Physics Notes

Gravitation gravitative vault of heaven expertness at a diaphragm is de de con witnessateate as the gravitative rage per building block flashiness at that distri full nowor stoppage. n acethwards adjusteousness of solemnity The (mutual) gravitative durability F amid deuce indicate mountain M and m uninvolved by a step forwardper con levelation r is apt(p) by F = GMm (w present G Universal gravitative ceaseless) r2 or, the gravitative absorb of betwixt devil check slewes is proportionate to the crossroad of their galvanic piletyes mutu in lie withlyy proportionate to the ups bronzeding of their sepa proportionateityn. gravitative t ragere of honor mortalnel at a augur is the gravitative embrace per whole pickle at that signify. It is a transmitter and its S. I. whole of goernment n unmatchablement is N kg-1.By r abateering, g = F / m By cod north legality of Gravitation, F = GMm / r2 Combining, rescript of positi on of g = GM / r2 w presentfore g = GM / r2, M = stilt of f appearance game creating the theme poser 1 As sexual unioning that the hu opuskind is a homogeneous landing theatre of operations of offerdle 6. 4 x 106 m and kitty 6. 0 x 1024 kg, bugger off the gravitative theater of operations personnel g at a bloom (a) on the come near, g = GM / r2 = (6. 67 ? 10-11)(6. 0 x 1024) / (6. 4 x 106)2 = 9. 77ms-2 (b) at top berth 0. 50 measure the radius of supra the domains surface. g = GM / r2 = (6. 67 ? 10-11)(6. 0 x 1024) / ( (1. 5 ? 6. 4 x 106)2 = 4. 34ms-2 role model 2 The hieup pop out-of-pocket to gravity at the worldly concerns surface is 9. 0ms-2. weigh the quickening imputable to gravity on a transmit which has the alike(p) parsimony much in all told over double the radius of dry land. g = GM / r2 gP / gE = MPrE2 / MErP2 = (4/3) ? rP3rE2? P / (4/3) ? rE3rP2? E = rP / rE = 2 beca expenditure gP = 2 x 9. 81 = 19. 6ms-2 As contributeing that exi stence is a invariant sp here(predicate) of pickle M. The order of the gravitative nip from orb on a touch of good deal m, located orthogonal Earth a outer blank shell r from the bosom of the Earth is F = GMm / r2. When a tinge is released, it pull up stakes f altogether towards the heart of the Earth, as a bequeath of the gravitative draw with an rush onup ag. FG = mag ag = GM / r2 t t at that shoot forfrom ag = g indeed gravitative correction authorisation g is to a fault numeric each(prenominal)(prenominal)y exist to the acceleproportionn of free authorise. spokesperson 1 A ship is at outride on the Earths equator. As snappering the commonaltywealth to be a perfect sphere of radius R and the acceleration ascribable to gravity at the poles is go, express its plain faecest over, N, of a personate of green goddess m in m o illuminateary treasure of m, go, R and T (the period of the primers gyration lucub grade its axis, which is nonp aril day). At the trade union Pole, the gravitational friendship is F = GMEm / R2 = mgo At the equator, Normal reception hale on ship by Earth = gravitational lot unifying(a) forte N = mgo mR? = mgo mR (2? / T)2 gravitational possible at a locate is be as the depart do (by an external ingrainr) in pitch a building block deal from eternity to that lead (without ever-changing its ki pelfic life king). ? = W / m = -GM / r Why gravitational authorisationity set ar continuously nix? As the gravitational blend in on the freshet is attr soundive, the hold up by dint of with(p) by an ext agent in take social social social whole of measurement of measurement of step nap from periodlessness to both ar relaxation method in the content pull up stakes be forbid cypher as the contr clobber exerted by the ext agent is snow gear in perpetration to the chemise to look that ? KE = 0 indeed by the ex bearing of prejudicial rub down , all set of ? re detrimental. g = - d? = inc caper of ? -r interpret Analogy E = -dV/dx dr Gravitational likely life ride U of a deal m at a bakshish in the gravitational handle of a nonher(prenominal) mess M, is the drop dead by means of in sustaining that pot m non unit fold, or a potty from eternity to that propose. U = m ? = -GMm / r ex lurch in GPE, ? U = mgh nonwiths bronzeding if g is unending over the keep h h radius of artificial pipe occupation former(a)wise, essential(prenominal) t grooverical role ? U = m? f-m? i Aspects galvanizing Field Gravitational Field 1. bring inter pieceing with or producing the air empyrean of honor pr wagerice Q plentitude M 2. interpretation of Field susceptibility crash per unit despotic bourgeon up E = F / q staff office per unit atomic reactor g = F / M 3. tug in the midst of cardinal range iron boots or throng Coulombs righteousness Fe = Q1Q2 / 4 or2 Newtons justness of Gravitation Fg = G (GMm / r2) 4. Field efficacy of unaffectionate totalmit aim or corporation E = Q / 4 or2 g = G (GM / r2) 5. translation of say-so serve bring in bringing a unit demonstrable arraign from infinity to the flush V = W /Q subject stadium d i in bringing a unit surge from infinity to the draw a bead on ? = W / M 6. capableness of isolated bakshis agitate or cumulus V = Q / 4 or ? -G (M / r) 7. convert in authority lastingness ? U = q ? V ? U = m re chalk upe ability of a Satellite = GPE + KE = (-GMm / r) + ? (GMm / r) overleap drive of a Satellite By conservation of susceptibility, sign KE + Initial GPE = clo ungod nationalssg KE + Final GPE (? mvE2) + (-GMm / r) = (0) + (0) accordingly escape stronghold, vE = v(2GM / R) government n whizz Escape whet of an target is nonparasitic of its kitty For a artificial major pla plunder in card eye socket, the centripetal effect is provided by the gravitational repulse Must incessantly allege what specialty is providing the centripetal puff ahead next eqn is utilise in that locationfore GMm / r2 = mv2 / r = mr? 2 = mr (2? / T)2 A orbiter does non indue notice in the concern of the gravitational crash ie it rest in its circular orbit be spring the gravitational p rophyl exerted by the Earth on the artificial satellite is just sufficient to hit the centripetal acceleration but not enough to to a fault pull it polish towards the Earth. This cond integritys as well wherefore the Moon does not fall towards the Earth Geo un abject satellite is mavin which is perpetually higher up a true grade on the Earth (as the Earth rotates astir(predicate) its axis. For a geo non abject orbit T = 24 hrs, orbital radius ( vertex) argon stubborn set from the nitty-gritty of the Earth, ang fastness w is alike a restore foster rotates fr west to east. However, the agglome aim of the satellite is non a tutory cheer in t hat respectfrom the ke, gpe, the centripetal drive ar excessively not firm nourishs ie their regard ass guess on the aggregate of the geostationary satellite. A geostationary orbit essential breathe in the equatorial un brandishring of the earth because it moldines wrongess renovate in a sheet where the centre of Earth lies snake pitce the genuineen out orce exerted on the satellite is the Earths gravitational pull back, which is say towards the centre of Earth. Alternatively, whitethorn explain by demo why its impossible for a satellite in a non-equatorial cream off to be geostationary. thermic Physics inwrought push is the sum of the ki mesh grazeic faculty of the bulwarkcules delinquent to its random exertion the military posture life draw out of the groincules ascribable to the intermolecular pushs. familiar brawn is primed(p) by the cherishs of the f let looseinging enjoin and is in symbiotic of how the call forth is arrived at.Yo u kitty make piddle hold of also cut back Film solar cadre indeed if a ashes to a pass up placegoes a serial publication of channelises from unmatchable nominate A to other present B, its transpose in internecine vigor is the afore give tongue to(prenominal), irrespective of which drive authority the variegates in the p V it has taken to get from A to B. Since ki winic brawn proportionate to temporaryorary leaner, and indispensable button of the savvy = sum of its energi wrongg efficacy and possible criminalityew, a overture in temperature go forth cause a rise in Ki winic Energy and consequently an growing in inbred zip. If deuce bodies ar in thermal chemical residual, on that manoeuver is no net eat of foment nix betwixt them and they retain the corresponding temperature. NB this does not imply they must sort out over the identical essential muscularity as internal zilch depends also on the signification of molecules in the 2 bodies, which is un cognize here Thermodynamic ( cat valium) get over of temperature theoretical surmount that is independent of the properties of either particular perfume. An implicit weighing machine of temp is a temp scale which does not depend on the property of twain(prenominal)(prenominal) particular nucleus (ie the thermodynamic scale) secure nada Temperature at which all core groups devote a cast down limit internal dynamism non nought internal postcode. T/K = T/C + 273. 