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MECHANICS - 6 LECTURES                              

Instantaneous: speed at certain moment of time Relative stuff, constant v’s then sub diff into v=d/t If acc. Then sub to t2=2x/a N1: rest/const. v unless F acted upon N2: ext. F gives acc  to F (F=ma) N3: F comes in pairs, = + opp, act on 1-another Normal force: opp. Weight F In circ: const. s, v changing cos acc (to centre) Cent. F incl, fric, normal-banked road, tension etc COM: where entire mass appears to act Fric: opp motion, depend on nature of surface As v  atmos fric , when =, @ terminal v Fd=Fd, for opp moments-law of lever L1: load, fulcrum, effort L2: effort, load, fulcrum- F multiplier, ankle L3: load, effort, fulcrum- v multiplier, elbow Work: transfer of E =Fd, unit J, Power: work/time, P=Fv Efficiency: work out/ work in, hot water>soapy water, Pbubble=4/r P when bubble small, if 2 connect air smallbig Capillarity: balance of cohesive and adhesive F between liquid + pore/tube, if co less, -ve menisus Cont. eqtn: consvn of mass, A1v1=A2v2 (vvelocity) Bernoulli: P1+1/2pv2+pgh1=P2+1/2pv2+pgh2 P-absolute, conservation of energy Torricelli’s: speed of efflux v= 2g(hsurface-h0) Viscosity: velocity depends of d from wall of pipe Strain rate=velocity/pipe length Shear-stress/strain-rate=(F/A)/(v/L)=n n is viscosity Hot water less viscos than cold water Use Poiseulle’s law for laminar/viscos flow in pipe Re=PvL/n, Re3000-turbulent Free diffusion: slow, due to random thermal motion, high conclow conc, ave d is xrms Flow slow as random, large distance, small displac As more go to low conc, prob of 1 going back Osmosis: semi perm membrane, water goes from low solute to high solute, height on 1 side, more P on taller side-stops water going to other side

THERMODYNAMICS – 5 LECTURES   

Thermal eqlbm: final temp when 2 things combine Heat: energy which goes from one thing to another Thermal energy: not in process of transfer

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Higher temp doesn’t always mean highr thermal E As temp , atoms faster + spread apart, L=L0T,  depends on material Ideal Gas law: PV=NkT=nRT (N-atom, n-mol)(T in K) Partial Pressures: PV=N1kT+N2kT, P=P1+P2, P1/2 are P they would have if occupied entire space Temp: ave thermal E per molecule, Thermal E (U): U=3/2NkT=3/2nRT- monoatomic gas Real Gas: PV=nRT fails when in liquid/solid form Phase change region: liquid and vapour coexist, p determined by Tsaturated vapour P Phase change: use Q=mL Q+ve when E added Specific heat: use Q=mcT, c always +ve Dew point: temp when condensation occurs Moisture content: mass of moist per kg dry air MC found w IGL and n=m/M, ma/mw=0.621Pw/Pa Dry bulb: normal air temp Wet bulb: temp when moist evaporated so rh 100% and energy has been removed from air At 100%rh dry bulb=wet bulb Conduction: S,L,G exchange thermal E without changing mean pos – slow, good conductors have loose outer e- Q/t=hcondAT (A is area) Convection: L,G one media moving fluid – more rapid Q/t=hconvAT Radiation: no medium needed, e-mag radiation Q/t=hradAT (between 2 surfaces, don’t exactly= In humans: U=Q-W+E, E from food Work efficiency: n=W/(E-U) U -ve if work done when E=0 = weight loss Work efficiency law: E-U=W/n, Q=W+U-E

ELECTRICITY- 5 LECTURES 

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Electric F: binds nuclei + e- to form atoms, atoms to form molecules and molecules to form matter Static electricity: like repel, opp attract, unit for charge is coulombC, charge is conserved Charge quantised (comes in packages), only multiples of qe (=1.6x10^-19C) Rubbing to insulators transfers e-, 1 +ve other -ve Conductors: have moving charged particles Insulators: charge can’t move freely Polarisation: separation of charge

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Coulombs law:

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|q 1|∨q 2∨ ¿2 r

(r d between charges)

F=k ¿   

F from many charges: calc the 2 F then add vectors Electric Field: has value for each point is space Test charge: what we are interested in, can work out F w Coulombs law, Source charges: produce F on test, F=qE, units NC^-1

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Electric field due to point:

