Mechanics

Scalars and VectorsScalars VectorsMass ForceTemperature AccelerationTime MomentumLength/distance DisplacementSpeed VelocityEnergy

Motion with constant acceleration• Acceleration could mean change in direction, speed or both

Free Fall• Only force acting on object in free fall is its weight• Objects can have initial velocity in any direction and still undergo free fall as long

as force providing initial velocity is no longer acting• Measuring g:

o measure height from bottom of ball bearing to trapdooro flick switch to simultaneously start timer and disconnect electromagnet,

releasing ball bearingo ball bearing falls, knocking trapdoor down and breaking circuit, stopping

timer

Displacement-time graphs• Gradient = velocity• Straight line means constant velocity• Curved line = acceleration• Decreasing gradient = deceleration

Velocity-time graphs• Gradient = acceleration• Area under graph = displacement• Can be negative to show opposite motion• Increasing gradient = increasing acceleration• Decreasing gradient = decreasing acceleration• Ultrasound position detector (data-logger) – more accurate (no human reaction

times), higher sampling rate than humans, see data displayed in real time

Mass, Weight and Centre of Gravity• The greater an object’s mass, the greater its resistance to a change in velocity

(inertia)• Centre of gravity – single point that you can consider whole weight to act through

(whatever its orientation)• Object always balances around this point, even though sometimes CofG can fall

outside object• Object stable if low centre of gravity and wide base area

• Object will topple over if vertical line drawn downwards from centre of gravity falls outside base area

Forces• Free-body force diagrams show all forces acting on a single body

Newton’s Laws of Motion• 1st law = A body at rest will stay at rest, a body in motion will continue to move in

a straight line at a constant velocity, unless acted upon by a resultant external force

• 2nd law = For a body of constant mass, the force applied is proportional to the acceleration

• 3rd law = If body A exerts a force on body B, body B exerts an equal and opposite force on body A

• Newton’s 3rd law pairs – same type of force

Work and Power• Work is the amount of energy transferred from one form to another when a force

causes a movement of some sort• 1 joule is the work done when a force of 1 newton moves an object through a

distance of 1 metre• Power is rate of doing work – amount of energy transformed from one form to

another per second• Power = work done / time• Watt is defined as rate of energy transfer equal to 1 J/s• Power = force x velocity

Conservation of Energy• Efficiency = useful power output / power input

Materials

Hooke’s Law• If you increase the load past the elastic limit, the material is permanently

stretched• Elastic deformation – material returns to original shape when forces are

removed. Atoms are pulled apart when material under tension. Atoms can move small distances relative to equilibrium position without changing position in the material. When load removed atoms return to equilibrium distance apart.

• Plastic deformation – material is permanently stretched. Some atoms move position relative to one another. When load removed, they don’t return to original positions

• Brittle materials fracture before reaching elastic limit

Stress and strain• Stress causes strain• Tensile forces stretch, compressive forces squash• Stress (Pa/Nm^-2) = F/A

• Strain = e/l• Breaking stress – stress big enough to break material• UTS (Ultimate Tensile Stress) – maximum stress that material can withstand• Elastic strain energy – energy stored in stretched material• Before elastic limit, all work done in stretching is stored as potential energy.

Beyond elastic limit, some work is done separating atoms, which is not stored as strain energy, so isn’t available when force released

• Area under graph – E=1/2Fe = E=1/2ke^2

Young Modulus• E (Pa/Nm^-2) = stress/strain• Gradient of stress against strain graph is Young Modulus• Area under graph is strain energy per unit volume

Behaviour of Solids• Brittle – snap suddenly without deforming plastically e.g. glass• Ductile – drawn into wires without losing strength e.g. copper• Malleable – beaten into sheets but may lose strength e.g. gold, brass• Hard – resistant to abrasion, cutting and indentation e.g. diamond• Stiff – high resistance to bending and stretching e.g. helmets, boots• Tough – absorbs lots of energy before breaking e.g. kayak polymers• Brittle fracture – when stress is applied, cracks at material’s surface get bigger

and bigger until material breaks completely• Copper – ions can move to prevent cracks getting bigger• See stress-strain graphs• Rubber returns to original length when load removed – elastically• Polythene is stretched to new shape – ductile and behave plastically

Properties of fluids• Fluid element – a part of a fluid in which all particles are flowing in same direction

at same rate (with same velocity) – small enough that it flows without breaking up, large enough that thermal motion/random movement of particles within can be ignored

• Flowline – path that a fluid element follows• Streamline – a stable flowline – every element on it follows same path• Streamlines parallel in laminar flow (all fluid elements flow in same direction) –

usually flowing slowly• Turbulent flow – fluid elements get mixed up – flowlines are unstable – usually

flowing quickly• Viscous drag – the force of friction produced by a flowing fluid – fluid elements

move past each other with different velocities, friction created• The higher the viscosity and the more turbulent the flow, the larger the viscous

drag• When an object moves through a fluid, friction is created between surface of

object and fluid• Upthrust = weight of fluid displaced• Fluid pressure – outward force exerted on all surfaces fluid is in contact with