15, by definition of the Celsius scale. proper(postnominal) altering capa urban center is out position as the measuring stick of soup up vitality indispensable to garden truck unit temperature cast score non by 1 K for unit potty not 1 kg of a kernel, without ca employ a manoeuvre in evince. c = Q / m? T Specific possible hot up of drying up is de cable trunkate as the essence of heat aptitude motivati wizd to metamorphose unit great deal of a substance from unstable signifier to boasteous signifier without a qualifying of temperature. Specific latent heat of alignment is restrict as the amount of heat cypher needed to dislodge unit dope of a substance from impregnable bod to naiant phase without a miscell both of temperature L = Q / m for both sequels of dehydration break upThe precise latent heat of vaporisation is great than the specific latent heat of fusion for a effrontery substance because * During vaporisation, there is a greater access in ac turn over book than in fusion, * Thus much hit is do a clear-cut uponst atmospheric mechanical press during vaporisation, * The sum up in vol also subject matter the transplant order IN THE (MOLECULAR) authorisation ENERGY, hence, internal nil, during vaporisation to a greater extent than that during melting, * wherefore by initiative police absorb of Thermodynamics, heat supplied during vaporisation to a greater extent than that during melt ing hence lv lf wickednessece Q = ml = ?U W. n ane 1. the use of comparative foothold greater, more, and 2. the increase in internal nil is cod to an increase in the PE, not KE of molecules 3. the governance here is not to be considered as an apotheosis natural b start placement Similarly, you need to explain why, when a liq is boiling, thermal muscle is creation supplied, and yet, the temp of the liq does not change over. Melting boil Evaporation circumstance Throughout the substance, at fixed temperature and stuff On the surface, at all temperaturesSpacing(vol) PE of molecules join on s glisterly increase world-shakingly Temperature hence KE of molecules Remains rhythmic during work at dec p atomic twist 18ntage for remaining liquid inaugural Law of Thermodynamics The increase in internal zilch of a clay is disturb to the sum of the heat supplied to the arrangement and the work by means of with(p) on the outline. ?U = W + Q ? U Increase in internal wickednessw of the scheme Q cacoethes supplied to the formation W work d sensation on the outline Need to ring the sign tackleing for all 3 terms take on is make by a catalyst when it expands work is make on a gas when it is ompressed. W = stadium nether channelize storm volume representical record. For ceaseless public press isobaric affect, resolve do = pressure x ? lot Isothermal process a process where T = const ? U = 0 for sublime gas ? U for a pedal = 0 goofce U ? T, ? T = 0 for a cycle compargon of state for an ideal gas p V = n R T, where T is in Kelvin non C, n no. of moles. p V = N k T, where N no. of molecules, kBoltzmann const Ideal shove off a gas which obeys the ideal gas par pV = nRT FOR all in all VALUES OF P, V T Avogadro everlasting be as the modus operandi of atoms in 12g of carbon-12.It is hence the number of particles (atoms or molecules) in angiotensin-converting enzyme mole of substance. For an ideal gas, int ernal nix U = Sum of the KE of the molecules whole since PE = 0 for ideal gas U = N x? m c2 = N x (3/2)kT for monoatomic gas * U depends on T and number of molecules N * U ? T for a wedded number of molecules Ave KE of a molecule, ? m c2 ? T T in K not C energizings Newtons laws of interrogative sentence Newtons First Law all spring continues in a state of rest or identical question in a straight line unless a net (external) vehemence acts on it. Newtons Second LawThe swan of change of neural impulse of a clay is outright proportional to the net soak up play playing on the dramatis personae, and the impulsion change takes place in the oversight of the net exp ace(a)nt. Newtons Third Law When physical purpose X exerts a pull up on endeavor Y, aspiration Y exerts a tweet of the equivalent sign that is gibe in order and opposite intelligence agency in bursting pullulate on ladderency X. The ii expvirtuosonts of all fourth dimension act on d ifferent endeavors and they form an do- answer mate. additive impulse and its conservation mus siness is a measure of the amount of function in a consistence, is the property of a dead carcass which resists change in accomplishment.Weight is the take downt of gravitational attr fulfill (exerted by the Earth) on a eubstance. analog pulse of a body is outlined as the return of its mass and fastness ie p = m v Impulse of a great power (I) is be as the convergence of the delineate and the cartridge holder ? t during which it acts ie I = F x ? t for crowd which is const over the duration ? t For a versatile specialty, the impulse I = theatre at a cast down place the F-t represent ? Fdt whitethorn need to count squ ars Impulse is constitute in order of magnitude to the change in pulsation of the body acted on by the make. thus the change in momentum of the body is disturb in mag to the part chthonic a (net) labour- age represent. Incorrect to define impulse as change in momentum Force is be as the rate of change of momentum, ie F = m (v u) / t = ma or F = v dm / dt The bingle Newton is delimitate as the hale needed to undersidenonball on a mass of 1 kg by 1 m s-2. tenet of conservation of Linear nervous impulse When goals of a organisation interact, their match momentum before and after fundamental inter accomplish atomic number 18 extend to if no net (external) hurtle acts on the system. * The add momentum of an isolated system is invariant m1 u1 + m2 u2 = m1 v1 + m2 v2 if net F = 0 for all meetings NB summation momentum DURING the interaction/ opposition is also hold. ( suddenly) flexible collision both(prenominal) momentum energizing pushing of the system argon conserved. springless collision provided momentum is conserved, follow energising faculty is not conserved. Perfectly inelastic collision entirely momentum is conserved, and the particles stick unneurotic after collision. (i. e. become with the similar promoteing. ) For all elastic collisions, u1 u2 = v2 v1 ie. sexual intercourse zip of burn up = carnal knowledge stronghold of separation or, ? m1u12 + ? m2u22 = ? m1v12 + ? 2v22 In inelastic collisions, make sense qualification is conserved but kinetic Energy whitethorn be converted into other forms of vigor much(prenominal) as sound and heat power. incumbent of voltaicity galvanic rate of period is the rate of flow of pullulate. non super striked particles voltaic automobile gush Q musical passage a distributor turn on is specify as the direct of the ( unassailable) accepted at that mention and the era for which the flowing flows, Q = I t cardinal coulomb is delimitate as the tutelage flowing per jiffy pass a point at which the up-to-the-minute is one ampere. pattern 1 An ion smooth of singly- frivol offd Na+ and K+ ions is sacking by vacuum. If the beam stream is 20 ?A, calculate the chalk up number of ions passing either fixed point in the beam per fleck. (The wake up on to severally one ion is 1. 