By MissCutielicious
Chapter 1 1.1.1 Momentum [ST] Answers 1)a) 5.4 x 10 7 kg m s -1 b) 4750 kg m s-1 2)a) If the batsman only changed the ball’s direction ery slightly! this is a smaller moment"m change than in the #orked exam$le! so less force #o"ld be needed. b) If the ball is ret"rned back in the direction of the bo#ler! this #o"ld be a greater greater moment"m change than in the #orked exam$le! so more force #o"ld be needed. %) &&00 ' 4) a)1025 ' s b) (he airbag takes a longer time to remoe the $assenger’s moment"m. (his means that it a$$lies less force to the $assenger! red"cing in"ry. 5) a) *ass + 1.15 kg ,1
b) ∆ p + p + 5.50 or 5.74 kg m s ' s c) F c) F + + 45 or 47 ' de$ending on ∆ p aboe/ p aboe/ d) andle mass#eight head #eightforce exerted by "ser handle) neglected e) ∆t goes goes "$ ∆ p goes p goes "$ ⇒ less force less force , , less effectie less effectiemore more force! force! more effectie more effectie
1.1.2 Collisions [ST] Answers 1) 0.0%1 m s -1 2)a) 0.2 m s -1 b) 100 ' %) In order to moe for#ard! the boy m"st ex$erience a force from the boat. (here is an e"al and o$$osite force from him onto the boat #hich moes the boat back#ards a#ay from him. 4)a) 3insert art#ork as $er belo# , note that at the bottom right of this $ic! all arro#heads meet #hich is #hy it looks a bit r"bbish/
$total + 14%0 kg m s -1 after + + 4.77 m s -1 b) t#aterfall + %7 s t bank + 4 s so they #o"ld land safely on the rierbank. 5) a) mass elocity 3ords or defined symbols6 '( ft / b) iii c) ii! or i and ii.8ine 2 9 1: 2 d) 'o net) external forcesno frictiondrag. 8ine iii. he ass"mes the force exerted by the other trolley is the res"ltant force) e) ;"itable collision described and s$ecific e"i$ment to meas"re elocities 3e.g. light gates/. *eas"re elocities before and after collision.
1.1.3 Energy in collisions [ST] Answers 1)a) %.%5 m s -1 b) 7.1% > -1% 2)a) .7% x 10 > b) 5 4&0 000 e? c) 5.4& *e? %) 'on-contact collisions are al#ays elastic! and no external forces act.
1.1.4 Real collisions [ST] Answers 1) 0.4&@ of the s$eed of light6 1.% x 10 & m s-1 2) It ends "$ in the other corner $ocket! moing at 4.24 m s -1 at 45A to the original line.
1.2.1 Angular dislacement [ST] Answers 1) 720 A b) π5 rad6 0.&% rad -1 2) %.4& rad s b) 4.71 rad s-1 c) .2 rad s -1 %) 1. rad s -1 4) ω + 7.27 x 10-5 rad s -16 + 4&5 m s -1 5)a) %&.& cm b) (he error is $ro$ortionately the same
1.2.2 Centrietal !orce [ST] Answers 1) 25%0 ' 2)a) 2.54 ' b) + 7%& ' m"ch smaller) c) Bt the $ole! the reaction force #o"ld be 7%& '6 at the e"ator! it #o"ld be 7%% '
1.2.3 All t"e !un o! t"e !air [ST] Answers 1)a) estimates in range 500 , 1500 kg b) estimates in range 10 , %0 m c) e.g. 1000 kg : 20 m gies + 1.1 m s -1
Chapter 2
2.1.1 Electric !ields [ST] Answers 1) 4. x 10 -17 ' 2) 000 ? m -1 %) 4. x 10 11m s-2 4)a) 1 x 10 5 ? m-1 c) D%000 ?
b) 1.&2 x 107 m s-1 0?
d) Bcceleration is in the o$$osite direction beca"se the $roton’s charge is the o$$osite sign to an electron6 and the acceleration is less as the $roton mass is greater than an electron’s.
