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x Deifneweigh tast hef orceonanobjec tduet oagravtia itona l ifeld g i e W hti sdeifnedast heforceo fanobjec tduet oagravtiaitona l ifeld . tIi savecto rquanttiy i e w , y ll a c it a m e h t a M . ) N ( n o t w e N t i n u e h t h ti w gh tcanbeexpresseda sW=mg ,wherem ist he d n a t c e j b o e h t f o s s a m g ist heacceleraitonduet ogravtiy. x Explaintha tachangei ngravtia itona lpoten ita lenergyi srelatedt oworkdone o t e c a f r u s s ’ h tr a E e h t m o r f t c e j b o n a e v o m o t e n o d k r o w e h t r e d i s n o C aheight ,h: e c r o f e r e h w ( gravtiyist heweigh)t s i k r o w e h t h c i h w r e v o t n e m e c a l p s i d e h t s a ( )t fi l e h t f o t h g i e h e h t o t l a u q e s i e n o d h g m = W , y ll a c it a m e h t a M x Performani nvesitga itonandgatherinforma itont odetermineavaluef or n o it a r e l e c c a duet ogravtiyusingpendulummo itonorcomputerassistedt echnology s m 8 . 9 e u l a v e h t m o r f s n o it a i r a v e l b i s s o p r o f n o s a e r y fi t n e d i d n a -2 y ti v a r g r o f e u l a v a g n i n i m r e t e D : n o it a g it s e v n I : m i A Todetermineavaluef o rg ,byobservingt hemoitono fas wingingpendulum : t n e m p i u q E -50gmas sorl argenutt oac ta spendulum -abou t1.2ml engtho fstirng -as uppor tatl eas tonemerteabovet heground( e.g .hookonceiilng) -stopwatch -anothe rpersont oassist : d o h t e M / 1 Adjustt hel engthoft hependulum ,l, oto nemerte. / 2 Se tupequipmen tass hown: t n e m e c a l p s i d x e c r o f = e n o d k r o W e c r o f = e n o d k r o W gravtiyxdisplacement t n e m e c a l p s i d x ] y ti v a r g x s s a m [ = e n o d k r o W t h g i e h x ] y ti v a r g x s s a m [ = e n o d k r o W/ 3 Se tpendulumgenltybypulilngi tback10˚ fromveritcal .Staritngatt heex rtemeo f . e d i s e m a s e h t t a k c a b g n i h s i n if , s d o ir e p l l u f 0 1 e m it , n o it o m e h t / 4 Divide itmeby10andr ecordi nt able .Calculateavaluef o rg ,using 4 22 T g S / 5 Repeats tep s3-4f ou rmore itme ,ss ho trenings t irngby5cmeach itme. / 6 Calculateanaveragevaluef o rg ,usingal l5t irals : s tl u s e R l a i r T Penduluml ength( m) Period( s) g s(m -2) T2 1 1 .01 2 .00 9.9680 4 .00 2 0 .97 1 .93 10.281 3 .72 3 0 .91 1 .97 9.256 3 .88 4 0 .85 1 .89 9.394 3 .57 5 0 .81 1 8.8 9.041 3 .53 e g a r e v A 9 .59 n /A Atlernaitvely ,plo tT2agains tl onanx-ygraphanddrawt he ilneo fbestf ti: s ( d e r a u q s T 2) length( m) 4 1.01 2 7 . 3 0.97 8 8 . 3 0.91 7 5 . 3 0.85 3 5 . 3 0.81 0 0. 0 0 0. 0 l e n o r o f n e k a t e m i T s i g n i w s e t e l p m o c T , d o i r e p e h t d e ll a c
: a l u m r o f e h t g n i s u ’ g ‘ e t a l u c l a C t n e i d a r g 4π g 2 L s v d e r a u q s T x 5 6 9 0 . 4 = y 0 5 . 0 1 5 . 1 2 5 . 2 3 5 . 3 4 5 . 4 0 0.2 0.4 0.6 0.8 1 1.2 ) m ( h t g n e l )d er au qs s( der au qs T t n e i d a r G ≈4.10( 3s f.). ). f. s 3 ( 3 6 . 9 .. . 8 8 8 2 6 . 9 0 1 . 