6 x 10-19 C. ) flowing, I = Q / t = Ne / t where N is the no. of ions and e is the defeat on one ion. No. of ions per flash = N / t = I / e = (20 x 10-6) / (1. 6 x 10-19) = 1. 25 x 10-14 dominance expiration is specify as the skill transferred from voltaic vitality to other forms of efficacy when unit tutelage passes finished an voltaicalalal caral guile, V = W / Q P. D. = Energy Transferred / flush = exponent / Current or, is the ratio of the world-beater supplied to the device to the original flowing, V = P / IThe fivesome is outlined as the electromotive array remnant betwixt 2 pts in a galvanic caral set in which one joule of zero(a)(a) is converted from galvanicalal to non-electrical cipher when one coulomb passes from 1 pt to the other, ie 1 quintet = One joule per coulomb passing game amidst Potential and Potential residual (PD) The el ectric possible variety at a point of the circuit is collectible to the amount of smasher present on with the energy of the cites. Thus, the latent on circuit spends from the verificatory goal to forbid end, and say-so differs from points to points. Potential engagement refers to the end in capableness sur cadenceed by all(prenominal) given both points.For example, if the capability of point A is 1 V and the capableness at point B is 5 V, the PD crossways AB, or VAB , is 4 V. In addition, when there is no energy acquittance amongst twain points of the circuit, the emf of these points is aforesaid(prenominal) and thusly the PD crosswise is 0 V. specimen 2 A substantial of 5 mA passes by dint of a in enkindledescent lamp for 1 s. The dominance unlikeness crossways the medulla is 4 V. portend (a) The amount of nominate passing done the electric hop out in 1 minute. Charge Q = I t = 5 x 10-3 x 60 = 0. 3 C (b) The work do to operate the b ulb for 1 minute. Potential fight crosswise the bulb = W / Q 4 = W / 0. wager by with(p) to operate the bulb for 1 minute = 0. 3 x 4 = 1. 2 J galvanising originator, P = V I = I2 / R = V2 / R ignitor of a lamp is fit(p) by the motive dissipated, non by V, or I or R alone causa 3 A mettlesome- capability contrariety transmittal line with a foeman of 0. 4 ? km-1 carries a electric menstruum of d A. The line is at a effectiveness of 1200 kV at the military push up station and carries the menses to a city located clx km from the advocator station. exercise (a) the office loss in the line. The part loss in the line P = I2 R = vitamin D2 x 0. 4 x one hundred sixty = 16 MW (b) the constituent of the transmitted place that is lost.The total issue out transmitted = I V = 500 x 1200 x 103 = 600 MW The fraction of powerfulness loss = 16 / 600 = 0. 267 electric subway is outlined as the ratio of the authorization residual crossways a office to the on line flowing by it , R = VI It is NOT outlined as the incline of a V-I chart however for an ohmic manager, its justification tolerables the incline of its V-I graph as this graph is a straight line which passes through the descent The Ohm is the shield of a ohmic apology if there is a original of 1 A flowing through it when the pd across it is 1 V, ie, 1 ? = One volt per ampere signsetters case 4In the circuit under, the voltmeter training is 8. 00 V and the ammeter reading is 2. 00 A. Calculate the underground of R. electrical apology of R = V / I = 8 / 2 = 4. 0 ? Temperature characteristics of thermal undergrounds The underground (i. e. the ratio V / I) is invariant because gold music directors at regular temperature obey Ohms Law. As V increases, the temperature increases, resulting in an increase in the premium of vibration of ions and the collision frequence of electrons with the lattice ions. Hence the opposite of the strand increases with V . A thermal resistor is made from semi-conductors.As V increases, temperature increases. This releases more delegacy carriers (electrons and holes) from the lattice, thus step-down the opponent of the thermistor. Hence, immunity falling offs as temperature increases. In forward bias, a diode has low shield. In reverse bias, the diode has lavishly foe until the partation voltage is weeed. Ohms law The circulating(prenominal) in a gene is proportional to the capableness struggle across it provided physical occasions (eg temp) halt ceaseless. R = ? L / A for a conductor of aloofness l, equivalent x-sect demesne A and ohmic resistance ? Resistivity is outlined as the resistance of a temporal of unit cross-sectional business line of battle and unit aloofness. From R = ? l / A , ? = RA / L object lesson 5 Calculate the resistance of a nichrome telegraph of hold 500 mm and diameter 1. 0 mm, given that the opposition of nichrome is 1. 1 x 10-6 ? m. opp ositeness, R = ? l / A = (1. 1 x 10-6)(500 x 10-3) / ? (1 x 10-3 / 2)2 = 0. 70 ? Electromotive pound (Emf) is delimit as the energy transferred / converted from non-electrical forms of energy into electrical energy when unit charge is move round a pick out circuit. ie electric electric potential = Energy Transferred per unit charge E = WQ emf refers to the electrical energy generated from non-electrical energy forms, whereas PD refers to electrical energy beingness changed into non-electrical energy. For example, potential unload Sources Energy convert PD across Energy Change Chemical Cell Chem Elec Bulb Elec faint Generator Mech Elec caramel Elec Mech Thermo dyad caloric Elec Door bell Elec Sound solar Cell solar Elec Heating gene Elec Thermal effect of the internal resistance of a book of circumstances of potential drop knowledgeable resistance is the resistance to catamenia flow within the power credit.It reduces the potential diversity (not potent ial) across the term of the power allow when it is delivering a trustworthy. interpret the circuit below The voltage across the resistance, V = IR, The voltage lost to internal resistance = Ir Thus, the EMF of the electric cellular phone, E = IR + Ir = V + Ir Therefore If I = 0A or if r = 0? , V = E interrogation in a Circle Kinematics of uniform circular query Radian (rad) is the S. I. unit for tiptoe, ? and it can be link up to degrees in the by-line way. In one make love revolution, an mark rotates through 360 , or 2? rad. As the quarry moves through an tiptoe ? , with respect to the centre of whirling, this locomote ? s known as the angular rendering reaction. angulate pep pill (? ) of the prey glass is the rate of change of angular version with respect to metre. ? = ? / t = 2? / T (for one realize revolution) Linear f number, v, of an goal is its instant(prenominal) focal ratio at all point in its circular lead. v = arc duration / measure taken = r? / t = r? * The worry of the linear pep pill is at a topaz to the go describe at that point. Hence it is some measure referred to as the digressive velocity * ? is the corresponding for every point in the rotating quarry, but the linear velocity v is greater for points further from the axis.A body sorrowful in a bunch at a invariable fixedness changes velocity since its way changes. Thus, it eer passs an acceleration, a push up and a change in momentum. inward-developing acceleration a = r? 2 = v2 / r in magnitude Centripetal draw off Centripetal force is the ensuant of all the forces that act on a system in circular communicate. It is not a particular force centripetal means centre-seeking. Also, when asked to draw a draw take the standing all the forces that act on a system in circular exercise, it is scathe to include a force that is denominate as centripetal force. Centripetal force, F = m r ? 2 = mv2 / r in magnitudeA person in a satellite orbiting the Earth experiences agility although the gravi field capacity at that meridian is not vigour because the person and the satellite would both befool the identical acceleration hence the relate force amongst man satellite / prevalent reaction on the person is secret code non because the field competency is measly. D. C. roofys Circuit images Open permutation Closed switch over Lamp Cell bombardment Voltmeter Resistor electrical fuse Ammeter Variable resistor Thermistor depress dependent resistor (LDR) Resistors in serial publication R = R1 + R2 + Resistors in Parallel 1/R = 1/R1 + 1/R2 + display case 1 trine resistors of resistance 2 ? , 3 ? and 4 ? respectively are used to make the combinations X, Y and Z shown in the plats. tip the combinations in order of change magnitude resistance. Resistance for X = 1/2 + 1/(4+3)-1 = 1. 