2.1.2 #ni!orm and radial !ields [ST] Answers 1) 'et field + Cero! so the net force + Cero. 2) 3insert a#! as $er fig 2.1.& sketch of t#o $l"s charges! exce$t this one sho"ld be t#o min"s charges. (he lines sha$e is identical! b"t all arro#s m"st be reersed./ %)a) &00 ? b) 'o difference 4) =harge concentrates near $oints or s$ikes. 5) 5.1% x 10 11 ? m-1
2.1.3 Coulom$%s &aw [ST] Answers 1) 2.12 x 10 -& ' 2)a) 1.14 x 10 17 ? m-1 b) 0.0%&4 ' %) (he meas"rements for r m"st be taken to the centres of the s$heres. Bn error here #o"ld lead to a dis$arity in the res"lts! com$ared #ith =o"lomb’s 8a#. 4) Bns#ers of the order of 10 -& m
2.1.4 'inding t"e electronic c"arge [ST] Answers a) 'egatie b) q E / e l e c t r i c f o r c e
m g / g r a v i t a t i o n a l fo r c e / w e i g h t
c) 2 x 10 5 ? m ,1 39 ' c ,1/ d) 4. x 10 ,1E = e) %
2.2.1 Storing c"arge [ST] Answers 1) 0.02 F 2)a) 0.0 = %) %.& x 10 -% > 4) 4.& x 10 -4 s
b) the charge #ill be shared so each ca$acitor #ill be 4?
2.2.2 C"arging and disc"arging caacitors [ST] Answers 1) %0 s 2) 1.%4 = %)a) 0.00&&E B b) bet#een 50 and 55 seconds c) decrease the resistance or the ca$acitance 4) Gra$h sho"ld sho# ex$onential decay from I0 + & x 10 -4 B to I 2secs + 0.11 x 10 -4 B6 τ + 0.5 s 5) a) 0.12 = b) %&0 > c) 150 H d) 0.00%0 s e) (ime is longer beca"se the rate of discharge decreases c"rrent decreases #ith time
2.3.1 Magnetic !ields [ST] Answers 1) It is "sed to find the direction of a force on a c"rrent-carrying cond"ctor in a magnetic field. (he th"mb of the left hand indicates the direction of the force! #hen the first finger is lined "$ #ith the magnetic field and the second finger lined "$ #ith the c"rrent! and fingers and th"mb all held at right angles to each other in three dimensions. 2)a) do#n b) into $age c) no force %)Bdantage (he motor $o#er can be altered for different a$$lications. disadantage It is more com$lex so there is more o$$ort"nity to break.
2.3.2 T"e strengt" o! electromagnetic !orces [ST] Answers 1)a) 4. x 10 -& ' b) 4 x 10-21 ' c) %.1 x 10 10 m s-1 #hich is faster than the s$eed of light 2) I + Jt and + lt6 F + KJ + KJlt + KIl %) r 'a2% + 0.0127 m6 r 'a22 + 0.0124 m (his difference of 0.% mm can easily be disting"ished by the machine.
2.3.3 (enerating electricity [ST] Answers 1) 1.&5 x 10 -% b t"rns 2)a) (he emf has a $"lse in one direction! follo#ed by a briefer! larger $"lse in the o$$osite direction. b) (he c"rrent moes in one direction! then dro$s to Cero before a higher c"rrent moes in the o$$osite direction. %) 0.14 ? (he ind"ced c"rrent ca"ses a magnetic field #hich tends to try and sto$ the coil t"rning. 4) &100 t"rns
2.3.4 )ind tur$ines [ST] Answers 1) 17 m 2) 11 B %) B sail to catch the #ind6 a magnetic field and a rotor coil to ind"ce emf. 4) st"dents’ o#n ans#ers 5) st"dents’ o#n ans#ers
Chapter 3 3.1.1 A nuclear atom [ST] Answers
1) st"dents’ o#n ans#ers 2) Bs the atom is so small! it has not been $ossible to image its str"ct"re. ;o indirect eidence has been "sed to infer the atomic str"ct"re. %);trengths (he largest mass is at the centre6 electrons do orbit the n"cle"s at arying distances eaknesses electron orbits are not all in the same $lane6 electrons orbit $ro$ortionately ten times f"rther a#ay than Ll"to’s orbit6 electron’s location in its orbit at any gien moment cannot be $redicted6 4)
3.1.2 Electrons !rom atoms [ST] Answers 1)a) 1.21 x 10 -10 m b) %.54 x 10 -11 m c) 1.%% x 10 -1% m d) ≈ 1.% x 10 -%& to 2.& x 10 -%& m 2) is idea #as a $"rely theoretical hy$othesis. (he
3.2.1 *article accelerators [ST] Answers 1) (he $articles get faster! b"t m"st s$end the same time inside each electrode. 2)a) 1.E& x 10 7 m s-1 b) %.27 x 10-20 kg m s -1 c) 0.2 ( d) 1.25 x 10 7 C %)a) 2.E7 x 10 m s-1 b) 7.%7 x 10-11 > c) b’s ans#er is m"ch less d) (he $roton’s mass increases significantly as it is accelerated
3.2.2 *article detection [ST] Answers 1) (he $.d. moes ions to each electrode and they are detected as a c"rrent $"lse. 2) 3need to check against final a#/ %) (he radi"s of the c"ring $ath is $ro$ortional to elocity! so the smaller radi"s c"re is the slo#er $art of the track after energy is lost thro"gh the metal barrier)
3.2.3 T"e &arge +adron Collider [ST] Answers 1 (he radi"s of c"rat"re of the track is $ro$ortional to the ratio masscharge.