4 4 ' 'g S2 # : n o i s s u c s i D n i s n o it a ir a V g wereduet or eaciton itmei n itmingt hes wing- theaccuracyoft hes topwatch , o s l A . e m it n o it c a e r n a h t e t a r u c c a e r o m h c u m s i fircitonbetweent hes tirngand ti sattachment s a l l e w s a arir esistance ,whichwouldhaves lowedt hes wingoft hependulum. g n i m r o f r e p y b d e v o r p m i e b d l u o c s tl u s e r e h t f o y ti li b a il e r e h T mulitplet iralsf ort hes ame h t g n e l . Also ,anyr esutlst ha tdono tconformwtiht hemajortiyoft her esutlse.g .avalueo f s m 7 -2 rf ‘g’o ,s houldbei gnoredandt het iralr epeatedunit lameasurementt ha tconformst o . d e n i a t b o s i y ti r o j a m e h t y b d e v o r p m i e b d l u o c t n e m ir e p x e e h t f o y ti d il a v e h T usinganattachmentf orthes tirngt ha t ir f e lt ti l s a e c u d o r p d l u o w citona spossible ,wtihou tcausingt hependulumt os wing . y ll a c it a r r e Theexpeirmen twa sconducteds ilgh ltyaboves eal evel( approximately50 e h t n o t c e f f e e m o s s a h e v a h d l u o c t i , h c u m e k il m e e s t o n y a m e d u ti tl a s i h t e li h W . ) s e rt e m e p o w t , y ll a n i F . s tl u s e r oplewerei nvolvedwtihpefrormingt heexpeirment- onet o itmet he . m u l u d n e p e h t f o o g t e l o t r e h t o n a d n a m u l u d n e p I twouldbebettert ohaveonlyoneperson r o o w t n e h w s e m it n o it c a e r n i s e c n e r e f fi d e r a e r e h t e s u a c e b s p e t s e s e h t f o h t o b m r o f r e p o t e p e r o m oplearei nvolved.. , g r o f e u l a v e l b a il e r y lr i a f a e v a g d o h t e m t s ri f e h T (9.59ms-2 ,) only0.21ms-2 sl tes hant he m 8 . 9 f o e u l a v d e h s il b u p s-2 .Usingthes econdmethodgaveas ilghltymoreaccuratevalueo f s m 3 6 . 9 -2. Thes econdmethodi smorevaildbecausei treile sont he ilneo fbestf ti ,which s tl u s e r t n a p e r c s i d y n a t u o e l u r o t s p l e h
x Gathersecondaryi nforma itont opredictthevalueo faccelera itonduet ograv tiyon s t e n a l p r e h t o : y b n e v i g s i t e n a l p a n o g f o e u l a v e h T s e rt e m n i t e n a l p f o s u i d a r g k n i t e n a l p f o s s a m 0 1 7 6 6 t n a t s n o c l a n o it a ti v a r g l a s r e v i n U G , e r e h w 2 1 3 1 1 2 u t e n a l P t e n a l P t e n a l P t e n a l P r m s g k m r m G g . ) ( t e n a l P V eal u g f o s m ( -2) s n o it a l u c l a C y r u c r e M 0 7 . 3 369709 370 ( 3s f.). 0 1 4 4 2 0 1 0 3 3 0 1 7 6 6 0 1 4 4 2 0 1 0 3 3 2 2 6 3 2 1 1 2 6 3 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . . ) . ( ) . ( . ) ( . . s u n e V 7 8 . 8 887450 887 ( 3s f.). 0 1 5 0 6 0 1 7 8 4 0 1 7 6 6 0 1 5 0 6 0 1 7 8 4 2 2 6 4 2 1 1 2 6 4 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . . h tr a E 9 0 .8 s r a M 0 7 . 3 370427 370 ( 3s f.). 0 1 0 4 3 0 1 2 4 6 0 1 7 6 6 0 1 0 4 3 0 1 2 4 6 2 2 6 3 2 1 1 2 6 3 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . . r e ti p u J 2 84 . 247894 248 ( 3s f.). 0 1 5 1 7 0 1 0 9 1 0 1 7 6 6 0 1 5 1 7 0 1 0 9 1 2 2 7 7 2 1 1 2 7 7 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . . n r u t a S 4 . 0 1 1043766 104 ( 3s f.). 0 1 3 0 6 0 1 9 6 5 0 1 7 6 6 0 1 3 0 6 0 1 9 6 5 2 2 7 6 2 1 1 2 7 6 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . . s u n a r U 3 8 . 8 ). f. s 3 ( 3 8 8 6 1 4 3 8 8 0 1 6 5 2 0 1 8 6 8 0 1 7 6 6 0 1 6 5 2 0 1 8 6 8 2 2 7 5 2 1 1 2 7 5 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . . o t u l P 3 2 6 . 0 ). f. s 3 ( 2 3 6 0 3 7 2 2 6 0 0 1 8 1 1 0 1 0 3 1 0 1 7 6 6 0 1 8 1 1 0 1 0 3 1 2 2 6 2 2 1 1 2 6 2 2 # u u u u u u s m r m G g m r g k m t e n a l P t e n a l P t e n a l P t e n a l P . .. . ) . ( ) . ( . ) ( . .
