and road reflectors all utilise
the idea of total internal reflection.
CONVEX LENSES
These lenses allow
light rays to
converge upon a
singular point at
the focal point.
Examples include
microscopes and
magnifying glasses.
CONCAVE LENSES
These lenses allow
light rays to diverge.
Examples include
flashlights and
peepholes.
REAL AND VIRTUAL IMAGES
Real images can be
projected. They occur when
the object distance is
greater than the focal
length.
Virtual images cannot be
projected. They occur when
the object distance is less
than the focal length.
Pinhole cameras create
real, inverted images.
LENS DIAGRAMS
LENS DIAGRAMS
THE LENS FORMULA
THE LENS FORMULA (worked example)
An object is placed 24cm away from a convex lens of 8cm focal
length. Calculate the image distance, v.
ELECTROSTATICS
When a silk cloth is
rubbed with a glass rod:
- The rod loses
electrons and
becomes +ve.
- The cloth gains
electrons and
becomes –ve.
Positive charges don’t move
because they are bound to
the nucleus of the atom.
INDUCTION
Objects can also be
charged by placing
them next to each
other and using a
charged object
within proximity.
This method is
called charging by
induction.
Examples of
technology that use
electrostatic forces:
• 1. Photocopiers
• 2. Electrostatic
painting
• 3. Electroplating
CHARGE
Charges are comprised of coulombs (C). Think of a coulomb as a
bundle of electrons that can either be stored or transmitted.
Worked example:
The makers of a cellphone have upgraded its
battery capacity from 4320C to 9000C. If a charger
delivers a current of 0.6A, how much more time will
it take to charge the new battery than the old?
ΔQ = 9000 – 4320 = 4680 C
Δt = ΔQ ÷ I = 4680 ÷ 0.6
= 7800 s (or 130 mins)
ELECTRIC FIELDS
An electric field is defined as a region around a charged particle or
object within which a force would be exerted on other charged
particles or objects.
Electric fields flow out
from positive and into
negative.
So flow occurs from
positive to negative.
Voltage
The amount of energy contained per unit of charge.
1 Volt = 1 Joule/Coulomb (J/C)
Also called potential difference and
emf (electromotive force).
Think of it as the ‘force’ that pushes
charges across a conductor.
Current
The number of unit charges that pass a point per second.
1 Ampere = 1 Coulomb/second (C/s)
If you have a 2A charger for your
phone, it will deliver 2 coulombs per
second to the battery.
Current flows ‘conventionally’ from
positive to negative.
RESISTANCE
The opposition to current flow in a circuit.
1 Ω= 1 Volt/Ampere (V/A)
Wires of thin diameter tend to
restrict flow of current and so
have greater resistance.
Longer wires also have greater
resistance due to heat losses.
Ohm’s Law
The current through a conductor is directly proportional to voltage
and inversely proportional to resistance.
Ohm’s Law (worked example)
A lamp is marked 12V, 3A. Calculate the lamp’s:
(i) Resistance
(ii) Energy if left on for a minute
(i) V = IR
R=V/I
= 12 / 3
=4Ω
(ii) P = VI
= 12 x 3
= 36 W
E =Pxt
= 36 x 60s
= 2160 J
OR
E = VIt
= 12 x 3 x 60
= 2160 J
Ammeters and
Voltmeters
Ammeters measure current.
They are connected in series
due to their low resistance.
Voltmeters measure voltage.
They are connected in
parallel due to their high
resistance.
Direct (d.c.) and
alternating current (a.c.)
d.c. is unidirectional and has
a mostly fixed value, e.g. AA
batteries.
a.c. is bidirectional and has
values that fluctuate
between positive and
negative, e.g. transformers,
power lines
Rectification
An a.c. can be converted to a
d.c. with the use of a
semiconductor diode or a
rectifier.
This produces half-waves in
a voltage-time graph.
If the diode is reversed, no
current will flow.
Primary and Secondary Cells
Voltage-Current
(VI) Graphs
The graph shapes for:
1. Ohmic conductor
2. Filament lamp
3. Electrolyte
4. Semi-conductor diode
Series Circuits
There is only one current path. If
either A or B is removed, no
current will flow.