2 If t#o easily detected $articles collide in a manner that a$$ears to break conseration of moment"m! then a third as yet "ndetected $article co"ld be inferred as haing carried the MmissingM moment"m. % (he intended searches may $rod"ce a ariety of $articles #ith ery different masses and energies. (his means that detectors #ith different siCes and sensitiities are needed! to monitor the ery different $ath c"rat"re and absor$tions of the ario"s $articles $rod"ced. 4 ;t"dentsM o#n ans#ers
3.3.1 Creation [ST] Answers 1)a) 2.5 x 10 -1% > b) %.E x 1020 C 2) 1.& x 10 -2& kg %)a) to consere moment"m b) 1.00 *e?c2 4)a) 3need to check against final a#/ b) it is the only lone track6 its energy m"st be more than the mass e"ialent and kinetic energy of all the others combined. c) (he incoming anti$roton has the straightest track demonstrating it has the most moment"m hence the most energy) d) 3need to check against final a#/ they hae e"al radii of c"rat"re! b"t c"re in o$$osite directions e) Bll tracks are $rod"ced in o$$osite $airs f) (he electron mass is m"ch less than the $ion! so it is likely to hae a track #ith smaller radi"s of c"rat"re. g) Nery $articles $artner moes off in the o$$osite direction.
3.3.2 T"e $ric,s o! matter [ST] Answers 1) It has the o$$osite charge to an electron! so it is $ositie. 2)a) "arks feel the string n"clear force! le$tons do not6 "arks cannot exist alone. b) Bll $ro$erties exce$t mass are o$$osite c) the m"on is m"ch more massie %) symmetry s"ggested there sho"ld be a $artner to bottom "ark! #ith a higher massenergy. 4) *ass + 175 Ge?c 26 charge + D1% 5)a) (hey are tiny b) In each generation! mass "m$s "$ significantly.
3.3.3 *article reactions [ST] Answers 1) 'e"tron is dd"6 $roton is ""d6 ;o in beta min"s decay! a do#n "ark is changed in to an "$ "ark. 2)a) Karyon has three "arks6 meson is a "arkanti"ark $air.
b) adrons feel the strong n"clear force! le$tons do not. %)a) charge is not consered b) charge is consered
3.3.4 More on t"e standard model [ST] Answers 1) B $article that carriestransmits a force 2) It is $ositiely charged! so the anti$article m"st be negatie. %) Lhotons $ass bet#een them 4) It ex$lains ho# $articles get their mass 5) $ → n D eD D νe conseres charge! baryon n"mber and le$ton n"mber. &) (he second reaction does not consere strangeness.
Chapter 4 4.1.1 +eat and temerature [ST] Answers 1) ∆θ + ∆Nmc 3t#o line maths/ L"tting in more energy m"st raise the tem$erat"re6 more mass #ill mean that the energy is shared more thinly so the tem$erat"re rise is less6 a greater s$ecific heat ca$acity means that by definition a lo#er tem$erat"re rise occ"rs for a certain energy addition. 2) 1.E seconds ass"ming no heat loss to s"rro"ndings. %) 2550 > kg -1 O -1 4) 525 m s -1 5) ans#ers in the range 500 , 2000 m s -1 &) 27 A = 7) total energy in a system
4.1.2 -inetic t"eory o! gases [ST] Answers 1)a) as $er fig. 4.1.E b) *eas"rements of $ress"re at different absol"te tem$erat"res lead to a gra$h of $ s (. B straight best fit line erifies the $ress"re la#. c) Nns"re that the e"i$ment cannot change ol"me6 and that it does not leak. 2) Bir molec"les hae a finite siCe6 they are a mixt"re of different ty$es of $articles. %) 100 mol 4) ;t"dents’ o#n ans#ers. 'eeds to allo# meas"rable ariation in ol"me for changing tem$erat"re. N.g. a gas syringe in a #ater bath.
