AS Physics PREPARATION: -Prefixes and Factors:

-SI units

Tera Giga Mega Kilo

T G M k

10 ¹² 9 10 10 6 10 ³

Centi Milli Micro Nano Pico

c m mu n p

10ˉ² 10ˉ³ 10ˉ6 10ˉ9 10ˉ¹²

- Trigonometry:

Distance: meters Mass: kilograms Time: seconds Electric current: ampere Temp difference: Kelvin Substance amount: Mole

PE= m a h PE= m v h t PE= m s h tt PE= kg m² sec²

-Percentage uncertainty Measuring instrument: Stopwatch Least count: 0.01 sec HALF least count: 0.005 sec Time for 10 swings: 15.78 Time for 1 swing: 1.578

0.05 x 100 = 0.32 % 15.78 0.05 x 100 = 1.578

Higher numbers get more accurate results

WHEN THERE IS A FORMULA: KE= ½ m v² → KE = m v v ½ is standard, isn’t wrong -Mass is measured in a balance LC= 0.001kg / HLC = 0.0005kg

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Total mass= HAS TO BE IN KG!! -Velocity has both time AND displacement Then ADD percentage uncertainties =TOTAL PORCENTAGE UNCERTAINTY

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3.16 %

EXAMPLE 24.3 = +24.35 -24.25 15.2 = +15.25 -15.15 18.6 = +18.65 -18.55 LC = 0.1m HLC = 0.05m Mean = 6925 + 6815 2

MAX VOLUME= 24.35 x 15.25 x 18.65 MAX V = 6925m続 MIN VOLUME= 24.25 x 15.15 x 18.55 MIN V = 6870m続

MAX MEAN MIN

Mean = 6870m続

0.05 x 100 24.3

= 0.21%

0.21 + 0.27 + 0.33

0.05 x 100 15.2

= 0.27%

= 0.8% ACCURATE

0.05 x 100 18.6

=0.33%

1. Forces and motion: -A force is a push or a pull and can be drawn by arrows. GRAVITATIONAL (or WEIGHT) W Acts on the centre of gravity of the object FRICTION Fr Acts against motion NORMAL CONTACT FORCE R Applied by surface to support the object Weight: vertical arrow from centre of gravity of the object pointing downwards (W=mg) SCALARS

VECTORS

Mass

Force

Speed

Velocity

Length

Acceleration

Distance

Displacement

Energy

Field strength

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Scalar quantities: Normal rules of arithmetic are applied when calculating its sizes Vector quantities: Not only size but DIRECTION are measured

SOHCAHTOA

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Resultant:

2N

R 3N

Θ 3N

R = Resultant

In closed figures:

R²= (3)² + (2) ² R²= 9 + 4 R= √13N

FIND SIZE WITH PYTHAGORAS

Tan Θ = 2/3 Θ= tan 2/3 Θ= 34º

FIND ANGLE WITH TANGENT

If: b

a

2N

c

b a

c

c a + b + c= 0 a

a+b=c b=c–a

To be on EQUILIBRIUM all vertical and horizontal components of vectors must add 0 Vertical and horizontal components:

Fv

F

Fh

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sin Θ= Fh/F Fh = F x sin Θ cos Θ= Fv/F Fv= F x cos Θ

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Moment or Turning force:

Moment = Force x Perpendicular distance to PIVOT -Moment: Vectors that can only have a clockwise (-) or anticlockwise (+) direction. -Unit is Nm

In order to be in balance, the sum of clockwise forces must be EQUAL to the sum of anticlockwise forces. NO RESULTANT FORCE Weight acts on the. CENTRE OF GRAVITY

If: There is CONSTANT ROTATION

Pressure P= F/A

Pressure = Force Unit: Area Pascal

1 Pascal = 1 Nmˉ²

Pressure at any point in the fluid has the same value in all directions Principle of hydraulic machinery:

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Density:

Density = Mass Volume

ALSO WRITEN ρ = m/v -Density: how much mass of an object in its space -Unit: kg mˉ³ OR g cmˉ³ (air= 1.2kg mˉ³) (water= 1000kg mˉ³)