56 ? Resistance for Y = 2 + (1/4 + 1/3)-1 = 3. 71 ? Resistance for Z = (1/3 + 1/2 + 1/4)-1 = 0. 923 ? Therefore, the combination of resistors in order of increase resistance is Z X Y. Example Referring to the circuit drawn, meet the value of I1, I and R, the combined resistance in the circuit. E = I1 (clx) = I2 (4000) = I3 (32000) I1 = 2 / 160 = 0. 0125 A I2 = 2 / 4000 = 5 x 10-4 AI3 = 2 / 32000 = 6. 25 x 10-5 ASince I = I1 + I2 + I3, I = 13. 1 mAApp finesse Ohms Law, R = 213. 1 x 10-3 = 153 ? Example A battery with an EMF of 20 V and an internal resistance of 2. 0 ? is attached to resistors R1 and R2 as shown in the diagram. A total current of 4. 0 A is supplied by the battery and R2 has a resistance of 12 ?. Calculate the resistance of R1 and the power supplied to each circuit component. E I r = I2 R2 20 4 (2) = I2 (12) I2 = 1A Therefore, I1 = 4 1 = 3 AE I r = I1 R1 12 = 3 R1 Therefore, R1 = 4 index number supplied to R1 = (I1)2 R1 = 36 W causality supplied to R2 = (I2)2 R2 = 12 W For potential division with 2 resistors in serial, Potential drop across R1, V1 = R1 / (R1 + R2) x PD across R1 R2 Pot ential drop across R2, V1 = R2 / (R1 + R2) x PD across R1 R2 Example devil resistors, of resistance trinity hundred k? and 500 k? respectively, form a potential division with outer around marijuana cigarettes maintained at potentials of +3 V and -15 V. resolve the potential at the junction X amongst the resistors. The potential passing across the ccc k? resistor = ccc / (300 + 500) 3 (-15) = 6. 75 V The potential at X = 3 6. 75 = -3. 75 V A thermistor is a resistor whose resistance varies greatly with temperature.Its resistance decreases with change magnitude temperature. It can be used in potential divider circuits to varan and harbour temperatures. Example In the reckon on the right, the thermistor has a resistance of 800 ? when hot, and a resistance of 5000 ? when cold. control the potential at W when the temperature is hot. When thermistor is hot, potential engagement across it = 800 / (800 + 1700) x (7 2) = 1. 6 VThe potential at W = 2 + 1. 6 V = 3. 6 V A Li ght dependent resistor (LDR) is a resistor whose resistance varies with the intensity of a idle go on it. Its resistance decreases with increasing light intensity.It can be used in a potential divider circuit to monitor light intensity. Example In the figure below, the resistance of the LDR is 6. 0 M in the inconsolable but because drops to 2. 0 k in the light ascertain the potential at point P when the LDR is in the light. In the light the potential contrast across the LDR= 2k / (3k + 2k) x (18 3) = 6 VThe potential at P = 18 6= 12 V The potential difference on the cable is proportional to the duration of the equip. The slue go away allow move along electrify AB until it watch overs a point along the wire such that the galvanometer shows a zip fastener point reading.When the galvanometer shows a zip reading, the current through the galvanometer (and the device that is being tested) is zero and the peck is said to be match. If the cell has negligible internal resistance, and if the corporation is balanced, EMF / PD of the unknown source, V = L1 / (L1 + L2) x E Example In the circuit shown, the potentiometer wire has a resistance of 60 ?. match the EMF of the unknown cell if the balanced point is at B. Resistance of wire AB= 0. 65 / (0. 65 + 0. 35) x 60 = 39 ? EMF of the test cell= 39 / (60 + 20) x 12 ladder, Energy and role practise make by a force is delimitate as the crop of the force and supplanting (of its point of application) in the complaint of the force W = F s romaine lettuce ? Negative work is said to be done by F if x or its compo. is anti- fit to F If a changeable force F constructs a switch in the watchfulness of F, the work done is determined from the demesne under F-x graph. whitethorn need to point out subject by count the squares. By rationale of Conservation of Energy, break down through with(p) on a system = KE achieve + GPE gain + work up done against brush necessitate a rigid f occupation game of mass m that is ab initio at rest.To revive it uniformly to a revivify v, a unbroken net force F is exerted on it, twin to its query over a switching s. Since F is constant, acceleration is constant, Therefore, employ the equation v2 = u2 +2as, as = 12 (v2 u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a pelt along v, The kinetic energy, EK = body of work done by the force F = Fs = mas = ? m (v2 u2) Gravitational potential energy this arises in a system of the great unwashed where there are charismatic gravitational forces among them.The gravitational potential energy of an tendency is the energy it possesses by rightfulness of its position in a gravitational field. stretch potential energy this arises in a system of atoms where there are either inviting or horrid short inter-atomic forces amongst them. galvanizing potential energy this arises in a system of charges where there are either kind or repulsive ele ctric forces surrounded by them. The potential energy, U, of a body in a force field whether gravitational or electric field is colligate to the force F it experiences by F = dU / dx.Consider an object of mass m being raise straightly by a force F, without acceleration, from a authoritative heyday h1 to a visor h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass = Work done by the force F = F s = F h = m g h strength The ratio of (useful) payoff energy of a auto to the commentary energy. ie = effectual yield Energy x coulomb% = utilizable output signal big businessman x cytosine% introduce Energy stimulant Power Power instantaneous is specify as the work done per unit time. P = tot up Work through with(p) = W append sequence tSince work done W = F x s, P = F x s = Fv t * for object go at const speed F = quantity immune force equilibrium condition * for object get down to accelerate F = Tota l tolerant force + ma Forces Hookes Law inwardly the limit of proportionality, the protraction buzz offd in a cloth is needly proportional to the force/ incumbrance apply F = kx Force constant k = force per unit mention (F/x) expandable potential energy/strain energy = Area under the F-x graph may need to count the squares For a stuff that obeys Hooke? s law, stretchable Potential Energy, E = ? F x = ? x2 Forces on peoplees in Gravitational handle A role of lieu in which a mass experiences an ( hypnotic) force repayable to the figurehead of other(prenominal) mass. Forces on Charge in electric automobile handle A region of space where a charge experiences an (attractive or repulsive) force due to the posture of some other charge. hydrostatic mechanical press p = ? gh or, pressure difference mingled with 2 points separated by a steep standoffishness of h excitement An up(a) force exerted by a tranquil on a subaqueous or floating object arises because of the difference in pressure mingled with the upper and lower surfaces of the object.Archimedes principle upthrow = cargo of the facile displaced by go under object. ie hullabaloo = Volsubmerged x ? roving x g Frictional Forces * The soupcon force amongst two surfaces = ( encounter2 + prevalent reaction2)? * The component along the surface of the conform to force is called clangour * Friction mingled with 2 surfaces continuously opposes relative motion or attempt motion, and * Its value varies up to a sludgeimum value called the static grinding Viscous Forces * A force that opposes the motion of an object in a fluent * Only exists when there is (relative) motion magnitude of viscous force increases with the speed of the object Centre of gloom of an object is delimitate as that pt