The voltage in the cell is ‘shared’
between A and B. Higher
resistances require more voltage.
Current is equal in all
components in series.
The total resistance, Rs, is the
sum of all resistances.
Rs = R1 + R2 …
Series Circuits (example)
Calculate the following:
(i) Total resistance
(ii) Current
(iii) Voltage through A
(i) Rs = R1 + R2
= 5 + 3 = 8Ω
(ii) I = V / R
= 6 / 8 = 0.75 A
(iii) V (A) = IR
= 0.75 x 5
= 3.75 V
Parallel Circuits
There are multiple paths. If
either A or B is removed, current
can still flow.
The voltage in each path is the
same as the voltage of the cell.
The current in each path is
determined by the path’s
resistance. Higher resistances
have lower currents.
Parallel Circuit Resistance
Resistance in a parallel circuit is
calculated with:
Parallel Circuit (Current)
Total current can be calculated
by finding the currents through
each path:
Path A → I = V/R = 6/5 = 1.2 A
Path B → I = V/R = 6/3 = 2.0 A
Total = 1.2 + 2.0 = 3.2 A
OR I = V/R = 6/1.875 = 3.2 A
(using total resistance)
Combined Series
and Parallel Circuit
In the circuit above, R2 and
R3 are in series on path B.
R1 will be parallel to the
other two.
A1 measures the total
current in the circuit (as it
is connected to the power
source). A2 measures the
current in Path A.
Combined Series
and Parallel Circuit
Reading on A2:
I=V/R
= 12 / 2 = 6A
Reading on A1:
= Current in Path A + Current in Path B
= 6A + 2A = 8A
Total current of Path B:
R = R2 + R3
=2+4=6
I =V/R
= 12 / 6 = 2A
Fuses and Wiring
Fuses are made of metals with
low melting points.
Fuse gets heated up → Fuse
breaks → Circuit is broken
Fuses and switches are always
connected to live wires. Neutral
wires complete the circuit. Ground
or earth wires deposit extra
electrons into the ground.
Electrical Hazards
1. Damp wires and broken
insulation can result in
electrocution or electrical
fires.
2. Electrocution can also occur if
the earth wire is improperly
connected, causing electrons to
build up in the frame of an
appliance.
Magnetism
- Temporary magnets (e.g. iron)
can be easily magnetized and
are usually found in
electromagnets.
- Permanent magnets (e.g.
steel) retain their magnetism
for a long time and are usually
found in compass needles and
metal detectors.
Magnetic Induction
An unmagnetized magnetic
material can be magnetized if it
is placed in the proximity of a
magnet or an electric field.
Magnetic fields run
perpendicular to electric fields,
and are part of the same force.
One cannot exist without the
other.
When the circuit is connected,
electrons will flow from the
battery to the iron nail,
temporarily magnetizing it.
Fleming’s Left Hand Rule
Two of the above quantities can
‘create’ the third once they are
perpendicular to each other:
Example: If a wire is moved (thrusted)
perpendicular to a magnetic field, a
current can be induced in that wire.
If a current-carrying wire is
perpendicular to a magnetic field, the
wire will be thrusted in a certain
direction.
Fleming’s Left Hand Rule (1st example)
What direction is the wire being thrusted?
Fleming’s Left Hand Rule (1st example)
Fleming’s Left Hand Rule (2nd example)
If the wire is being thrusted out of the page, is the current left or right?
Fleming’s Left Hand Rule (2nd example)
If the wire is being thrusted out of the page, is the current left or right?
Right Hand Grip Rule
The (x) means the current is going into the
page.
The dot (.) means the current is coming out of
the page.
Right Hand Grip Rule
Fleming’s Left Hand Rule in a Coil
The thrusts on AB and CD will create a turning force or moment. This
allows the coil to spin in a motor. No thrust will occur on BC because the
magnetic field is parallel, not perpendicular, to the current there.
d.c. motors
The motor converts electrical
to mechanical energy.
The motor spins due to forces
created by the current being
perpendicular to the magnetic
field.
d.c. motor (split ring)
The split ring (commutator)
breaks the circuit every halfturn.
