Physics IGCSE (Paper 2)

Speed

Speed

How fast you’re going with no regard to direction

Velocity

How fast you’re going, but also with the specified direction

Equation: Avg. speed, Distance, Time

v = s/t

Average speed = Distance moved/Time taken

[m/s] = [m]/[s]

Acceleration

How quickly velocity is changing

Equation: Acceleration, Change in velocity, Time

a = (v-u)/t

Acceleration = (Final velocity - initial velocity) / Time taken

[m/s²] = ([m/s]-[m/s]) / s

Equation: Final speed, Initial speed, Acceleration, Distance

v² = u² + 2as

(Final velocity)² = (Initial velocity)² + (2 x Acceleration x Distance)

[m/s]² = [m/s]² + 2 x [m/s²] x [m]

Distance-Time Graphs

• Gradient at any point = speed of object

• Flat section = stopped

• Steeper graph = faster speed

• Curve = acceleration

• Curve getting steeper = speeding up (increasing gradient)

• Levelling off curve = slowing down (decreasing gradient)

Velocity-Time graphs

• Gradient = acceleration

• Flat section = steady speed

• Steeper graph = greater acceleration/deceleration

• Uphill section = acceleration

• Downhill section = deceleration

• Area under any part of graph = distance travelled in that time interval

• Curve = changing acceleration

Investigating motion

• Set up apparatus as in diagram, holding car still just before light gate

• Mark a line on ramp to make sure car starts from same point each time

• Measure distance between each light gate - need this to find car’s average speed

• Let go of car just before light gate so it starts to roll down slope

• Light gates should be connected to computer
  When car passes through each light gate, a beam of light is broken and time is recorded by software

• Repeat experiment several times to get average time taken for car to reach each light gate

• Use these times and distances to find average speed of car on ramp and average speed of car on runway - divide distance between light gates by average time taken for car to travel between gates

Gravity

Gravity attracts all masses, but only noticeable when one of the masses is very big

This has three effects:

• On surface of planet, makes things accelerate towards ground

• Gives everything weight

• Keeps planets, moons, satellites in orbit

Weight vs Mass

• Mass is amount of ‘stuff’ in object - same value anywhere in universe

• Weight is caused by pull of gravity

• Object has same mass on Earth and Moon - but different weight

  1kg mass weighs less on Moon (1.6N) than Earth (10N) because force of gravity pulling on it is less

• Weight is force measured in newtons
  Mass is not a force

Equation: Weight, Mass, Gravity

W = mg

Weight = Mass x Gravitational field strength

[N] = [kg] / [N/kg]

Force

A push or pull

Vector quantity with size + direction

Gravity/Weight

When close to a planet this acts straight downwards

Reaction force

Acts perpendicular to surface and away from it (if surface is horizontal, reaction force acts straight upwards)

Electrostatic force

Between two charged objects

Direction depends on type of charge (like charges repel, opposites attract)

Thrust

e.g. push or pull due to engine/rocket speeding something up

Drag/air resistance/friction

Slows the object down

Lift

e.g. due to aeroplane wing

Tension

in a rope or cable

Drawing the forces acting on a body

• Many forces act on everything, but usually not noticed because they balance out

• Any object with weight feels reaction force back from the surface it’s on
  Otherwise it would just keep falling

• When an object moves in fluid (air, water etc.), it feels drag in opposite direction to motion

Friction

If an object has no force propelling it, it always slows down and stops due to friction (force that opposes motion)

To travel at steady speed, objects need driving force to counteract friction

Static friction

Friction between solid surfaces which are gripping

Can be reduced by putting lubricant (oil/grease) between surfaces

Sliding friction

Can be reduced by putting lubricant (oil/grease) between surfaces

Friction between solids often causes wear of two surfaces in contact

Drag

Keeping shape of object streamlined (sports car, boat hull) reduces drag in fluids
Lorries + caravans have ‘deflectors’ to make them more streamlines + reduce drag

Roof boxes on cars spoil their streamlined shape so slow them down
For a given thrust, higher drag = lower top speed of car

Opposite extreme is parachute (need as high drag as possible)

In fluid, friction always increases as speed increases

Newton’s First Law of Motion

As long as forces on object are balanced, it will stay still, or if already moving, it carries on at same velocity