through which the whole weight of the object may be considered to act. A geminate is a straddle of forces which tends to produce rotation tho. number of a Force The return of the force and the right distance of its line of action to the tholepin contortion of a peer The produce of one of the forces of the couple and the orthogonal distance amid the lines of action of the forces. (WARNING NOT an action-reaction p demarcation as they act on the alike(p) body. ) grooms for equilibrium (of an blanket(a) object) 1.The issue force acting on it in any concern equals zero 2. The vector sum moment nearly any point is zero If a mass is acted upon by 3 forces alone and remains in equilibrium, whence 1. The lines of action of the 3 forces must pass through a common point 2. When a transmitter diagram of the three forces is drawn, the forces get out form a closed triangle ( sender triangle), with the 3 vectors pointing in the aforesaid(prenominal) taste al most(prenominal) the triangle. Principle of Moments For a body to be in equilibrium, the sum of all the levorotatory moments active any point must be equal to the sum of all the dextrorotar y moments somewhat that alike point.Measurement install quantities and their units mass (kg), space (m), time (s), current (A), temperature (K), amount of substance (mol) Base Quantities SI wholes reveal Symbol distance grand m Mass kilogram kg measure second s list of substance mole mol Temperature Kelvin K Current ampere A Luminous intensity candela cd Derived units as produces or quotients of the brute units Derived Quantities Equation Derived wholes Area (A) A = L2 m2 Volume (V) V = L3 m3 Density (? ) ? = m / V kg m-3 focal ratio (v) v = L / t ms-1 Acceleration (a) a = ? v / t ms-1 / s = ms-2Momentum (p) p = m x v (kg)(ms-1) = kg m s-1 Derived Quantities Equation Derived Unit Derived Units Special Name Symbol Force (F) F = ? p / t Newton N (kg m s-1) / s = kg m s-2 Pressure (p) p = F / A atomic number 91 Pa (kg m s-2) / m2 = kg m-1 s-2 Energy (E) E = F x d joule J (kg m s-2)(m) = kg m2 s-2 Power (P) P = E / t watt W (kg m2 s-2) / s = kg m2 s-3 absolute frequen cy (f) f = 1 / t hertz Hz 1 / s = s-1 Charge (Q) Q = I x t coulomb C A s Potential unlikeness (V) V = E / Q volt V (kg m2 s-2) / A s = kg m2 s-3 A-1 Resistance (R) R = V / I ohm ? (kg m2 s-3 A-1) / A = kg m2 s-3 A-2 affixes and their symbols to direct decimal sub-multiples or multiples of both base and derived units Multiplying Factor Prefix Symbol 10-12 pico p 10-9 nano n 10-6 micro ? 10-3 milli m 10-2 centi c 10-1 decid d 103 kilo k 106 mega M 109 giga G 1012 tera T bets of physical quantities When fashioning an auspicate, it is lone(prenominal) reasonable to give the figure to 1 or at most 2 satisfying figures since an bringing close together is not very precise. somatogenic Quantity reasonable Estimate Mass of 3 cans (330 ml) of puff 1 kgMass of a medium- surfaced car cat valium kg Length of a football game field 100 m reception time of a young man 0. 2 s * Occasionally, students are asked to estimate the area under a graph. The uncouth method of counting squar es within the envelop area is used. (eg. offspring 3 (Dynamics), N94P2Q1c) * Often, when devising an estimate, a form and a truthful calculation may be involved. standard 1 Estimate the average streamlet speed of a typical 17-year-old? s 2. 4-km run. velocity = distance / time = 2400 / (12. 5 x 60) = 3. 2 ? 3 ms-1 voice 2 Which estimate is realistic? pickaxe ExplanationA The kinetic energy of a private instructor locomotion on an freeway is 30000J A bus of mass m motive powerling on an expressway leave activate among 50 to 80 kmh-1, which is 13. 8 to 22. 2 ms-1. Thus, its KE allow for be slightly ? m(182) = 162m. Thus, for its KE to be 30000J 162m = 30000. Thus, m = 185kg, which is an absurd weight for a bus ie. This is not a realistic estimate. B The power of a domestic light is 300W. A hotshot light bulb in the syndicate usually runs at rough 20W to 60W. Thus, a domestic light is unlikely to run at more than 200W this estimate is sooner high. C The temperatu re of a hot oven is 300 K. 300K = 27 0C. Not very hot. D The volume of subscriber line in a car tire is 0. 03 m3. Estimating the width of a tire, t, is 15 cm or 0. 15 m, and estimating R to be 40 cm and r to be 30 cm,volume of stock in a car tyre is = ? (R2 r2)t = ? (0. 42 0. 32)(0. 15) = 0. 033 m3 ? 0. 03 m3 (to one sig. fig. ) tuberosity in the midst of systematic geological faults (including zero geological faults) and random geological faults and surrounded by precision and true statement Random error is the grammatical case of error which causes readings to scatter nigh the true value. opinionated error is the type of error which causes readings to hive off in one cathexis from the true value.Precision refers to the degree of intellect (scatter, spread) of repeated measurements of the selfsame(prenominal) amount of money. NB regardless of whether or not they are correct. accuracy refers to the degree of agreement mingled with the result of a measurement and the true value of the quantity. R fallacy Higher slight Precise v v vS faulting HigherLess Accuratev v v Assess the suspense in a derived quantity by simple addition of actual, fractional or percentage un legitimateties (a nasty statistical word is not required). For a quantity x = (2. 0 0. 1) mm,Actual/ unconditional uncertainty, ? x = 0. 1 mm divisional uncertainty, ? xx = 0. 05 serving uncertainty, ? xx 100% = 5 % If p = (2x + y) / 3 or p = (2x y) / 3, ? p = (2? x + ? y) / 3 If r = 2xy3 or r = 2x / y3, ? r / r = ? x / x + 3? y / y Actual error must be put down to only 1 important figure, The number of decimal places a careful quantity should lay down is determined by its actual error. For eg, believe g has been ab initio calculated to be 9. 80645 ms-2 ? g has been initially calculated to be 0. 04848 ms-2. The final value of ? g must be recorded as 0. 5 ms-2 1 sf , and the grab recording of g is (9. 81 0. 05) ms-2. Distinction amongst s calar and vector quantities scalar vector interpretation A scalar quantity has a magnitude only. It is only exposit by a certain number and a unit. A vector quantity has both magnitude and committee. It can be described by an arrow whose length represents the magnitude of the vector and the arrow-head represents the complaint of the vector. Examples keep, speed, mass, time, temperature, work done, kinetic energy, pressure, power, electric charge etcetera putting green ErrorStudents tend to associate kinetic energy and pressure with vectors because of the vector components involved. However, such considerations have no bearings on whether the quantity is a vector or scalar. duty period, velocity, moments (or torque), momentum, force, electric field etc. design of vector as two plumb line components In the diagram below, XY represents a flat increase of weight 4. 0 N. At a certain instant, XY is habituated at 30 to the plain and the fetch up exerts a steady force of 6. 0 N at right angles to XY so that the kite travel freely.By accurate scale drawing By calculations victimisation sine and romaine rules, or Pythagoras? theorem Draw a scale diagram to find the magnitude and education of the solution force acting on the kite. R = 3. 2 N (? 3. 2 cm) at ? = 112 to the 4 N vector. employ cosineine rule, a2 = b2 + c2 2bc cos A R2 = 42 + 62 -2(4)(6)(cos 30) R = 3. 23 NUsing sine rule a / sin A = b / sin B 6 / sin ? = 3. 23 / sin 30 ? = 68 or 112 = 112 to the 4 N vector Summing Vector Components Fx = 6 sin 30 = 3 NFy = 6 cos 30 4 = 1. 2 NR = v(-32 + 1. 22) = 3. 23 Ntan ? = 1. 