Chapter 5 .1.1 /uclear radiation [ST] Answers 1) α 2$2n6 D2 charge6 large mass6 highly ioniCing6 lo# $enetration6 absorbed by $a$er! skin or a fe# cm of air6 little haCard o"tside the body6 extremely haCardo"s inside body6 β single electron6 -1 charge6 tiny mass6 moderately ioniCing6 moderate $enetration6 absorbed by seeral metres of air! or a fe# mm of al"mini"m6 moderate haCard inside and o"tside the body
γ high fre"ency e-m $hoton6 no charge6 no mass6 lo# ioniCation6 highly $enetrating6 energy significantly red"ced by seeral metres of concrete! or a fe# cm of lead6 little haCard inside or o"tside body! $rolonged ex$os"re can increase cancer risk. 2) 0.4& K %) α $articles sto$$ed by a layer of dead skin cells o"tside the body. Bfter handling! the emitter co"ld be ingested from the fingers. 4) (he granite bedrock emits significant amo"nts of radon gas #hich is an al$ha emitter #hich co"ld be breathed in. 5) ;t"dents’ o#n ans#ers! incl"ding backgro"nd co"nt check and corrected co"nt #ith ario"s absorbers.
.1.2 Rate o! radioacti0e decay [ST] Answers 1)a) 1.%7 x 10 -11 s-1 c) 4.15 x 10 -E s-1 2) 5.4 10E atoms %) tP + & ho"rs 4) l ∝ 1tP 3t#o line maths/
b) 7.&% x 10-10 s-1
.2.1 /uclear !ission and !usion [ST] Answers 1) $roton 1.505 x 10 -10 > ne"tron 1.507 x 10 -10 > electron .1E x 10 -14 > 2) 1.E x 10 -11 > 124 *e?) %)a) 7.% *e? b) KN $er n"cleon goes "$ by 0.& *e? c) Nk + 2.07 x 10 -15 >6 rms s$eed + 7 000 m s -1 4) Q + E5 5) 7.17 x 10 21 *e? &) 17% *e? 7) Koth fission and f"sion $rod"cts hae higher binding energy $er n"cleon than the start n"clei. (his means that they are more tightly bo"nd so there is less mass $er n"cleon. (his dro$ in mass is released as energy.
.2.2 /uclear ower stations [ST] Answers 1) costs to b"ild6 costs to decommission6 f"el $rice6 amo"nt of f"el needed6 $o#er o"t$"t6 costs to dis$ose of rad#aste6 enironmental im$act6 $"blic o$inion6 and all these com$ared #ith the alternaties 2) st"dents’ o#n ans#ers %) in case of an emergency! a mechanical system #o"ld not fail safe. 4) st"dents’ o#n ans#ers
Chapter 6 .1.1 Simle "armonic motion [ST] Answers 1)a) e"ilibri"m! mg balanced #ith kx6 aboe em! mg D air resistance R kx-d)6 belo# em! mg S air resistance D kxDd). 'K the direction of air resistance de$ends on the exact moment chosen b) air resistance is ariable 2)a) 4.2 s b) 1.5 rad s-1 c) kee$ still6 take meas"rements oer a large n"mber of s#ings -1 %) 4.4 rad s 4)a)c)d) as $er fig &.1.5 e)f)g) as $er fig &.1.7 b) as $er fig &.1.5 acceleration gra$h 5)a) re$eating isochrono"s oscillations ca"sed by a restoring force #hich is $ro$ortional to the dis$lacement. b) 0.EE m c)d)e) 3need to see final a#/
.1.2 S+M mat"ematics [ST] Answers 1) seconds N k + Cero6 Nkmax + 1.5 x 10 -% > 2) GLN → ON D GLN → NLN D ON D GLN → NLN → NLN D ON D GLN → ON D GLN → GLN and re$eat %) Intermolec"lar stresses in the string ca"se a heating effect! slo#ing the bob as kinetic energy conerts to heat. 4) x& + 0.077 m6 & + 0.14 m s -16 a& + 0.% m s -2
.2.1 amed and !orced oscillations [ST] Answers 1) st"dents’ o#n ans#ers 2) Bt that s$eed! engine fre"ency is at a resonantnat"ral fre"ency for that $art of the dashboard. %) ;ignificant dam$ing! $erha$s by adding a foam $ad! co"ld dissi$ate the ibration energy. Blternatiely! altering the nat"ral fre"ency of the dashboard $art! $erha$s by ta$ing a #eight to it! #o"ld aoid the resonance occ"rring. (his co"ld also be achieed by neer driing fast eno"gh to ca"se resonanceT 4) Underdam$ing red"ces am$lit"de of oscillations a little #ith each cycle. erdam$ing sto$s oscillations entirely by ret"rning to e"ilibri"m ery slo#ly. =ritical dam$ing allo#s nearly normal oscillation s$eed back to the e"ilibri"m $osition! #here the system is sto$$ed.