Electricity

Charge, Current and Potential Difference• Current is rate of flow of charge• Current flows + to –• Electrons flow – to +• 1 coulomb (C) is the amount of charge that passes in 1 second when the current

is 1 ampere• Attach ammeter in series• Different materials have different numbers of charge carriers• In a metal there are loads of charge carriers, making n big, so drift velocity only

needs to be small even for a high current• Semiconductors have less charge carriers than metals so their drift velocity

needs to be higher for same current• Gases are insulators, but apply a high enough voltage and electrons are ripped

from atoms, giving ions• Potential difference (voltage) is the energy converted per unit charge moved• The PD across a component is 1 volt when you convert 1 joule of energy moving

1 coulomb of charge through the component (1V=1JC^-1)

Resistance and Conductance• A component has a resistance of 1Ω if a potential difference of 1V makes a

current of 1A flow through it• Resistance depends on: length (longer the wire, more difficult for a current to

flow); area (wider the wire, easier for electrons to pass); resistivity depends on material, temperature, light intensity

• The resistivity of a material is the resistance of a 1m length with a 1m² cross-sectional area. (Ωm)

• Ohm’s law – At constant temperature, the current through an ohmic conductor is directly proportional to the pd across it

Current-Voltage Characteristics• Metallic conductor are ohmic – see previous note (Figure 3)• Filament lamp – coiled up metal wire which gets hot due to flowing current,

increasing atomic vibrations, restricting flow of electrons, so resistance of a metal increases as temperature increases

• Ions vibrate more when heated, electrons collide with them more often, losing energy

• Semiconductors – less charge carriers so worse at conducting electricity. If energy supplied to it, more charge carriers released, which makes them excellent sensors for detecting changes in environment

• NTC thermistors (Negative Temperature Coefficient) – a resistor whose resistance depends on temperature. Resistance decreases as temperature goes up, as increasing temperature gives more electrons enough energy to escape their atoms, creating more charge carriers.

• LDR (Light Dependent Resistor) – as light intensity increases, resistance decreases – this time light provides the energy that releases electrons

• Diodes designed to let current flow in 1 direction (forward bias/direction)

• Forward bias – threshold voltage of 0.6V before they will conduct• Reverse bias – resistance very high so very tiny current flows

Electrical Energy and Power• Power is rate of transfer of energy• 1 watt = 1 joule per second

EMF and Internal Resistance• Resistance comes from electrons colliding with atoms and losing energy• In a battery chemical energy makes electrons move which collide with atoms in

the battery creating internal resistance. This is why they warm up• EMF – the amount of electrical energy produced for each coulomb of charge• PD across load resistance (R) is the energy transferred when 1C of charge flows

through load resistance – terminal pd (V)• Lost volts (v) – energy wasted per C overcoming internal resistance• Energy per C from source = energy per C used in R + energy per C wasted in r• E = V + v• High voltage power supplies – very high internal resistances so they are safer if

accidentally short-circuited (small current flows)

Conservation of Energy and Charge in Circuits• Kirchhoff’s 1st law – total current entering a current = total current leaving it• Energy transferred to a charge is EMF, energy transferred from a charge is PD• Kirchhoff’s 2nd law – total e.m.f. around a series circuit = sum of p.d.s across

each component

The Potential Divider• Potential divider – circuit with a voltage source and resistors in series• LDR or NTC thermistors used and transistor as switch (off when voltage low, on

when voltage high).

Imaging and Signalling (Waves)

The Nature of Waves• A progressive wave carries energy from one place to another without transferring

any material• Period – time taken for a whole vibration/wavelength• Frequency – number of vibrations per second passing a given point• Phase difference – amount by which one wave lags behind another• Intensity is the rate of flow of energy per unit area at right angles to the direction

of travel of the wave (Wm^-2)• Intensity proportional to square of amplitude of wave• f = 1/T (frequency is inverse of period)• Time taken to travel 1 wavelength is the period of the wave

Longitudinal and Transverse Waves• All electromagnetic waves are transverse, and ropes and water ripples

• Graphs can be displacement against distance along path of wave, or displacement against time for a point as the wave passes

• Longitudinal – sound and some earthquake shock waves, alternate compressions and rarefactions of medium (so sound can’t go through vacuum)

• Polarising a wave – filtering out vibrations in all directions but one• Polarising filter – only transmits vibrations in one direction• If you direct a beam of unpolarised light at a reflective surface, then view

reflected ray through polarising filter, intensity of light leaving filter changes with orientation of filter because light partially polarised when reflected