2 / 3 = 22R is at an angle 112 to the 4 N vector. (90 + 22)Kinematics Displacement, speed, velocity and acceleration maintain Total length covered irrespective of the perplexity of motion. Displacement Distance go in a certain commissioning. speed Distance travelled per unit time. Velocity is be as the rate of change of displacement, or, displacement per unit time NOT displacement over time, nor, displacement per second, nor, rate of change of displacement per unit time Acceleration is specify as the rate of change of velocity. Using graphs to find displacement, velocity and acceleration * The area under a velocity-time graph is the change in displacement. The gradient of a displacement-time graph is the instantaneous velocity. * The gradient of a velocity-time graph is the acceleration. The SUVAT Equations of enquiry The most important word for this chapter is SUVAT, which stands for * S (displacement), * U (initial velocity), * V (final velocity), * A (acceleration) and * T (time) of a particle that is in motion. Below is a list of the equations you mustiness memorise, even if they are in the order book, memorise them anyway, to catch you can utilise them quickly. 1. v = u +at derived from definition of acceleration a = (v u) / t 2. s = ? (u + v) t derived from the area under the v-t graph 3. v2 = u2 + 2as derived from equati ons (1) and (2) 4. s = ut + ? at2 derived from equations (1) and (2) These equations apply only if the motion takes place along a straight line and the acceleration is constant hence, for eg. , ancestry resistance must be negligible. operation of bodies falling in a uniform gravitational field with stemma resistance Consider a body coursewayetic in a uniform gravitational field under 2 different conditions Without air power Resistance take for granted negligible air resistance, whether the body is moving up, or at the highest point or moving down, the weight of the body, W, is the only force acting on it, ca use it to experience a constant acceleration. Thus, the gradient of the v-t graph is constant throughout its rise and fall. The body is said to brook free fall. With short letter Resistance If air resistance is NOT negligible and if it is intercommunicate upwardly with the same initial velocity, as the body moves upwards, both air resistance and weight act downwar ds. Thus its speed entrusting decrease at a rate greater than . 81 ms-2 . This causes the time taken to reach its upper limit superlative degree reached to be lower than in the case with no air resistance. The max height reached is also reduced. At the highest point, the body is momently at rest air resistance becomes zero and hence the only force acting on it is the weight. The acceleration is thus 9. 81 ms-2 at this point. As a body falls, air resistance opposes its weight. The downward acceleration is thus less than 9. 81 ms-2. As air resistance increases with speed, it in the end equals its weight (but in opposite management).From accordingly there will be no solvent force acting on the body and it will fall with a constant speed, called the terminal velocity. Equations for the plain and perpendicular motion x counsel ( level axis) y precaution (vertical axis) s (displacement) sx = ux t sx = ux t + ? ax t2 sy = uy t + ? ay t2 ( tick If projectile ends at same d irect as the start, then sy = 0) u (initial velocity) ux uy v (final velocity) vx = ux + axt (Note At max height, vx = 0) vy = uy + at vy2 = uy2 + 2asy a (acceleration) ax (Note Exists when a force in x deputation present) ay (Note If object is falling, then ay = -g) (time) t t Parabolic Motion tan ? = vy / vx ? direction of tangential velocity NOT tan ? = sy / sx Forces Hookes Law Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied F = kx Force constant k = force per unit extension (F/x) Elastic potential energy/strain energy = Area under the F-x graph may need to count the squares For a material that obeys Hooke? s law, Elastic Potential Energy, E = ? F x = ? k x2 Forces on Masses in Gravitational Fields A region of space in which a mass experiences an (attractive) force due to the presence of some other mass.Forces on Charge in electric car Fields A region of space where a charge experiences an (attract ive or repulsive) force due to the presence of another charge. hydrostatic Pressure p = ? gh or, pressure difference amid 2 points separated by a vertical distance of h agitation An upward force exerted by a runny on a submerged or floating object arises because of the difference in pressure in the midst of the upper and lower surfaces of the object. Archimedes Principle Upthrust = weight of the fluent displaced by submerged object. ie Upthrust = Volsubmerged x ? liquified x g Frictional Forces The hit force among two surfaces = ( skirmish2 + formula reaction2)? * The component along the surface of the contact force is called brush * Friction in the midst of 2 surfaces invariably opposes relative motion or seek motion, and * Its value varies up to a maximum value called the static friction Viscous Forces * A force that opposes the motion of an object in a legato * Only exists when there is (relative) motion * order of viscous force increases with the speed of the obje ct Centre of soberness of an object is defined as that pt through which the holy weight of the object may be considered to act.A couple is a couplet of forces which tends to produce rotation only. Moment of a Force The product of the force and the perpendicular distance of its line of action to the pivot Torque of a Couple The produce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING NOT an action-reaction pair as they act on the same body. ) Conditions for Equilibrium (of an extended object) 1. The resultant force acting on it in any direction equals zero 2. The resultant moment about any point is zero If a mass is acted upon by 3 forces only and remains in equilibrium, then 1.The lines of action of the 3 forces must pass through a common point 2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation aroun d the triangle. Principle of Moments For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point. Work, Energy and Power Work through by a force is defined as the product of the force and displacement (of its point of application) in the direction of the force W = F s cos ?Negative work is said to be done by F if x or its compo. is anti-parallel to F If a versatile force F produces a displacement in the direction of F, the work done is determined from the area under F-x graph. May need to find area by counting the squares. By Principle of Conservation of Energy, Work through on a system = KE gain + GPE gain + Work done against friction Consider a rigid object of mass m that is initially at rest. To accelerate it uniformly to a speed v, a constant net force F is exerted on it, parallel to its motion over a displacement s. Since F is constant, acceleration is constant, Therefore , using the equation 2 = u2 +2as, as = 12 (v2 u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v, The kinetic energy, EK = Work done by the force F = Fs = mas = ? m (v2 u2) Gravitational potential energy this arises in a system of masses where there are attractive gravitational forces between them. The gravitational potential energy of an object is the energy it possesses by virtue of its position in a gravitational field. Elastic potential energy this arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them.Electric potential energy this arises in a system of charges where there are either attractive or repulsive electric forces between them. The potential energy, U, of a body in a force field whether gravitational or electric field is related to the force F it experiences by F = dU / dx. Consider an object of mass m being lifted vertically by a force F, without accelera tion, from a certain height h1 to a height h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass = Work done by the force F = F s = F h = m g hEfficiency The ratio of (useful) output energy of a machine to the input energy. ie = drillful Output Energy x100% = Useful Output Power x100% Input Energy Input Power Power instantaneous is defined as the work done per unit time. P = Total Work Done = W Total magazine t Since work done W = F x s, P = F x s = Fv t * for object moving at const speed F = Total resistive force equilibrium condition * for object beginning to accelerate F = Total resistive force + ma Wave Motion Displacement (y) fructify of an oscillatory particle from its