This prevents the coil from
reversing direction, allowing it
to spin continuously.
d.c. motors
To generate more turning force:
1. Add more turns in the coil
2. Increase the current
3. Use stronger magnets
a.c. generators
The generator converts
mechanical to electrical
energy.
An outside energy source (e.g.
wind) spins the external
rotator, which turns the wire
loop in the magnetic field.
This generates current.
a.c. generators
To generate more current:
1. Add more turns in the coil
2. Rotate the coil faster
3. Use stronger magnets
Electromagnetic Induction
The voltage induced in a coil is
proportional to the rate of
magnetic force across it.
– Faraday’s Law
Electromagnetic Induction
No current or voltage is induced if the magnet is not moving
relative to the coil. The galvanometer needle points up at zero.
TRANSFORMERS
Transformers can either increase or
decrease voltage, by decreasing or
increasing current.
Step-up transformers increase voltage
by having more secondary turns than
primary.
Step-down transformers decrease
voltage by having less secondary turns.
TRANSFORMERS
Transformers need a.c. power sources to allow for a constantly
changing magnetic field in the primary turns. This electromagnetizes
the core and induces a current in the secondary turns.
TRANSFORMERS
Transformers need a.c. power sources to allow for a constantly
changing magnetic field in the primary turns. This electromagnetizes
the core and induces a current in the secondary turns.
TRANSFORMERS FORMULAS
TRANSFORMERS (worked example)
Electrical power produced by
Powergen in Trinidad is stepped
up from 11,000V at 8000A to
110,000V for transmission to
Tobago.
(i) If the number of turns in the
secondary coil is 900, calculate
the number of turns in the
primary coil for an ideal
transformer.
(ii) Calculate the transmission
current for the ideal
transformer in (a).
TRANSFORMER LOSSES
Transformers that have no power losses are called IDEAL.
The following factors result in power losses, and how to limit them:
1. HEAT LOSSES – Use thicker, lower-resistance wires
2. EDDY CURRENTS – Laminate the core.
3. HYSTERESIS (magnetization delay) – Use a perm-alloy core.
LOGIC GATES
Logic gates are electronic operators that send signals based on
satisfied conditions (1 – true) or unsatisfied (0 – false).
There are 5 types you should know, for now:
1. NOT gate
2. AND gate
3. OR gate
4. NAND gate
5. NOR gate
NOT GATE
These invert the signal from input to output.
AND GATE
The only positive (1) output is when both inputs are 1. Can be used
in username and password systems.
OR GATE
A positive (1) output is obtained when there is at least one positive
(1) input. Can be used for burglar alarm systems.
NAND and NOR GATES
SOLVING LOGIC GATE PROBLEMS
SOLVING LOGIC GATE PROBLEMS
SOLVING LOGIC GATE PROBLEMS
SOLVING LOGIC GATE PROBLEMS
PARTICLES IN THE ATOM
PARTICLES IN
THE ATOM
Nucleons (protons and
neutrons) are held
together in the nucleus
by strong nuclear forces.
Electrons orbit the
nucleus in shells.
This is the Bohr model.
PARTICLES IN
THE ATOM
ATOMIC NUMBER
The number of protons in
the atom. In this case, the
atomic number is 6.
MASS NUMBER
The number of protons
and neutrons in the
atom. In this case, the
mass number is 12.
RUTHERFORD GOLD
FOIL EXPERIMENT
A source fires a stream of +ve alpha
particles through a thin slice of gold
foil.
A detector strip illuminates in the
spots where the particles collide. Only
the particles that hit or come close to
a gold nucleus are deflected. Most
don’t.
Scientists who did experiment:
GEIGER, MARSDEN, RUTHERFORD.
RUTHERFORD GOLD FOIL EXPERIMENT
ISOTOPES
Isotopes are atoms of the same element, with the
same atomic number but different mass number.
They have the
same number of
protons but
different number
of neutrons.
USES OF RADIOISOTOPES
RADIOACTIVE DECAY
Radioactive decay is spontaneous and random. It occurs
when a nucleus gets far from a 1 proton : 1 neutron ratio.