WHAT IS P IN TERMS OF HEIGHT, GRAVITY AND DENSITY? V=m ρ

Ah=m ρ

A= m ρ h

m = gm ρh P

A= F P

A=gm P

A=gm P

Pm=gmρh P=gmρh m

P=gρh Elastic and Plastic: ELASTIC: Returns to its original shape once a force has been removed PLASTIC: Does NOT return to its original shape once a force has been removed HOOKE’S LAW= extension of a material is PROPORTIONAL to the stretching force If double the stretching force the extension also doubles

Materials obey Hooke’s Law, until reaching LIMIT OF PROPORTIONAL ITY (turning plastic)

Metals are ductile after point E, they retain a new shape (DEFORM) Rubber or any polymeric solid don’t follow Hooke’s Law; remain plastic until it breaks Glass is BRITTLE, follows Hooke’s Law until it snaps

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Energy storage: Energy in spring = Area under graph

F= K X Area: ½.F.X ½.K.X.X = ½ K X²

-Elastic materials absorb energy -More extension, more force Previous method can only be applied before limit of proportionality Apply integrates if finding the area after such limit (since it’s a curve)

Stress, Strain and Young Modulus: Stress= Pressure Units: Pascal

Strain: RATE between the initial length and extension NO UNITS

δ=F A

ε=X L Young’s Modulus E= Stress Strain

Young Modulus: Unit = Pa The greater Young Modulus, the stiffer the material It stretches LESS for a given force

E= FL AX

Metals: -Have polycrystalline structure, small crystals with atoms arranged in regular patterns -Ductile behaviour beyond elastic limit is due to atoms’ slip planes slipping against each other -Slips occur because of the movement of an edge dislocation: defect in the pattern of atoms -Metals result in NECKING, width of sample is reduced STRESS INCRESES AS AREA DECRESES -Small dislocations -Heat carbon can

crystals make strong metals since cannot move past grain boundaries enlarges the grains. Slow cooling, diffuse out: metal is annealed Fast cooling, excess carbon doesn’t diffuse: metal is brittle

Processes to change grain or crystal sizes: WORK-HARDENING: Metals are hammered, stretched or bent while it’s cold = STRONG ANNEALING: Heating and slow cooling= DUCTILE, LESS WILLING TO BREAK QUENCING: Heating and quickly cooling = STRONG BUT BRITTLE TEMPERING: Heating, quickly cooling and hammered = STRONG AND TOUGH -Failure: Creep= Deformation caused by constant load. Cause movements of dislocations and necking

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Fatigue= Repeated cycles of stretching, vibration or rotation cause cracks. Stress built up due to the reduction in cross-sectional area; crack enlarges Polymers: Consist of LONG CHAIN MOLECULES -Amorphous: their molecules have no ordering -Semi-amorphous: have both crystalline and amorphous regions. These are also thermoplastics because they soften up with heat (the bonds in their molecules are weak) -Cross-linking: adding different substances to a polymer in order to make it stronger -Thermoset: Property of a cross-linked polymer, hardens with increasing temperature -Rubber: Stress and strain graphs The gradient represents the stiffness (how difficult is the material to stretch) With gradual stretching rubber becomes LESS stiff as the chains of molecules uncoil Once this has happens, rubber becomes STIFFER

Area found in hysteresis loop = ENERGY Lost energy is transferred to the molecules by HEAT

Composite Materials: Laminated materials= Thin sheets of material joined together on right angles Force tensing: in parallel= STRONG, across= WEAK, to break material Fibre composites= Small pieces of material glued together They are lighter, not affected by fatigue. Force tensing: STRONG and EQUAL in every direction Particle composites= (CONCRETE) Mixture of substance with others to increase strength Force compressing: STRONG, tensing: WEAK Concrete is cast around steel bars in tension in any construction (Steel reinforces the concrete) NEWTON: 1: An object maintains its state (motion or at rest) unless there’s a RESULTANT force 2: (MOMENTUM) 3: To every action, there is an equal and opposite reaction

2ND LAW: Momentum: -Momentum: Unwillingness of an object to change its VELOCITY -Unit is kg msˉ¹

Momentum = Mass x Velocity

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Momentum = mv v = Change in velocity Momentum = mv – mu Rate = mv – mu t Force = m ( v-u ) t F = ma