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Arrows point opposite to where e- would go If 2+ source, calc EF due to each source, sum result Electric Potential: electrostatic F conservative, PE only depend on start + end points, symbol V unit V V=U/q, only interested in diff, EF is -gradient V=-EFx Capacitance: charge transferred/PD,C bySA/d Parallel plate capacitor: large SA + close C=E(A/d), E permittivity of insulator (how easy to polarise) Energy Storage: U=1/2CV^2 Adding Capacitors: P: C=1+2+3, Q=1+2+3, V=1=2=3 S: 1/C=1/C1 + 1/C2…, Q=1=2=3, V=1+2+3 Current: I=Q/t,(charge/t),convention opp to real Ohms law: V=IR, good conductors have small R Current: like flow via pipe, PD: pressure diff, Resistance: how long/skinny pipe is R depends on geometry: R=P(L/A), a is area In series: Rt=1+2+3, V=1+2+3, I same Parallel: 1/R=1/R1+1/R2…, V same I=1+2+3 P=E/t=VI, in resistors- P=I^2R E shocks: 4 things determine how dangerous: 1. amount of I 2. path taken via body 3. Duration 4. frequency (DC more dangerous than AC) Charging Capacitor: q=qf(1-e(-t/T)) Discharging capacitor: q=q0e(-t/T) T=RC -q/t=-q/(RC), q charge and C current

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OPTICS - 5 LECTURES

k ∨Q∨ ¿2 r |E|=¿

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Visible light from 400-700nm, f=c/ c=3x10^8m/s Reflective screens rough on  scale, light goes all d Refraction: bending of light cos media change N=c/v, v velocity in media, n refractive index Light slows when not going through vac or air Reflection; i=r, if source d >2m basically parallel N1sin1=n2sin2 – Snell’s law In water can see wider angle above due to refract Total internal refraction:c=sin^-1(n2-n1), 2out 1in Ray diagrams: trace path of light, replace pic w arrow, optical axis; through centre of lens/mirror, focus:F Converging/convex: focused on point Diverging/concave: rays diverge (looks like its from 1 point) f: flocal length, d from lens to focal point, in m P: optical power, =1/f, measured in diopters D 3 rays: 1. Top, refracts, through 2nd focal point 2. Either from top, focal point, refracts (para/below optical axis) or focus, top of object, refracts (para/above optical axis) 3. Top, middle of lens (no refraction), stays linear Real: rays converge where image seen Virtual: rays appear to converge on other side of lens (same side as viewer), need lens to see do, from object to lens is +ve di from lens to real is +ve, if to virtual then -ve converge: f +ve, diverge f -ve, h from head to tail of arrow Thin lens: 1/di+1/do=1/f=P, -d=concave Magnification: =hi/ho=-(di/do) m1 larger, -ve then inverted image Mirrors either plane or spherical (latter ‘cave or ‘vex), image always virtual, spherical: f=R/2 (r radius, C centre of curvature) D from object to mirror +ve, so is mirror to real image, d from virtual to mirror +ve, height from head to tail of arrow ‘cave: f. P, C +ve, ‘Vex: f, p C -ve, mirror eqtn: 1/di+1/d0=1/f Cornea and lens work together to achieve refraction, light focuses on retina-acts like screen, lens can adjust focal lengthaccommodation. Di(lens to retina) about 2cm, 0.02m Near point: closest point objects can be seen clearly When object very distant do=m 1/=0 Myopia: shortsighted, can’t see far objects clearly, image focuses before retina, has ‘far-point’, eye too long or cornea too curved- use diverging lens to compensate of over converge Hypermetropia longsighted, can’t see close objects clearly, image focused beyond retina, common in kids-small eyes, use converging lens to compensate for under converging Presbyopia: occurs w ageing, near point gets further away, due to lack of elasticity in lens Astigmatism: lens lumpy (2 parts have diff focal points), some directions more blurry than others, diff parts of lens focus on diff parts of retina n=/n, -in vac, n-another media, n-refractive index Diffraction: bending of wave around edges of opening, opening must be small relative to  Double slit: get light, dark, light, dark pattern (light in phase/constructive, dark out/destructive) Single slit: get bell curve of lightness (brighter in centre) m=Dsin (m=1,2 etc), sin=/D, y=L/D, D size of slit,  angle to where we are measuring, y distance along screen to where we are measuring Circular arpiture: sin=1.22(/D) Resolving P: limit to ability of instrument to make distinct images of close objects, determined by diffraction patterns of lens and arpitures of instrument m=1.22(/D), D needs to be big to see large objects  in rads S=r Blue light has smallest , best resolution