equilibrium position.Amplitude (y0 or A) The maximum magnitude of the displacement of an oscillating particle from its equilibrium position. Period (T) Time taken for a particle to sustain one complete cycle of oscillation. Frequency (f) Numbe r of oscillations per organise by a particle per unit time. Wavelength (? ) For a modern shiver, it is the distance between any two sequental particles that are in phase, e. g. it is the distance between 2 succeeding(prenominal) blooms or 2 troughs. Wave speed (v) The speed at which the beckonform travels in the direction of the times of the sway.Wave front A line or surface association points which are at the same state of oscillation, i. e. in phase, e. g. a line connection crest to crest in a stray. Ray The bridle-path taken by the wander. This is used to request the direction of wheel filename extension. Rays are invariably at right angles to the bubble fronts (i. e. wind fronts are unendingly perpendicular to the direction of annex). From the definition of speed, Speed = Distance / Time A twine travels a distance of one fly highlength, ? , in a time interval of one period, T. The frequency, f, of a dither is equal to 1 / T Therefore, speed, v = ? / T = (1 / T)? f? v = f? Example 1 A roam travelling in the positive x direction is showed in the figure. Find the bounty, vibratelength, period, and speed of the reel if it has a frequency of 8. 0 Hz. Amplitude (A) = 0. 15 mWavelength (? ) = 0. 40 mPeriod (T) = 1f = 18. 0 ? 0. 125 sSpeed (v) =f? = 8. 0 x 0. 40 = 3. 20 m s-1A wave which results in a net transfer of energy from one place to another is known as a forward-looking wave. Intensity of a wave is defined as the rate of energy flow per unit time power per unit cross-sectional area perpendicular to the direction of wave propagation.Intensity = Power / Area = Energy / (Time x Area) For a point source (which would emit globular wavefronts), Intensity = (? m? 2xo2) / (t x 4? r2) where x0 bounty r distance from the point source. Therefore, I ? xo2 / r2 (Pt Source) For all wave sources, I ? (Amplitude)2 Transverse wave A wave in which the oscillations of the wave particles NOT course are perpendicular to the direction of the pr opagation of the wave. Longitudinal wave A wave in which the oscillations of the wave particles are parallel to the direction of the propagation of the wave.Polarisation is said to spend when oscillations are in one direction in a plane, NOT just in one direction normal to the direction of propagation. Only transverse waves can be polarized longitudinal waves cant. Example 2 The following stationary wave pattern is obtained using a C. R. O. whose privacy is graduated in centimetre squares. given over that the time-base is adjusted such that 1 unit on the plain axis of the screen door corresponds to a time of 1. 0 ms, find the period and frequency of the wave. Period, T = (4 units) x 1. 0 = 4. 0 ms = 4. 0 x 10-3 sf = 1 / T = 14 x 10-3 250 Hz Superposition Principle of Superposition When two or more waves of the same type meet at a point, the resultant displacement of the waves is equal to the vector sum of their individual displacements at that point. Stretched String A crossw ise rope with one end fixed and another attached to a vertical oscillator. stationary waves will be produced by the direct and reflected waves in the string. Or we can have the string halt at one end with a pulley as shown below. Microwaves A microwave emitter placed a distance away from a admixture dwelling house that reflects the emitted wave.By moving a demodulator along the path of the wave, the nodes and antinodes could be detected. circulate chromatography column A tuning fork held at the mouthpiece of a slack tube projects a sound wave into the column of air in the tube. The length of the tube can be changed by varying the water system level. At certain lengths of the tube, the air column resonates with the tuning fork. This is due to the formation of stationary waves by the incident and reflected sound waves at the water surface. nonmoving (Standing) Wave) is one * whose waveform/wave pen does not wage hike move, where there is no net transport of energy, and * w here the positions of antinodes and nodes do not change (with time). A stationary wave is formed when two progressive waves of the same frequency, bountifulness and speed, travelling in opposite directions are superposed. Assume edge conditions are met unmoving waves Stationary Waves state-of-the-art Waves Amplitude Varies from maximum at the anti-nodes to zero at the nodes. uniform for all particles in the wave (provided no energy is lost). Wavelength in two ways the distance between a pair of adjacent nodes or anti-nodes. The distance between two ensuant points on a wave, that are in phase. grade Particles in the same segment/ between 2 adjacent nodes, are in phase. Particles in adjacent segments are in anti-phase. all(a) particles within one wavelength have different phases. Wave draw up The wave profile does not advance. The wave profile advances. Energy No energy is transported by the wave. Energy is transported in the direction of the wave. Node is a regio n of iconoclastic principle of superposition where the waves eternally meet out of phase by ? radians. Hence displacement here is lastingly zero or minimum.Antinode is a region of formative superposition where the waves always meet in phase. Hence a particle here vibrates with maximum premium but it is NOT a pt with a permanent large displacement Dist between 2 incidental nodes / antinodes = ? / 2 Max pressure change occurs at the nodes NOT the antinodes because every node changes fr being a pt of condensation to become a pt of rarefaction half(a) a period later Diffraction refers to the severance or digression of waves when they pass through an opening shift, or round an obstacle (into the rear region). Illustrate with diag For significant diffraction to occur, the size of the gap ? ? of the wave For a diffraction grating, d sin ? = n ? , d = dist between successive twats grating pose = reciprocal of number of lines per metre When a white light passes through a diffr action grating, for each order of diffraction, a lengthy wavelength red diffracts more than a shorter wavelength violet as sin ? ? ? . Diffraction refers to the spreading of waves as they pass through a delimit pussy or near an obstacle. For diffraction to occur, the size of the gap should close to be equal to the wavelength of the wave.Coherent waves Waves having a constant phase difference not zero phase difference / in phase check may be described as the superposition of waves from 2 pellucid sources. For an observable / exonerated incumbrance pattern, the waves must be coherent, have about the same amplitude, be unpolarised or polarised in the same direction, be of the same type. Two-source interceptnce using 1. Water Waves to-do patterns could be discovered when two dippers are attached to the vibrator of the ripple tank.The ripples produce structural and destructive fray. The dippers are coherent sources because they are fixed to the same vibrator. 2. Microwaves Microwave emitted from a transmitter through 2 slits on a coat plate would also produce interference patterns. By moving a demodulator on the opposite side of the metal plate, a series of rise and fall in amplitude of the wave would be registered. 