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MOMENTUM

FORCE (Objects must stop at t = 10 sec)

20m/s 1000kg

F = m (v-u) t F = 1000 (0-20) 10 F = -2000N

20 x 1000 = 20 000kg m/s

20m/s 2000kg

20 x 2000 = 40 000kg m/s

F = m (v-u) t F = 2000 (0-20) 10 F = -4000N

Momentum with inelastic objects M before collision= M after collision m1 + m2 = mT (5 x 10) + (15 x 0) = (25 x vT) 50 = 25 x vT vT= 2m/s Kinetic energy is DIFFERENT after collision

Depending where it points, a velocity can be positive or negative. This affects the equation

MASSES ALWAYS ADD

Ke1

Ke2

KeT

½ mu² ½.10.5² =125J

½ mu² ½.15.0² =0J

½ mv² ½.25.vt² 12.5 x (2)² =50J

Momentum with elastic objects

(8 x 10) + (12 x -4) 80 – 48 mT= +32 →

Ke = ½ mv² (½ x 8 x 10²) + (½ x 12 x 4²) 400 + 96 Ke = 496J 1 V2 = 8 – 2 V1 3

(8 x V1) + (12 x V2) 32 = 4 (2V1+3V2) 8 = 2V1+ 3V2

Ke = ½ mv² (½ x 8 x V1²) + (½ x 12 x V2²) 496 = 2 (2 V1²+3 V2²) 4 V1² + 6 V2² 248 = 2 V1²+3 V2² Ke = 2 (2 V1²+3 V2²) J Replace in 2 By using GENERAL FORMULA 2 you obtain:

248 = 2 V1² + (8 – 2 V1) (8 – 2 V1) 248 = 2 V1² + (64 – 16 V1 – 16 V1 + 4 V1²) 248= 6 V1² - 32 V1 + 64 0= 6 V1² - 32 V1 -184

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1

V1 (1) = + 8.8 V1 (2) = - 3.48

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If: V1 = 8.8 8 = 2 V1 + 3 V2 8 = 17.6 +3 V2 -9.6 = 3 V2 V2 = -3.2 m/s

If: V1 = -348 8 = 2 V1 + 3 V2 8 = -6.96 +3 V2 14.96 = 3 V2 V2 = 4.99 m/s

Impulse:

Impulse = Force x Time = Change in Momentum

-Impulse: (of a force) is the change in momentum that it causes -Change in momentum during a collision -Measured in Ns or kg m sˉ¹

Work: -Work: Caused by a force -Depends on SIZE & DIRECTION of force and its DISPLACEMENT -Measure in Joules (J)

Work = Force x Displacement W=FxS Energy: -Cannot be done of undone -It can be trasfered or changed -Uit is Joules (J)

KE = ½ mv ² PE = mgh

Efficiency: -How much of the energy or power given out is used up

Efficiency = useful energy output ÷ total energy input Power:

Power = Work = Force x Velocity Time Electricity: I= Current: Movements of particles through spaces between atoms inside a conductor V= Voltage: Measure of energy available to move the charge around the circuit R = Resistance: The opposition of the current

AMPS A VOLTS V OHMS Ω

-Conductors: V = I change x R depending on the voltage, material of Current passing through a conductor conductor (resistivity) and the physical dimentions of the conductor

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Examples of current being used on three different conductors

-Wire kept at constant temperature -Straight line: current is directly proportional to the voltage (Ohm’s Law) IαV CONSTANT RESISTANCE

-Filament Lamp do change temperature when current pass through it -Current increases, so do the resistance -+temp = +collisions Impeding ELECTRIC FLOW INCREASING RESISTANCE

Resistance = Gradient

-Diode only allow current pass in one direction. -Change an alternating current (AC) into a direct current (DC)

-Resistivity:

ρ

Any materials’ property which performs resistance in an electric current The longer the wire, the bigger the resistance Doubling the cross-sectional area halves the resistance

