PhysicsAndMathsTutor.com 1

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1 PhysisAndMathsTutor.om. (a (i beam splitter [or semi-silvered mirror] (ii a ompensator [or a glass blok] allows for the thikness of the (semi-silvered mirror to obtain equal optial path lengths in the two branhes of the apparatus 3 (b (i onentri rings an interferene pattern [alt: whole view shows one shade beause there is a onstant phase differene] (ii fringes [or rings] shift 5 extra for l gives one omplete fringe shift [or fration of wavelength extra auses notieable fringe shift or notieable hange of intensity (if uniform] 4 ( (i rotate apparatus through 9 observe the fringes at the same time observed fringes did not hange [or shift] (ii speed of light in free spae is invariant [or does not depend on motion of soure or observer or no evidene for absolute motion] max 3 []. (a (i l = (t =. 5 9 =.5m (ii l l (..5 = l (3. l. 5 =.59 m

2 PhysisAndMathsTutor.om (b (i m = m or m (. (3. m m =.6m (. (3. [or = or.77 7 kg] kineti energy = (m m [or =.6m or (3 ] = 9. (J (ii total k.e. = ( 7 9. = 9. 5 (J 5 9. k.e. per seond 9 = 6W max 5 5 [] 3. (a no hange in the fringe pattern on rotation the speed of light is the same in the two diretions the speed of light from a light soure on Earth is unaffeted by the motion of the Earth [or the speed of light is invariant or independent of the motion of the soure or observer] the laws of dynamis annot be applied to light no ether max 3 (b (i distane 6Toneyear time = yr speed. (ii L = 6 [or 6 light years] L L = 6(. (=.6 6= 9.6

3 PhysisAndMathsTutor.om 3 (iii t = years t =t = (. =.6 = yr age = + = 33 yr 6 [9] 4. (a (i speed of light (in free spae independent of motion of soure and of motion of observer [alternative (i speed of light is same in all frames of referene ] (ii laws of physis have same form in all inertial frames inertial frame is one in whih Newton s st law of motion obeyed laws of physis unhanged in oordinate transformation from one inertial frame of referene to any other inertial frame max 4 (b (i m m =. 7 kg =. ( (.996 (ii t =. 6 s t t =. 6 (.996 (s =.46 5 (s s(= t = = 736 m

4 PhysisAndMathsTutor.om 4 [alternative (ii 6 l t = 657 (m orret substitution of l in l = l l 657 l =.996 l = 736 m 6 [] 5. (a as speed, mass infinite gain of E k auses large gain of mass when speed is lose to gain of E k auses small gain of speed when speed is lose to E k = ½mv valid at speeds << max 3 QWC (b (i E k = ev =.6 9. (= 3.3(6 9 J (ii (use of m = E k gives gain of mass = 3.7 (kg (3 3.7 = m 7 = m.67 mass of proton = m +m (=3 m 6 9 (using E k = gives gain of mass = 3. 6 (kg 3 m mass of proton = 4 m 4 ( 3 = v v 3 /.99 v =.999 =.99(7 m s 3 [] 6. (a (i (use of v = d gives v = 4 t 6.4 =.(6 m s (ii atual length = 4 m

5 PhysisAndMathsTutor.om 5 (use of v l l / gives /.6 length in partile frame, l = 4 3 (allow C.E. for value of v l = (4.3 = 7(.5 m 4 (b time between two events depends on speed of observer / [or v t t or roket time depends on speed of traveller] traveller s journey time is the proper time between start and stop [or t is the proper time or t is the time on Earth] journey time measured on Earth > journey time measured by traveller [or t > t or roket time slower/less than Earth time] traveller younger than twin on return to Earth 4 [] (i v =.96 m s 5 9 (ii t = 5 ns v t 5 / /.96 = 5 3. = 5 ns QWC [4]

6 PhysisAndMathsTutor.om 6. (a (i two beams (or rays reah the observer interferene takes plae between the two beams bright fringe formed if/where (optial path differene = whole number of wavelengths (or two beams in phase [or dark fringe formed if/where (optial path differene = whole number +.5 wavelengths] (or two beams out of phase by C/ / /½ yle (ii rotation by 9 realigns beams relative to diretion of Earth s motion no shift means no hange in optial path differene between the two beams ( time taken by light to travel to eah mirror unhanged by rotation distane to mirrors is unhanged by rotation ( no shift means that the speed of light is unaffeted [or disproves other theory] max 5 (b the speed of light does not depend on the motion of the light soure or that of the observer [7] 9. (a Newton s laws obeyed in an inertial frame [or inertial frames move at onstant veloity relative to eah other] suitable example (e.g. objet moving at onstant veloity / (b (i (use of t = t gives t = (ns t = 9 (.995 =. 7 s /

7 PhysisAndMathsTutor.om 7 (ii time taken distane = s speed time taken = half-lives, whih is time to derease to 5% intensity / [alternative sheme: (use of l = l v gives l = (m / (.995 l = =. m time taken. = 3.6 s.995 = half-lives, whih is time to derease to 5% intensity ] 5 [7]. (i E k (= ev (= =. (J (.76 (J (ii (use of E = m gives m =. (3 7 =. m 7.m =. 7 (kg.67 (allow C.E. for value of E k from (i, but not 3rd mark m = m + m (=. m / (iii (use of m = m v gives.m = v / =. =.7 m s 7 / [7]

8 PhysisAndMathsTutor.om. (a (i t = (s (use of t = t v gives t = (.994 =73 s (ii distane (=.994t = =. m (. m (allow C.E. for value of t from (i 4 (b spae twin s travel time = proper time (or t time on Earth, t = t v t> t [or time for traveller slows down ompared with Earth twin] spae twin ages less than Earth twin travelling in non-inertial frame of referene max 3 / [7] v. (a m = m v gives =. =.99 v (=.995 =.9(5 m s 3 v (b m = m m infinity as v [or m inreases as v inreases] E k (= m m infinity as v v = would require infinite E k (or mass whih is (physially impossible Max 3 [6] 3. (i time taken dis tane 34 speed (9 s

9 PhysisAndMathsTutor.om 9 (ii use of t = t ( v / / where t = ns and t is the half-life in the detetors frame of referene 9 9 t 57(.6 s / (.95 time taken for π meson to pass from one detetor to the other = half-lives (approx (in the detetors' frame of referene half-lives orrespond to a redution to 5%, so 75% of the π mesons passing the first detetor do not reah the seond detetor alternatives for first 3 marks in (ii. use of t = t ( v /, where t = ns = 57.6(ns (.95 / journey time in detetor frame (= t = 57.6ns ( half-lives. use of t = t ( v / where t = 9 ns = journey time in detetor frame t =37ns journey time in rest frame = ns ( half-lives [5] 4. (a (i speed of light in free spae independent of motion of soure and of motion of observer (ii laws of physis have the same form in all inertial frames inertial frame is one in whih Newton s st law of motion is obeyed laws of physis unhanged in oordinate transformation from one inertial frame to another max 4

10 PhysisAndMathsTutor.om (b (i m (= m ( v / / =.9 (.995 / (kg =.9 7 kg (ii E (= m =.9 7 (3. =.7 J (iii E K (= E m =.7 (.9 (3. =.5 J 6 []