x Analysei nforma itonusingt heexpres isonF=mgtodeterminet heweightf orcef ora s t e n a l p r e h t o n o y d o b e m a s e h t r o f d n a h t r a E n o y d o b l u c l a c e b n a c t c e j b o n a n o e c r o f t h g i e w e h t f o e d u ti n g a m e h T atedusingas ilghltyatlered : w a l d n o c e s s ’ n o t w e N f o m r o f F=mg .Thedriecitonoft heweightf orcei st hes ameast he l e if l a n o it a ti v a r g e h t f o n o it c e ri d datt hel ocaitonoft heobjec t.ie.t owardst hecenrteoft he . h tr a E ti v a r g o t e u d n o it a r e l e c c a e h T yatt heEatrh’ss urfacei s9.8ms-2 .Theweigh to fa465kg llama : s w o ll o f s a d e t a l u c l a c e b n a c ). f. s 2 ( 0 0 6 4 7 5 5 4 8 9 5 6 4 s m 8 . 9 g 5 6 4 -2 N g m W g k m # u . : s t e n a l p t n e r e ff i d n o a m a ll g k 5 6 4 e m a s e h t r o f y ti v a r g o t e u d n o it a r e l e c c A t e n a l P Valueo fg s m ( -2) Weigh tForce Calcula itons y r u c r e M 3 0 .7 0 0 7 1 W mg 465u3.70 1720.5#1700N( 2s f.). s u n e V 8 .87 0 0 1 4 W mg 465u8.87 4124.55#4100N( 2s f.). h tr a E 9 .8 4600 - s r a M 3 .70 0 0 7 1 W mg 465u3.70 1720.5#1700N( 2s f.). r e ti p u J 2 4.8 0 0 0 2 1 W mg 465u24.8 11532#12000N( 2s f.). n r u t a S 1 0.4 0 0 8 4 W mg 465u10.4 4836#4800N( 2s f.). s u n a r U 8 .83 4100 W mg 465u8.83 4105.95#4100N( 2s f.). o t u l P 0.623 2 90 W mg 465u10.4 293.88#290N( 2s f.).