Newton’s Second Law of Motion

If there is unbalanced force, object accelerates in that direction

Equation: Force, Mass, Acceleration

F = ma

Force = Mass x Acceleration

[N] = [kg] x [m/s²]

Newton’s Third Law of Motion

If object A exerts force on object B, then object B exerts an equal and opposite force on object A

e.g. swimming, push back against water with arms + legs, and water pushes you forwards with equal-sized force in opposite direction

Vector quantities

Have size and direction

e.g. force, velocity, acceleration, momentum

Scalar quantities

Only size, no direction

e.g. mass, temperature, time, length

Resultant force

When multiple forces act on object, you can find resultant force acting on object by adding/subtracting - need to know size of all different forces acting on object and their direction

Terminal velocity

Frictional forces increase with speed - but only up to a certain point

• When object first starts to fall, it has much more force accelerating it than resistance slowing it down

• As velocity increases, resistance builds up

• Resistance force gradually reduces acceleration until resistance force is equal to accelerating force
  At this point, object can’t accelerate any more, it has reached terminal velocity

Factors affecting terminal velocity

• Accelerating force acting on all falling objects is gravity
  All objects would accelerate at the same rate without air resistance

• Air resistance causes things to fall at diff speeds, and terminal velocity of object is determined by its drag compared to its weight
  Drag depends on shape and area

Stopping distance

Distance covered in the time between driver first spotting a hazard and the car coming to complete stop

Stopping Distance = Thinking Distance + Braking Distance

Factors affecting thinking distance

• Reaction time - affected by tiredness, drugs, alcohol and old age

Factors affecting braking distance

• Speed - faster speed = further distance before stopping

• Mass of vehicle - larger mass = longer time to stop

• Quality of brakes - worn/faulty brakes increase braking distance

• Grip - depends on road surface, weather conditions (e.g. icy), tyres

Equation: Moment, Force, Perp distance from pivot

M = Fd

Moment = Force x perpendicular Distance from pivot

[Nm] = [N] x [m]

Centre of gravity

The point at which the weight of an object acts

A freely suspended object swings until centre of gravity is vertically below point of suspension

Finding centre of gravity

• Suspend shape and a plumb line from same point, and wait until they stop moving

• Draw line along plumb line

• Repeat but suspend shape from different pivot point

• Centre of gravity is where two lines cross

Principle of moments

If object is balanced:

Total Anticlockwise moments = Total Clockwise moments

Upwards forces with heavy object on light beam

• If a light rod (no weight) is being supported at both ends, upwards force provided by each support isn’t always the same

• If heavy object is placed on rod, support closest to object provides larger force

Equation: Pressure difference

p = h x ρ x g

Pressure difference = Height x Density x Gravitational field strength

[Pa] = [m] x [kg/m³]

Investigating how extension varies with applied force

• Set up apparatus as in diagram

• Measure length of spring using mm ruler when no load is applied
  Ensure ruler is vertical and measure spring at eye level (this is spring’s natural length)

• Add one mass at a time and allow spring to come to rest, then measure new length of spring
  Extension = change in length from original length

  Repeat process until you have enough measurements

• Once done, repeat experiment and calculate average value for length of spring for each applied weight

• Repat experiment using metal wire or rubber band instead of spring

Hooke’s Law

Extension of stretched wire is proportional to load/force

Metal spring (or other object) also obeys Hooke’s law if a pair of opposite forces are applied to each end

Force-extension graph

There’s a limit to force you can apply for Hooke’s law to stay true

First part of graph shows Hooke’s law being obeyed - straight-line relationship between force and extension

When force becomes great enough, graph starts to curve

If you increase force past elastic limit (marked E on graph), material is permanently stretched

When all force is removed, material will be longer than at the start

Elastic behaviour

Ability of material to recover to original shape after forces causing deformation have been removed

Equation: Momentum, Mass and Velocity

p = mv

Momentum = Mass x Velocity

[kg m/s] = [kg] x [m/s]

Conservation of momentum

Momentum Before = Momentum After

Equation: Force, Change in momentum, Time

F = (mv-mu) / t

Force = Change in momentum / Time

[N] = [kg m/s] / [s]