• Plane of polarisation is the plane in which a wave moves and vibrates• Some materials (crystals) rotate plane of polarised light• Arrange 2 polarising filters so that no light leaves 2nd one• Place material being tested between 2 filters (now some light gets through)• Rotate 2nd filter until no light leaves (angle that you rotate filter is the angle the

material rotates the plane of polarisation)

Ultrasound Imaging• Interface – boundary between 2 different media• If media very different, most of energy is reflected• If media quite similar, most of energy is transmitted• Ultrasound directed into body using transducer. If air between transducer and

skin, most reflected as air very different medium to skin. Gel applied to transducer to increase proportion of ultrasound that enters body. When ultrasound reaches interface, it is reflected. Computer attached to transducer calculates distance of interface from skin by timing how long it takes for reflected waves to return

• Sonar – ships send sonar pulses towards seabed and pulses reflected back from submerged objects

• Sound waves travel in opposite direction to car when car moving away from observer, so are stretched out

• Change in sound waves depends on speed• Police radar guns measure speed of cars using microwaves, ultrasound

sonography monitors function of blood vessels• Shorter wavelengths diffract less, so spread out less, so location of interfaces are

mapped more precisely – high frequency, short wavelength used by ultrasound scanners

• Transducers cannot transmit and receive at same time – if reflected waves reach it while it’s transmitting, information lost and image quality reduced. So ultrasound pulses must be short so that reflections from interfaces don’t reach transducer before pulse has ended. Gap between pulses must be long so that all reflected waves from one pulse return before next pulse transmitted

• Scientists consider safety, social issues, ethical/moral issues, cost

Electromagnetic Spectrum• Travel at almost 3 x 10^8 m/s• Transverse waves consisting of electric and magnetic fields which oscillate at

right angles to each other and to direction of travel• Carry energy, can be polarised

Type Production Uses Penetration Effects on humans

Radio waves Oscillations in electric fields (oscillating electrons in an aerial)

radio transmissions

pass through matter

no effect

Microwaves Electron tube oscillators/masers

radar/microwave cookery /TV transmissions

mostly pass through matter/ cause heating

absorbed by water – danger of cooking human body

Infrared Natural/artificial heat sources

heat detectors/ night-vision cameras/ remote controls/ optical fibres

mostly absorbed by matter, causing heating

heating (excess can harm body systems)

Visible light Energy-level transitions in atoms and natural/artificial light sources

human sight/ optical fibres

absorbed by matter, causing heating

used for sight – too bright can damage eyes

Ultraviolet e.g. sun sunbeds/ security markings

absorbed by matter, slight ionisation

tans skin – can cause skin cancer/ eye damage

X-rays Energy-level transitions in atoms/ bombarding metal with electrons

to see damages to bones and teeth/ airport security cameras/ to kill cancer cells

mostly pass through matter, cause ionisation

cancer due to cell damage / eye damage

Gamma rays Inside nucleus /radioactive decays of nucleus

irradiation of food/ sterilisation of medical instruments/ to kill cancer cells

mostly pass through matter, cause ionisation

Wave Phenomena

Refractive Index• The absolute refractive index of a material, n, is the ratio between the speed of

light in a vacuum, c, and the speed of light in that material, v.• n = c/v• 1n2 = v1/v2• 1n2 = n2/n1• When light enters optically denser medium, it’s refracted towards normal• When light enters optically less dense medium, refracted away from normal• n1sini = n2sinr• Refractometer accurately measures refractive index of a material. Machine

shines beam of light at sample. Then you view refracted beam through a microscope and measure angle of refraction

• Refractive index has to be very accurate – making lenses, in forensic investigations

• Optical fibres have high refractive index but surrounded by cladding with lower refractive index. Light always hits boundary between fibre and cladding at angle bigger than critical angle so all light is totally internally reflected

• Signal can carry more energy due to high frequency of light, light doesn’t heat up fibre (no energy lost as heat), no electrical interference

Superposition and Coherence• Superposition happens when 2 or more waves pass through each other• At the instant the waves cross, the displacements due to each wave combine• Principle of superposition – when 2 or more waves cross, the resultant

displacement = vector sum of the individual displacements• If crest and trough not same size, destructive interference not total• For noticeable interference, the 2 amplitudes should be nearly equal• In phase – 2 points at same point in wave cycle – same displacement and

velocity – phase difference of 0 or multiple of 360º (2π)• Out of phase – points with phase difference of multiples of 180º (π)• 2 waves in phase because both came from same oscillator• To get interference patterns when observing waves of different

wavelength/frequency, the 2 or more sources must be coherent (have same wavelength and frequency and fixed phase difference between them)

• Constructive or destructive interference at a point depends on path difference (how much one wave has travelled to get to that point compared to other wave)