R α

Length Area

R= Resistance

R =ρ L A

Since

ρ is a CONSTANT

ρ = RA L

Resistance (unit Ω) is a property of an individual component in a circuit Resistivity (unit Ω m) is a property of the material. -Current: Conduct electricity by charged particles inside conductors METALS → Negatively-charged free electrons (move from negative to positive) NON-METALS → Both positive and negatively charged ions (move in a random way)

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-Overall flow of CHARGE is the electric current -Current = rate of flow of charge -Unit of charge is COULUMB

I=Q T

Q=IxT

-Energy transfer: Charge transfers energy in a continuous way └ Energy transfer from the source to the charge └ Energy transfer from the charge to the components ELECTROMOTIVE FORCE (e.m.f.) = Total work done from source to the charge (6V battery transfers 6 J of energy to each coulomb of charge that moves on the circuit) e.m.f (symbol E), is measured in V, where 1 volt = 1 joule/Coulomb (1 J/C ˉ¹)

E=W Q

POTENTIAL DIFFERENCE (p.d.) = Work done from charge to a component Energy transferred per unit charge from he charge to the circuit p.d (symbol V) Also measured in V, where 1 volt = 1 joule/Coulomb (1 J/C ˉ¹)

V=W Q

-Electrical Power:

Power = Current x Potential difference P=IxV

P = I² x R

P = V² / R

Electric Field Strength = Volume / Distance E= V D

Change in Energy transfer = Potential difference x Current x Time E=VxIxT

Energy transferred by a current

Force = Energy x Charge F=ExQ -Resistance: IN SERIES → R = R1 + R2 + R3

→ I IS CONSTANT

IN PARALLEL →

1 =1 + 1 + 1 R R1 R2 R3

→ V IS CONSTANT

-Internal resistance (r) Energy needed to move each coulomb of charge THROUGH the cell Unit is Volts

e.m.f = terminal p.d. + p.d. across internal resistance E = V + Ir

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Kirchhoff’s laws: TOTAL CURRENT THAT ENTERS A JUCTION = TOTAL CURRENT THAT LEAVES THE JUNTION TOTAL E.M.F = SUM OF ALL POTENTIAL DIFFERENCES

-Electromagnetism: NORTH ALWAYS SEEKS THE SOUTH Any electric current in a magnetic field experiences a FORCE Determined by FLEMING’S LEFT HAND RULE Size of a force depends on: -direction if the current relative to the magnetic field -size of current -length of conductor in magnetic field -strength of magnets Force= TESLA (or B for MAGNETIC FIEL STREGHTH) x Current -Gas pressure: Particles move in a random and rapid motion Temperature increases force & frequency of collisions = Increases pressure Kelvin scale: absolute scale of temperature. Unit Kelvin (K) and relationship with Celsius scale is Temp/K = θ/ºC +273 (or absolute zero of gas)

Changing temperature involves changing internal energy in an object Thermal contact: more energy moves form HOT to COLD than vice versa ENERGY TRANSFER required to change temperature of an object depends on Temperature change Mass Material it’s made of

Energy transfer = Mass x Specific heat capacity x Change in temperature E∆ = mc ∆ θ YOU

PARTICLES

Push

Repel

Pull

Attract

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Changing an object’s phase requires energy SOLID → LIQUID →→→GAS More energy to change from liquid to gas than from solid to liquid Energy absorbed or released during phase change is LATENT HEAT.

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-Radioactive decay: Neutrons (neutral charge) + Protons (positive charge) = NUCLEI Electrons (negative charge) = orbit around the nuclei RUTHERFORD: Atoms are empty spaces with regions of positive charged regions to explain the back-scattering of alpha particles Rutherford experiment: -most alpha radiation travel straight through -little radiation is deflected -tiny number is scattered out

IN A NEUTRAL ATOM THE NUMBER OF PROTONS IS EQUAL TO THE NUMBER OF ELECTRONS Increasing or decreasing the number of neutrons creates an ISOTOPE Since it has the number of protons/electrons has the same properties of the original element

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Radiation: Unstable atom must lose or win a particle, it is radioactive Random and unpredictable process Radiation they produce = IONISING RADIATION Three main types:

ALPHA and BETA radiation changes number of protons and neutrons GAMMA radiation goes along alpha and beta, and corresponds to the nucleus losing excess energy

EXAMPLE It decays, giving out 7α + 9β What is left? 242 Pu 94

-4-4-4-4-4-4-4

=

-2-2-2-2-2-2-2

=

214 Hg 80

-0-0-0-0-0-0-0-0-0

= 214 – 0 = 214

--1--1--1--1--1--1--1--1--1

= 80 + 9 =

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242 – 28 = 214 94 – 14 =

Hg ← Mercury Isotope

80

Ac ← Actinium Isotope

89

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Half life EXAMPLE: 8 kg of Uranium Half-life= 6500 years How much left after 26000 years?