RADIATION AND HEALTH- 5 LECTURES     

Ground State: tightly bound, lowest E (E comes in chunks) e- gain E w photon, up E levels, e- emit photon if going down Photons: E=hf, h Plancks constant, p=E/C, p=h/ Ionisation E: binding E of e-, determined by atom and e- orbital Electron Volt: measure of E, 1eV=1.602x10^-19J

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v of proton found w E in J

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Bohr’s theory of H atom: ang momentum quantised, E of orbitls Z2 En= 2 E 0 Z for H=1, E’s -ve, takes E to unbind e-

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v =√ (

2E ) m

n

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Coulomb attraction  w Z, E Z dependant

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Most nef for n=1, states labelled by n, principle quantum no. E0=13.6eV (E to ionise H), applies to H like atoms w 1 e of emitted photon given by E=hc/, v=p/m (for v of e-) Atomic no.: Z, no protons, Atomic mass: A, protons and neutron Nucleon: proton/neutron, Nuclide: nucleus, Isotopes: same atom, diff no. neutrons, Isotones: same neutrons, diff protons isobars: same no. nucleons, diff protons, isomers: =protons +neutrons, diff E states AMU: 1amu=1.66x10^-27kg, convert to E w E=mc^2 Strong Nuc F: between P+N, like glue, only affects near particles Binding E: mass of components>mass of atom, diff mass deficit Nuc like drop of liquid, need E (latent heat) to break apart atom must loose E when put together, E atom< E parts binding E =  stable atom,  to iron, then  w large radius Stability Diagram: N against P, large nuclei have more N to overcome e-static repulsion from P Fusion: joining small nuclei, larger + more stable atom made Fission: breaking of big Nuclei smaller nuclei mass no. >56 Decay: unstableless unstable nucleus, random but can determine probability + work out no. which should’ve decayed Radiation: Z may change (ie change in element), Z>82 all r-actve Alpha: He nuclei, +ve charge, lots of Ek, slowed rapidly with collisions, strong ionisers and heavy Beta: e- or positrons, (latter antiparticle of former) -ve or +ve Low mass + loose E quickly, NP get B-(and antineutrino), PN get B+(and neutrino), MN same AN changes by 1 Gamma: photons, high E +frequency, AN or AM don’t change, state of excitation of nuc does change e- capture: reverse beta decay, e- captured by nuc N-no. atoms, A: nuclear activity (formulae on sheet) A units Bq=2.7x10^-11Ci (Ci curie, 3.7x10^10 decays per sec (dps) ½ life: =0.693/ =decay constant

−0.693 t t 0.5 N=N 0 e ¿

), can sub in

A for that if needed Bremsstrahlung: (breaking) e- decel, give off E as photons, max photon E=Ek gained by e- from acc potnl used-Ek goes to photn Generation of Xrays: EF ionizes gas, +ve ions accanode + free e-, eacc in EF near cathode, hot glass face of tube + generate Xrays, v and I independent in Crooke’s tube V: rays more penetrating, more atoms ionized, more rays generated so intensity  Heated filament: emits e-, EF acc e-, e- strike anode + generate rays, heat generated @ target, beam intensity and v independent Max E of ray determined by tube V, 1000V=>1000eV Range:  shortest, then ,  most penetrating (if have same E Attenuation: exponential process Interaction w matter: : chonky, interact more often + make more ionization but don’t go far, dangerous to bio tisc if close :small + light, collisions produce big changes in d and velocity Both create same no ion pairs but over diff distances X+ radiation: most interaction w orbiting e-, completely absorb photon E, partial absorbing-new lower E photon traveling in diff d, ionization of atoms + freeing of orbital e- -create new particls Higher atomic no tend to be more attenuating X+ interaction w matter: Pelectric effect: photon completely absorbed by e-, get free e- and ion, depends on e- binding E PEE in Xray: ray absorbed, expels photo e-, outer e- drops into vacant orbital + emits Xray in process Crompton effect: photon acts like particle(like 2 billiard balls collide)E and p conserved, incoming photon loses E, changes  + direction Pair production: high E ray photons spontaneously convert into epositron pair, E conserved into matter + anti matter Biological Effect: Pertermistic; cells killed-reduces organ function Stochastic: cell don’t die, gets mutation (ie cancer), 1st treatment blood transfusion,  dangerous as dumps all in 1 place Absorbed dose: in Gy (1 gy=1Jkg^-1=100rad, D=E/m, E: E lost from beam, m: mass of material into which E absorbed Dose equivalent: DE< does in terms of biological effect, relative biological effectiveness RBE=1 for y X +B 0.03MeV, =2.5 thermal neutrons (...