Unstable atoms that
undergo decay lose
mass over time due
to release of alpha,
beta and gamma
radiation.
TYPES OF RADIATION
Alpha particles are helium
nuclei (2p, 2n).
Beta particles are fastmoving electrons.
Gamma rays are highfrequency e.m. waves.
TYPES OF RADIATION
TYPES OF RADIATION
Alpha is stopped
by paper.
Beta is stopped
by aluminium.
Gamma is
stopped by lead.
CLOUD CHAMBERS
Cloud chambers are sealed dishes filled with alcohol or
vapours that show the trails of radiation emissions.
Alpha has thick
trails.
Beta has thinner,
jagged trails.
Gamma has scattered
spots.
RADIATION IN
MAGNETIC FIELDS
Use Fleming’s Left Hand Rule.
Current (beta particles) to the
right. They are deflected more
because they weigh less.
Alpha goes the opposite
direction. Gamma is
undeflected.
RADIATION IN ELECTRIC
FIELDS
Positive alpha particles
deflect towards
negative plate.
Negative beta particles
deflect towards positive
plate.
Gamma rays are neutral,
so remain undeflected.
RADIATION SAFETY
After Marie Curie (who discovered radium)
succumbed to radiation-related disease, safety
precautions were introduced.
1. Store radioactive materials in lead
containers.
2. Wear safety gloves or use forceps when
handling
3. Stay behind protective screens when
necessary
4. Wear Hazmat suits in irradiated
environments
ALPHA DECAY
An alpha particle
(helium nucleus) is
lost.
The atomic number
decreases by 2 and
the mass number
decreases by 4.
BETA DECAY
A beta particle (fastmoving electron) is
lost.
The atomic number
increases by 1 and
the mass number
remains unchanged.
WRITING DECAY EQUATIONS
HALF-LIFE
Half-life is the time taken for a radioactive
substance to decay by half.
For e.g. Iodine-131 has a half-life of 8 days. If there
were 1000 atoms at first, there would be 500
atoms after 8 days, and 250 atoms after a further 8
days.
HALF-LIFE (1st worked example)
An 800mg sample of radon decays over a period of
20 days until only 25mg remains. What is the halflife of radon, in days?
800 → 400 → 200 → 100 → 50 → 25
Number of half-lives = 5
5 half-lives = 20 days
1 half-life = 20 days / 5 = 4 days
HALF-LIFE (2nd worked example)
If iodine-131 has a half-life of 8 days, how many
days must pass before it reaches 1/16th its mass?
1→ ½ → ¼ → 1/8 → 1/16
Number of half-lives = 4
Time elapsed = 4 x 8 days = 32 days
HALF-LIFE GRAPH
NUCLEAR ENERGY
NUCLEAR ENERGY
Pros:
1. It is more efficient than fossil fuels and yields much more
useable electrical energy.
2. It produces no greenhouse gases, does not contribute to climate
change.
Cons:
1. There is a risk of nuclear meltdown, e.g. Chernobyl
2. Radioactive waste is difficult to dispose of.
CALCULATING NUCLEAR ENERGY
The formula for nuclear energy is given as:
CALCULATING NUCLEAR ENERGY (example)
Calculate the energy released in the
reaction above.
CALCULATING NUCLEAR ENERGY (example)
First, add the masses on the left:
2.014 + 3.016 = 5.03 u
CALCULATING NUCLEAR ENERGY (example)
Then, add the masses on the right:
4.003 + 1.009 = 5.012 u
CALCULATING NUCLEAR ENERGY (example)
Subtract the difference:
▲m = 5.03 - 5.012
= 0.018 u
CALCULATING NUCLEAR ENERGY (example)
Convert the ‘u’ to ‘kg’:
▲m = 5.03 - 5.012
= 0.018 u x (1.66 x 10-27 kg)
= 2.988 x 10-29 kg
CALCULATING NUCLEAR ENERGY (example)
c = speed of light
(3 x 108 m/s)
Use Einstein’s formula to calculate E:
▲E = ▲mc2
= 2.988 x 10-29 kg x (9 x 1016)
= 2.6892 x 10-12 J
c2 = 9 x 1016 m/s