Waves: Used to transfer ENERGY Consist of vibrations or oscillations Two types:

LONGITUDINAL: Vibrations of particles are along or parallel to the direction of the wave TRANSVERSE: Vibrations are at right angles to the direction of wave travel Wavelength: Amplitude: Speed: Frequency: Period:

One complete cycle of the wave Maximum displacement of wave from mean position Speed at which the profile moves through space Number of vibrations per second, measured in Hz Time taken for a vibration to occur

Frequency =

Speed =Frequency x Wavelength Using angles on wave-graphs: complete cycle is 360掳Period v= fx位

Changing phase= NOT changing the wave itself but its position

=

1 . Period 1 . Frequency

PHASE DIFFERENCE: Difference in angles between the first and second wave from the same point

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Intensity: -How much energy is received from a wave depending on how far the source is and its power -Unit is W mˉ²

Intensity = Power Area

Area is measured at right angles to the direction of travel

-Refraction Light changes speed when it passes through a material of a different density and bends Change in velocity causes change in direction There is always some reflection coming from the point the light hits the object Change in speed is described by the REFRACTIVE INDEX = n n: ratio of the speed of light in a vacuum to the speed of light in the material, ABSOLUTE REFRACTIVE INDEX

n = Speed of light in vacuum Speed of light in material RELATIVE REFRACTIVE INDEX: Light moving from one material to another. Refractive index between two materials is the ratio of speed of light in material 1 and 2

n = Speed of light in material 1 Speed of light in material 2 Snell’s law: Relates change in direction to the change in speed that takes place in a refraction

Sin i = Speed of light in material 1 = Refractive index Sin r Speed of light in material 2 between two materials

Critical Angle:

n= 1. Sin C

Fibre Optics: Light hit boundary at angles GREATER THAN critical angle None of it goes out the fibre, has a larger RANGE More energy can be carried out May be affected by multipath dispersion: Pulses become elongated because of bends of fibre It uses digital signals ADVANTAGES: -Noise or distortion can be removed -carry MORE information than analogue

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-can be REGENERATED since it has determined values when amplified. (If you amplify a noisy analogue signal, it becomes even MORE distorted) Diffraction:

Superposition: Two or more waves cross each other They must be transferred on the same material In two-source interference: Waves crossing ON PHASE create CONSRTRUCTIVE INTERFERENCE Waves crossing OUT OF PHASE create DESTRUCTIVE INTERFERENCE

Interference of light: Same source, double slits = Give superposition of waves (of light) Bright and dark fringes are projected in a screen due to superposition Separation between fringes depends on: -separation of the slits -wavelength of light -distance between slits and screen

In a PRISM: BLUE LIGHT has a HI frequency, bends MORE RED LIGHT has a LOW frequency, bends LESS Standing waves: Doesn’t move through space, HAS STATIONARY PROFILE (Vibrating strings and vibrating air in columns in musical instruments) No flow of energy along a stationary wave Waves are exactly 180º out of phase Made by superposition of two waves of same wavelength moving on different directions

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N: NODES = Displacement of waves, always ZERO A: ANTINODES = Points were wave vibrate at max amplitude

Wavelength of stationary wave is twice the distance between two adjacent nodes or antinodes

STANDING WAVE ON GUITAR STRING

STANDING WAVE IN MUSCIAL COLUMNS

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-Prefixes and Factors: -SI units Higher numbers get more accurate results Total mass= HAS TO BE IN KG!! -Velocity has both time AND displace...

Published on May 21, 2012

-Prefixes and Factors: -SI units Higher numbers get more accurate results Total mass= HAS TO BE IN KG!! -Velocity has both time AND displace...

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