• Constructive interference at any point an equal distance from both sources, or where path difference is whole number of wavelengths. Here waves are in phase and reinforce each other

• Constructive interference – path difference = nλ• Destructive interference – path difference = (n+½)λ

Stationary (Standing) Waves• A standing wave is the superposition of 2 progressive waves with the same

wavelength, moving in opposite directions• Demonstrate standing waves by setting up driving oscillator at one end of

stretched string with other end fixed• If oscillator produces exact number of waves in time it takes a wave to get to the

end and back again, the original and reflected waves reinforce each other. At these resonant frequencies you get a standing wave where pattern doesn’t move

• Each particle vibrates at right angles to string• Node – amplitude is 0• Antinodes – maximum amplitude• At resonant frequencies, an exact number of half wavelengths fit onto string• Lowest possible resonant frequency – fundamental frequency – 1 loop with node

at each end• 2nd harmonic (1st overtone) – twice the fundamental frequency – 2 loops with

node in middle and at each end• 3rd harmonic (2nd overtone) – 3 times fundamental frequency – 1½ wavelengths fit

on string (3 loops)

• Transverse standing waves from on strings of stringed instruments, waves sent in both directions and reflected back at both ends

• Longitudinal standing waves form in wind instrument or other air column – if sound source placed at open end of air column/wind instrument, there will be some frequencies for which resonance occurs and a standing wave set up. Closed end – node forms there. Lowest resonant frequency when length is ¼λ

• Antinodes form at open ends. If both ends open, lowest resonant frequency when length is ½λ

Diffraction• Diffraction – the way that waves spread out as they come through narrow gap or

go round obstacles• When gap lot bigger than wavelength, diffraction unnoticeable• Gap several wavelengths wide, noticeable diffraction• Most diffraction when gap same size as wavelength• Waves mostly just reflected back if gap smaller than wavelength• Demonstrate diffraction by shining laser light through narrow slit onto screen,

amount of diffraction altered by changing width of slito or use white light instead of laser, keep size of slit constant and vary

wavelength by putting colour filters over slit• Diffraction occurs around edges of obstacle, shadow behind it. The wider the

obstacle compared with wavelength, the less diffraction, so a longer shadow• If wavelength of light wave is about same size as gap, you get diffraction pattern

of light and dark fringeso bright central fringe with alternating dark and bright fringes on either sideo the narrower the slit, the wider the diffraction patterno need to use coherent light source for this

• Diffraction patterns for electrons was first direct evidence for electrons showing wave-like properties

Light – Wave or Particle• A photon is a quantum of EM radiation• EM waves only exist in discrete packets• A photon acts as a particle and transfers all or none of its energy when

interacting with another particle, like an electron• An electronvolt is the kinetic energy gained by an electron when it is accelerated

through a pd of 1 volt• 1 eV = 1.6 x 10^-19 J• When you accelerate an electron between 2 electrodes, it transfers some

electrical potential energy (eV) into kinetic energy

The Photoelectric Effect• Free electrons on metal surface absorb energy from high frequency UV light,

making them vibrate. If an electron absorbs enough energy, the bonds holding it to metal break and it is released. Electrons emitted are photoelectrons

• No photoelectrons are emitted if radiation is below threshold frequency• Photoelectrons emitted with variety of kinetic energies from 0 to some maximum.

Maximum kinetic energy increases with frequency of radiation and is unaffected by intensity

• No. of photoelectrons emitted per second α intensity of radiation• The minimum amount of energy needed to break bonds holding electrons there

is work function, depends on metal• If energy gained is less than work function, electrons shake about, then release

energy as another photon, causing heating but no electron emission• f = φ / h• Kinetic energy of electrons is independent of intensity because they can only

absorb 1 photon at a time• hf = φ + ½ mvmax²

Energy Levels and Photon Emission• Transitions between definite energy levels so energy of each photon can only

take a certain allowed value

Wave-Particle Duality• Light produces interference and diffraction patterns, showing light acting as a

wave• Light acts as a particle – photoelectric effect – all the energy in the photon is

given to one electron• de Broglie – if wave-like light showed particle properties (photons), particles like

electrons should be expected to show wave-like properties• λ = h / mv• Electron diffraction shows wave nature of electrons• Diffraction patterns observed when accelerated electrons in a vacuum tube

interact with the spaces in a graphite crystal• Spread of lines in diffraction pattern increases if wavelength is greater• Smaller accelerating voltage (slower electrons) gives widely spaced rings• Increase electron speed and the diffraction pattern circles squash together• λ for electrons accelerated in vacuum tube is about same size as EM waves in X-

ray part of spectrum• You only get diffraction if particle interacts with object of about same size as de

Broglie wavelength• Light blurs out detail more than electron-waves, so an electron microscope can

resolve finer detail than a light microscope