.2.2 Resonance ro$lems and daming solution [ST] Answers 1) (he driing fre"ency of the soldiers marching feet matched the nat"ral fre"ency of the bridge. (his ca"sed resonance and the am$lit"de of oscillation #as so great that it ca"sed fail"re of the bridge str"ct"re. 2) (he dam$er red"ces oscillation am$lit"de! red"cing stresses on the bridge girders. %) Kody caities hae resonant fre"encies and there is a $artic"larly strong one in the chest at aro"nd 7 C. (h"s the m"sic ca"ses resonance of the dancer so they ibrate more than antici$ated for the ol"me of the m"sic. 4) st"dents’ o#n ans#ers
Chapter 7 .1.1 'rom ales to galaies [ST] Answers 1) (he graitational field strength of Narth is E.1 ' kg -1 at its s"rface. 2) &.0 x 10 -& ' %) 2.0 x 10 20 ' 4) 1.5 x 10 11 m
.1.2 (ra0itational !ields [ST] Answers 1) 7.5 m s -2 2) atom F + %.&E x 10 -7 ' Ll"to F + 4.E4 x 10 1& ' (he solar system force is 102% x bigger for a system #hich is 10 22 x larger %) 1.%& x 10 -4 kg 4) %.4& x 10 m
.2.1 Stellar roerties [ST] Answers 1) 7.15 x 10 2 2)a) 5.0 x 10 -7 m b) Btmos$heric absor$tion -7 %) 1.%5 x 10 m 4a) 3need to see final a#/ b) ariation in total energy o"t$"t 5) a) V ri + 2&0 nm 2&% nm) W =et + 10 nm 05 nm! 00 nm) b) .% 10 m ,2 c) V ri $eak at X 2&0 nm 3e.c.f. their al"e/ 3bio"sly to left of 400 nm/! W =et $eak at X 00 nm 3e.c.f./ 3bio"sly to right of 700 nm/ also! Brea V ri Y area W =et. d) V ri at bl"e end of s$ectr"m6 W =et at red end! K( o"tside isible region
.2.2 Classi!ying stars [ST] Answers 1) 1.2 x 10 57 $rotons6 4.22 x 10 %E $rotons f"se $er second 2) a)b) as $er fig 7.2. %) &.&7 x 10 22 m s-2 4)a) as $er fig 7.2.10 b) starts at the to$ middle of the diagram6 moes slightly right6 then s"$ernoa and ne"tron starsblack holes are not $lotted on the diagram. 5) e-4 has an "n"s"ally high KNn"cleon and so is a ery stable n"cle"s. (h"s m"lti$les of this are also ery stable. &)a) (o f"se aboe Iron-5& #o"ld inole a dro$ in KNn"cleon and so #o"ld need energy to be $"t in. b) In a s"$ernoa ex$losion energy is aailable to f"se n"clei to higher masses than 5&.
.3.1 istances to t"e stars [ST] Answers 1) 1.%2 $c
2)a) 1.14 x 10 17 m b) 12 ly c) %.& $c d) 7.5& x 10 5 BU %) 7.57 x 10 1 m 4) (rigonometric $arallax is not reliable at more than 200 $c. 8"minosity decreases #ith distance6 or l"minosity can ary oer time #ith some stars. 5)a) 1.02 x 10 -7 m-2 b) 2.&% x 10-5 m c) m"ch less energy! at generally longer #aelengths
.3.2 T"e age o! t"e #ni0erse [ST] Answers 1)a) &&E.411 nm b) 4.5 *$c 2) 10 , 20 Gyr %)a) 3need to see final a#/ 4)a) s ,1 km s ,1 k$c ,1 km s ,1 *$c ,1 b) t + 1 3;"bstit"te al"e of to obtain t/. Bss"ming since the start of time all galaxies are traelling at constant s$eed! and there are no graitational attractie forces. Bss"ming that the Unierse ex$ands at a constant rate.
.3.3 T"e !ate o! t"e #ni0erse [ST] Answers 1 a) B change in the fre"ency#aelength of the lightradiation from a so"rce) beca"se of relatie motion bet#een so"rce and obserer. b) 9ecession) elocity $ro$ortional to galaxy distance 3'( stars/. 9ed shift d"e to a galaxy moing a#ay from Narthobserer.
By MissCutielicious