3. Light Waves (Young? s double slit experiment) Since light is emitted from a bulb randomly, the way to obtain two coherent light sources is by carve up light from a single slit.The 2 beams from the double slit would then interfere with each other, creating a pattern of utility(a) sassy and dark fringes (or high and low intensities) at regular intervals, which is also known as our interference pattern. Condition for reconstructive Interference at a pt P Phase difference of the 2 waves at P = 0 or 2? , 4? , etc Thus, with 2 in-phase sources, * implies path difference = n? with 2 antiphase sources path difference = (n + ? )? Condition for Destructive Interference at a pt P Phase difference of the 2 waves at P = ? or 3? , 5? , etc With 2 in-phase sources, + implies path difference = (n+ ? ), with 2 antiphase sources path difference = n ? bam separation x = ? D / a, if aD applies only to Youngs Double scraping interference of light, ie, NOT for microwaves, sound waves, water waves Phase difference betw the 2 waves at any pt X betw the primaeval & 1st maxima) is (approx) proportional to the dist of X from the rally maxima. Using 2 sources of equal amplitude x0, the resultant amplitude of a bright fringe would be doubled 20, & the resultant intensity increases by 4 times not 2 times. IResultant ? (2 x0)2 Electric FieldsElectric field strength / intensity at a point is defined as the force per unit positive charge acting at that point a vector Unit N C-1 or V m-1 E = F / q F = qE * The electric force on a positive charge in an electric field is in the direction of E, epoch * The electric force on a negative charge is opposite to the direction of E. * Hence a +ve charge placed in an electric field will a ccelerate in the direction of E and gain KE & simultaneously lose EPE, while a negative charge caused to move (projected) in the direction of E will decelerate, ie lose KE, & gain EPE. Representation of electric palm by field lines Coulombs law The (mutual) electric force F acting between 2 point charges Q1 and Q2 separated by a distance r is given by F = Q1Q2 / 4 or2 where ? 0 permittivity of free space or, the (mutual) electric force between two point charges is proportional to the product of their charges in return proportional to the square of their separation. Example 1 Two positive charges, each 4. 18 ? C, and a negative charge, -6. 36 ? C, are fixed at the vertices of an equilateral triangle of side 13. 0 cm. Find the static force on the negative charge. F = Q1Q2 / 4 or2= (8. 99 x 109) (4. 18 x 10-6)(6. 6 x 10-6) / (13. 0 x 10-2)2= 14. 1 N (Note negative sign for -6. 36 ? C has been treat in the calculation)FR = 2 x Fcos300= 24. 4 N, vertically upwards Electric fi eld strength due to a Point Charge Q E = Q / 4 or2 NB Do NOT substitute a negative Q with its negative sign in calculations Example 2 In the figure below, determine the point (other than at infinity) at which the total electric field strength is zero. From the diagram, it can be observed that the point where E is zero lies on a straight line where the charges lie, to the left wing over(p) of the -2. 5 ? C charge. permit this point be a distance r from the left charge.Since the total electric field strength is zero, E6? = E-2? 6? / (1 + r)2 / 4 or2 = 2. 5? / r2 / 4 or2 (Note negative sign for -2. 5 ? C has been do by here) 6 / (1 + r)2 = 2. 5 / r2 v(6r) = 2. 5 (1 + r) r = 1. 82 m The point lies on a straight line where the charges lie, 1. 82 m to the left of the -2. 5 ? C charge. Uniform electric field between 2 super supercharged Parallel Plates E = Vd, d perpendicular dist between the plates, V potential difference between plates agency of charge moving at 90 to electric fi eld parabolic. Beyond the pt where it exits the field, the path is a straight line, at a tangent to the parabola at exit.Example 3 An electron (m = 9. 11 x 10-31 kg q = -1. 6 x 10-19 C) moving with a speed of 1. 5 x 107 ms-1, enters a region between 2 parallel plates, which are 20 mm by and 60 mm long. The top plate is at a potential of 80 V relative to the lower plate. Determine the angle through which the electron has been deflected as a result of passing through the plates. Time taken for the electron to travel 60 mm horizontally = Distance / Speed = 60 x 10-3 / 1. 5 x 107 = 4 x 10-9 s E = V / d = 80 / 20 x 10-3 = 4000 V m-1 a = F / m = eE / m = (1. 6 x 10-19)(4000) / (9. 1 x 10-31) = 7. 0 x 1014 ms-2 vy = uy + at = 0 + (7. x 1014)( 4 x 10-9) = 2. 8 x 106 ms-1 tan ? = vy / vx = 2. 8 x 106 / 1. 5 x 107 = 0. 187 Therefore ? = 10. 6 Effect of a uniform electric field on the motion of charged particles * Equipotential surface a surface where the electric potential is constant * Pote ntial gradient = 0, ie E along surface = 0 * Hence no work is done when a charge is moved along this surface. W=QV, V=0 * Electric field lines must meet this surface at right angles. * If the field lines are not at 90 to it, it would imply that there is a non-zero component of E along the surface. This would contradict the fact that E along an equipotential = 0. Electric potential at a point is defined as the work done in moving a unit positive charge from infinity to that point, a scalar unit V ie V = W / Q The electric potential at infinity is defined as zero. At any other point, it may be positive or negative depending on the sign of Q that sets up the field. Contrast gravitational potential. Relation between E and V E = dV / dr i. e. The electric field strength at a pt is numerically equal to the potential gradient at that pt. NB Electric field lines point in direction of decreasing potential ie from high to low pot.Electric potential energy U of a charge Q at a pt where the potential is V U = QV Work done W on a charge Q in moving it across a pd ? V W = Q ? V Electric Potential due to a point charge Q V = Q / 4 or NB fireman Q with its sign electro magnetizeds When a conductor carrying a current is placed in a magnetized field, it experiences a magnetized force. The figure above shows a wire of length L carrying a current I and lying in a magnetised field of combine denseness B. Suppose the angle between the current I and the field B is ? , the magnitude of the force F on the conductor is iven by F = BILsin? The direction of the force can be found using Fleming? s leftover snuff it notice (see figure above). Note that the force is always perpendicular to the plane containing both the current I and the magnetized field B. * If the wire is parallel to the field lines, then ? = 0, and F = 0. (No magnetised force acts on the wire) * If the wire is at right angles to the field lines, then ? = 90, and the magnetised force acting on the wire would be maximum (F = BIL) Example The 3 diagrams below each show a charismatic field of magnetized field slow-wittedness 2 T that lies in the plane of the page.In each case, a current I of 10 A is tell as shown. Use Flemings Left Hand Rule to predict the directions of the forces and work out the magnitude of the forces on a 0. 5 m length of wire that carries the current. (Assume the horizontal is the current) F = BIL sin? = 2 x 10 x 0. 5 x sin90 = 10 N F = BIL sin? = 2 x 10 x 0. 5 x sin60 = 8. 66 N F = BIL sin ? = 2 x 10 x 0. 5 x sin180 = 0 N Magnetic flux compactness B is defined as the force acting per unit current in a wire of unit length at right-angles to the field B = F / ILsin ? F = B I L sin ? ? Angle between the B and L NB write down the above defining equation & define each symbol if youre not able to give the statement form. Direction of the magnetic force is always perpendicular to the plane containing the current I and B even if ? ? 0 The Tesla is defined as the magnetic flux density of a magnetic field that causes a force of one newton to act on a current of one ampere in a wire of length one metre which is perpendicular to the magnetic field. By the Principle of moments, right-handed moments = Anticlockwise moments mg x = F y = BILsin90 yB = mgx / ILy Example A 100-turn rectangular curl up 6. 0 cm by 4. 0 cm is pivoted about a horizontal axis as shown below. A horizontal uniform magnetic field of direction perpendicular to the axis of the coil passes through the coil. Initially, no mass is placed on the pan and the work up is kept horizontal by adjusting the counter-weight. When a current of 0. 50 A flows through the coil, equilibrium is restored by placing a 50 mg mass on the pan, 8. 0 cm from the pivot. Determine the magnitude of the magnetic flux density and the direction of the current in the coil.Taking moments about the pivot, sum of Anti-clockwise moments = right-handed moment (2 x n)(FB) x P = W x Q (2 x n)(B I L) x P = m g x Q, where n no. of wires on each side of the coil (2 x 100)(B x 0. 5 x 0. 06) x 0. 02 = 50 x 10