x Deifnegravtia itona lpoten ita lenergyast heworkdonet omoveanobjectf roma d l e if l a n o it a ti v a r g a n i t n i o p a o t y a w a e c n a t s i d e g r a l y r e v , r m m G Ep 1 2 h ti w t n i o p e m o s t a t c e j b o n a f o y g r e n e l a it n e t o p l a n o it a ti v a r g e h T inagravtiaitona l ifeldi s : s a d e n if e d theworkdonet omovingt heobjectf romani n ifntiedistancet oapointi na d l e if l a n o it a ti v a r g s i y g r e n e l a it n e t o p l a n o it a ti v a r g e h t , d l e if l a n o it a ti v a r g a m o r f y a w a e c n a t s i d e ti n if n i n a t A . o r e z A sanobjec tmovest owardst hes ourceoft he ifeld .ie.t hecenrteo faplanet , . e v it a g e n s e m o c e b y g r e n e l a it n e t o p l a n o it a ti v a r g Atlhought hi svaluei snegaitve ,tir epresent s s a , m o r f y a w a t c e j b o n a h s u p o t d e ri u q e r e r o f e r e h t s i k r o W . e n o d k r o w . e .i p E n i e g n a h c a s a l l e w towardst heEa trh. y ll a c it a m e h t a M : ) 2 2 1 2 1 3 1 1 -2 1 m ( t e n a l p f o s u i d a r t e n a l p f o s s a m d l e i f e h t n i h t i w g n i v o m t c e j b o n a 0 1 7 6 . 6 t n a t s n o c . v a r g l a s r e v i n u G y g r e n e l a i t n e t o p . v a r g , e r e h w u r m m s g k m E r m m G E p p
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x S eo lv problem sandanalyseinforma itont ocalculate the d n a l a t n o z i r o h s ti m o r f e li t c e j o r p a f o y ti c o l e v l a u t c a : g n i s u s t n e n o p m o c l a c it r e v s e v o m n e h t d n a , d e h c n u a l s i t a h t t c e j b o y n a s i e li t c e j o r p A onlyundert hei n lfuenceo f y ti v a r g . Example sareaballt hati ss rtuck ,abu llets hel lonce tii sf ried .Ar ocke to rmissliei s T O N aprojectlie. d e s y l a n a e b n a c e li t c e j o r p a f o y r o t c e j a rt e h T ast wos eparatemoitons : x ( l a t n o z i r o H -axis )moiton,r epresenitngconstan tveloctiy y ( l a c it r e V -axis )mo iton,r epresenitngconstan tacceleraitona t“g” ,downwards : n o it o m e li t c e j o r P r o f s n o it a u q E ) 1 Resolvei niitall aunchveloctiyintoveritca landho irzonta lcomponent 2 2 2 2 2 2 1 2 t a t u y t u x y a u v t a u v u v y y x y y y x x ' ' ' Ux y Δ l a c it r e V , y ti c o l e v Vy l a t n o z ir o H , y ti c o l e v Vx Uy Ux U θ Angleofl aunch x Δ =r ange=t ota lho irzonta ldistance Ux Uyθ
U T T .cos n i s . u u u uy & x) 2 Ho irzonta lmoitoni sconstant, s oal lyouneedi s vx ux and 'x uxt ) 3 Veritca lmoitoni sconstan tacceleraitona t“g” e s u , y ti c o l e v l a c it r e v d n if o T d n if o T veritca ldisplacement ,use r o t s t n i o P emember: -themo itoni ss ymmetirca,ls ot heelapsed itmei shaflt hef u llf ilght -veritca ldisplacement, 'y ha sanegaitves ign -a tti speakheight ,vy 0 -Maximumrangei sachievedwtihal aunchangleo f ˚45 ,.ie .T 45q -ho irzonta lveloctiyi sconstan t.ie .v x ux -Use vy uy ayt to ifnd “t”a tmaxheight( whenvy=0 )o r ifndvya tagiven itme - eU s 2 2 1 ta t u y y y ' to ifndΔy a tagiven itme ,orf indt he itmet of allt hroughagiven f i( t h g i e h uy= ) 0 : s m e l b o r P e l p m a x E ) 1 Aprojectliei s ifredwtihaveloctiyo f50m/ sa tanangleo f30°t ot hehorizontal . . e li t c e j o r p e h t f o e g n a r e h t e n i m r e t e D ). f. s 3 ( 0 2 2 .. . 