Example of Force from change in momentum

How safety features work

• Larger force = faster change of momentum

• Similarly, if momentum changes very quickly (like in car crash), forces on body will be very large + more likely to cause injury

• So cars are designed to slow people down over longer time when they crash → smaller force → less severe injury

Crumple zones

Crumple on impact, increasing time taken for car to stop

Seat belts

Stretch slightly, increasing time taken for wearer to stop, reducing forces acting on chest

Air bags

Slow you down more gradually

Electrical conductors

Materials that conduct charge easily - current can flow through

Usually metals e.g. copper + silver

Electrical insulators

Don’t conduct charge very well - current can’t flow

e.g. plastic + rubber

Static charge

Charge which builds up in one place and is not free to move
More common on insulators, where current can’t flow

Electrostatic charge

• Common cause of static electricity is friction
  When two insulating materials are rubbed together, electrons are scraped off one and dumped on the other

• Leaves a +ve electrostatic charge on one and -ve electrostatic charge on the other

• Which way electrons are transferred depends on two materials involved

Static charge on conductors

• Static charges can occur on conductors too - cars often get static charge on outside because they gain/lose electrons from air rushing past them

• Charged conductor can be discharged safely by connecting to earth with metal strap
  Electrons flow down strap to ground if charge is negative and flow up the strap from ground if charge is positive

Experiment: charging insulating materials by friction

• Static charges can be caused by friction

• e.g. polythene + acetate rods being rubbed with cloth duster

• When polythene rod is rubbed with duster, electrons move from duster to rod
  Rod becomes negatively charged + duster is left with equal positive charge

• When acetate rod is rubbed, electrons move from rod to duster
  Duster becomes negatively charged + rod is left with equal positive charge

Laws of attraction

Unlike charges attract

Like charges repel

Sparks

• As electric charge builds on isolated object, voltage between object and earth (0 volts) increases

• If voltage gets large enough, electrons can jump across gap - spark

• Can also jump to any earthed conductor nearby - which is why you can get static shocks from clothes, or getting out of a car

• Usually happens when gap is small

Lightning

• Rain drops + ice bump together inside storm clouds, knocking off electrons → top of cloud = positively charged, bottom of cloud = negative

• Creates huge voltage + big spark

Fuelling

• As fuel flows out of filler pipe, static can build up

• Can easily lead to spark

• Solution: make nozzles out of metal so charge is conducted away instead of building up

• Have earthing straps between fuel tank and fuel pipe

Inkjet printer

• Tiny ink droplets are forced out of fine nozzle, making them electrically charged

• Droplets are deflected as they pass between two oppositely charged metal plates

• Droplets are attracted to plate of opposite charge + repelled from plate with same charge

• Size + direction of voltage across each plate changes so each droplet is deflected to hit different place on paper

• Lots of tiny dots make up printout

Photocopier

• Image plate is positively charged
  Image of what you’re copying is projected onto it

• Whiter bits of what you’re copying make light fall on plate and charge leaks away in those places

• Charged bits attract negatively charged black powder, transferred onto positively charged paper

• Paper heated so powder sticks

Series circuits

• Components connected in a line, end to end, between +ve and -ve of power supply

• If you remove/disconnect one component, circuit is broken + all stop working

• Not very useful, only a few things are practically connected in series e.g. fairy lights

Voltage in series circuit

• There’s a bigger supply p.d. when more cells are connected in series

• Total p.d. of supply is shared between components

• p.d. of each component depends on its resistance

Current in series circuit

• Current same everywhere, I₁ = I₂

• Size of current depends on total p.d. and total resistance of circuit

Resistance in series circuit

• Total resistance of circuit depends on number + type of components

• Total resistance is sum of resistance of each component in circuit

Parallel circuits

• Each component is separately connected to +ve and -ve of supply

• If you remove/disconnect one component, others are hardly affected

• This is how most things are connected
  e.g. cars and household electrics
  Each light switch in your house is part of branch of parallel circuit (turns one light on/off)

• Everyday circuits often contain mixture of series and parallel parts - rules of series circuits apply to components on same branch

Current in parallel circuit

• Current shared between branches

• Total current flowing around circuit = total of all currents through separate components

• There are junctions where current splits or rejoins

• Total current going into junction = total current leaving it

• Current through branch depends on resistance, higher resistance = lower current

Voltage in parallel circuit

• P.d. is same across all branches, V₁ = V₂

Resistance in parallel circuit

• Total resistance of circuit decreases if you add second resistor in parallel

Wire voltage-current characteristics

Current through wire is proportional to voltage

Resistor voltage-current characteristics

Current through resistor is proportional to voltage

Different resistors have different resistances

Metal filament lamp voltage-current characteristics

As temp of metal filament increases, resistance increases

Diode voltage-current characteristics

Current only flows through diode in one direction

Ammeter

• Measures current (in amps) through component

• Must be placed in series anywhere in main circuit

Voltmeter

• Measures voltage (in volts) across component

• Must be placed in parallel around component

Investigating V-I characteristics

• Component, ammeter and variable resistor are in series, so can be put in any order

• Voltmeter must be placed in parallel around component under test

• As you vary variable resistor, it alters current flowing through circuit

• Allowing you to take pairs of readings from ammeter and voltmeter

Effect of changing resistance on current

More resistance = less current

LDR

• Changes resistance depending on how much light it receives

• In bright light, resistance falls

• In darkness, resistance is highest

• Useful for various electronic circuits e.g. burglar detectors

Thermistor

• Temperature-dependent resistor

• Hot = resistance drops

• Cool = resistance increases

• Useful for temperature detectors e.g. car engine temp sensors, thermostats

LED

• Light-emitting diodes emit light when current flows through them in forward direction

• Used for numbers on digital clocks and traffic lights

• Unlike light bulb, don’t have filament that can burn out

LEDs and lamps can be used to…

indicate presence of current in circuit

Often used in appliances to show they’re switched on

Equation: Voltage, Current and Resistance

V = IR

Voltage = Current x Resistance

[V] = [A] x [Ω]

Current

Rate of flow of charge around a circuit

Equation: Charge, Current and Time

Q = It

Charge = Current x Time

[C] = [I] x [s]

In solid metal conductors, current is…

a flow of negatively charged electrons

Plugs

• Have three wires - live, neutral, earth

• Only live and neutral wires usually needed, but earth wire stops you getting hurt if something goes wrong

• LIVE WIRE alternates between HIGH +VE AND -VE VOLTAGE of 230V

• NEUTRAL WIRE always at 0V

• Electricity normally flows in through live and neutral wire

• EARTH WIRE and fuse are just for safety

Double insulation

If appliance has plastic casing and no metal parts showing, it’s said to be double insulated

Plastic is insulator, so stops current flowing - meaning you can’t get a shock
Anything with double insulation doesn’t need earth wire

Earthing and fuses

• If fault develops in which live touches metal case, then because case is earthed, big current flows through live wire, case and earth wire

• Surge in current melts the fuse, cutting off the live supply

• This isolates the whole appliance, making it impossible to get electric shock from case
  Also prevents risk of fire caused by heating effect of large current

Circuit breakers

• Protect circuit from damage if too much current flows

• When circuit breakers detect surge in current, they break circuit by opening a switch

• Circuit breaker can easily be reset by flicking a switch on the device
  This makes them more convenient than fuses (have to be replaced once melted)

Heating effect in resistors

When there is electrical current in resistor, there is energy transfer which heats resistor

Because electrons collide with ions in lattice that make up resistor as they flow through it
This gives ions energy, causing them to vibrate and heat up

Heating effect increases resistor’s resistance - so less current flows

Heating effect can cause components in circuit to melt - so circuit stops working

Use of heating effect in resistors

Toasters contain coil of wire with very high resistance

When current passes through coil, temp increases so much that it glows and emits IR (heat) radiation which cooks bread

Equation: Power, Current and Voltage

P = IV

Power = Current x Voltage

[W] = [A] x [V]

Fuse ratings

• Fuses have current ratings and should be rated as near as possible but just higher than the normal operating current

• To work out the fuse needed, you need to work out the current that item normally uses

Equation: Energy, Current, Voltage and Time

E = IVt

Energy transferred = Current x Voltage x Time

[J] = [A] x [V] x [s]