7 4 8 4 2 9 . 0 2 2 8 . 9 ) 0 3 n i s 0 5 ( 2 0 3 s o c 0 5 8 . 9 ) 0 3 n i s 0 5 ( 2 8 . 9 0 3 n i s 0 5 8 . 9 0 3 n i s 0 5 0 0 , t h g il f -fl a h e h t r e d i s n o C 8 . 9 0 3 s o c 0 5 0 3 n i s 0 5 2 1 1 2 m t u x t a u v t s m v s m a u u x y y y y y x y # q u q ' q ? q q q q ) 2 Mlitiarybomb smus tbedroppedf romanatltiudeo f15000mwhent heplanei s s m 0 0 3 t a l e v e l g n i y lf -1. ) s m 8 . 9 ( -2 y y y y u a t a v ) s m 8 . 9 ( 2 1 2 -2 'y uyt ayt ay
? d e s a e l e r e b s b m o b e h t t s u m t n o r f n i r a f w o H ) a m t u x f s s t t t t a t u y s m u s m u m y x y y y x 0 9 5 6 1 3 5 5 0 0 3 3 3 5 5 3 3 3 8 3 2 5 5 9 4 0 0 0 5 1 8 9 2 1 0 0 0 0 5 1 2 1 0 0 0 3 0 0 0 5 1 2 2 1 1 ' # ' ' ) . ( ). . ( . .. . . . ) . ( ) b Howf as twillt heybegoing i(nmagntiude )whent heyhtit heground? ). f. s 3 ( 0 1 9 1 6 9 3 4 3 4 9 1 6 4 9 1 4 5 0 0 3 4 9 1 4 5 3 5 5 8 9 0 0 0 3 8 9 0 0 0 3 3 5 5 1 2 1 2 2 2 2 1 1 2 1 1 u # s m s m v v v s m t a u v s m u v s m a s m u s m u s t y x y y y x x y y x . .. . . ) . ( ) ( . ) . ( . . . x Describethet rajectoryo fanobjec tundergoingprojectliemo itonwtihint heEarth’ s s t n e n o p m o c l a c it r e v d n a l a t n o z i r o h f o s m r e t n i d l e if l a n o it a ti v a r g . d r a w n w o d t n a t s n o c h ti w , c il o b a r a p s i ) e c n a t s i s e r ri a g n ir o n g i( e li t c e j o r p a f o y r o t c e j a rt e h T t a r e l e c c a iona t“g .” The rtajectorycanbeanalysedbyconside irng ti sho irzonta landveritca l s i e li t c e j o r p e h t f o n o it o m l a t n o z ir o h e h T . t h g il f e h t g n ir u d s e c n a t s n i r a l u c it r a p t a s t n e n o p m o c o t e u d e m it e h t ll a g n i g n a h c s i n o it o m l a c it r e v s tI . y ti c o l e v t n a t s n o c a gravtiy ,whichcause s s m 8 . 9 t a e t a r e l e c c a o t e li t c e j o r p e h t -2downwards. x DescribeGallieo’ sanalysi so fprojectliemo iton e n o n t a h t e c it o N oft heequaiton susedf o rprojectliemoitoneve ruset hemassoft he ri e h t f o s s e l d r a g e r ,s t c e j b o l l A . e li t c e j o r p mass ,acceleratewtihgravtiyatt hes amer ate. 4 6 5 1 ( o e li l a G -1642 )pefrormedanexpeirmentt overfiyt his .Hedroppedobject soft hes ame t a h t d n u o f e H . a s i P n i r e w o t g n i n a e l e h t m o r f ,s s a m t n e r e f fi d h ti w t u b , e p a h s d n a e z i s e j b o l l a , s s a m f o s s e l d r a g e r ct sh tit hegroundatt hes ame itme. e n il c n i n a n w o d s ll a b n o n n a c d e ll o r o s l a e H t(herewasf irciton )andwa sablet os ee2 . n o it a r e l e c c a l a c it r e v t n a t s n o c d n a y ti c o l e v l a t n o z ir o h t n a t s n o c : s n o it o m
x Performa ifrst-handi nvesitga iton ,gathersecondaryi nforma itonandanalysedata t h g il f f o e m it , e g n a r , d e h c a e r t h g i e h m u m i x a m , y ti c o l e v l a n if d n a l a it i n i e t a l u c l a c o t d n a s r e g g o l a t a d , s n o it a l u m i s g n i s u y b s n o it a u ti s f o e g n a r a r o f e li t c e j o r p a f o s i s y l a n a r e t u p m o c r e h c n u a l e li t c e j o r P : t n e m ir e p x E : m i A o c o T nsrtuc taworkingmode lo faprojectliel aunche randt ol aunchi ta tat argett ogathe r d n a y ti c o l e v , e c r o f g n i d u l c n i t h g il f s ’ e li t c e j o r p e h t f o s t c e p s a s u o ir a v g n it a l u c l a c r o f a t a d . e g n a r :t n e m p i u q E - projectliel auncher - stee lbal lbeairngs( smal lenought of tii nprojectliel aunche rbarre)l - scienitifcs cales - digtia lvideocamera - target( cricleo fdiamete r5%ofr ange) : e t o N Theexpeirmentr equriest heassistanceo fanothe rpersondu irngt hel aunchingoft he . e li t c e j o r p : e r u d e c o r P ) 1 Weighandr ecordt hemas soft hes tee lbal lwtihas cienitifcs cale. ) 2 Se tupequipmen tass hownbelow: ) 3 Places tee lballi nbarre lo fprojectliel auncher .Pul lbackendofs oildplungerr od n e ir f a t e G . tl e f e b n a c e c r o f n o i s n e t g n o rt s a l it n u m c 0 2 t s a e l t a dt ohelphold . e s a b r e h c n u a l e h t f o d n e k c a b e h t n w o d t e g r a T e g n a R
) 4 Askanassistantt os e tupt hevideocamerar eadyt or ecordt heprojectlie’sf ilgh t . d e h c n u a l n e h w ) 5 Aimt hel aunche ratt het arge tandadjustt heangleofl aunchaccordingt ot he .t e g r a t e h t f o e g n a r ) 6 Releaset heendoft her odandwatcht hebal lbeairnggo! ) 7 Repeats tep s1-6a smany itme sa spossibleun it laccuracyi si mproved .Oncet he s e l b a ir a v e s e h t p e e k , d e n i m r e t e d s i h c n u a l f o e l g n a d n a h c t e rt s f o t n u o m a d e ri s e d a ir t h c a e n i )t n a t s n o c ( d e ll o rt n o c lt oprovider eilabler esutls . ) 8 Measuret hedisplacemen toft heprojectliei nt hel aunche r t(hi swli ldependon .l a ir t h c a e r o f h c n u a l f o e l g n a e h t d n a ) d e ll u p s i d o r r e g n u l p e h t k c a b r a f w o h ) 9 Usegathereddatat ocalculate/determinevaluesf o:r -ho irzon talandveritca lcomponent soft heiniita lveloctiy - theresu tlanti niita lveloctiy -averageacceleraiton &netf orceo fprojectliewhliei nl aunche .r -range fil aunchedf rom50mclfif -veloctiyonequatrert hrough tisf ilght
: s tl u s e R a D d e r e h t a G t a f o t n e m e c a l p s i D projectliei nl auncher ,s =0.284m , h c n u a l f o e l g n A T = ˚ 31 , e li t c e j o r p f o s s a M m=0.015kg : n o i s s u c s i D , y ti c o l e v l a t n o z ir o h l a it i n I ux=5.6ms-1 , y ti c o l e v l a c it r e v l a it i n I uy=3.4ms-1 , y ti c o l e v t n a tl u s e r l a it i n I v=6.6ms-1 ,031˚ abovehorizontal , r e h c n u a l n i e li h w e li t c e j o r p f o n o it a r e l e c c a e g a r e v A aav=76.7ms-2 , r e h c n u a l n i e li h w e li t c e j o r p n o e c r o F t e N Fne t=1.15N f fi l c m 0 5 m o r f d e h c n u a l fi e g n a R = 12 m 0. t h g il f f o e m it h g u o r h t r e tr a u q e n o y ti c o l e V =5.8 sm -1 , 10 6˚ abovehorizontal . o N l a i r T Timeo f t h g il f t ), ( s Ran( gme)'x , Hoif tfof nrot amrgt aer/tgdeitst( amn)ce 1 0 .70 4 .0 Offt arget- 90 .0 2 0 .67 4 .0 Offt arge t- 10 .1 3 0 .78 4 .0 Offt arge t- 50 .1 e g a r e v A 0 .72 4 .0 n /a
y ti t n a u Q Data Calcula itons( al lanswerst o2s f.). l a it i n I l a t n o z i r o h ( y ti c o l e v ux) t s s m x v a 072 0 4 . . ' 1 6 5 2 7 0 0 4 ' ms t x ux . . . l a it i n I l a c it r e V ( y ti c o l e V uy) q 1 3 6 5 1 T s m ux . u u 56u 31q 34ms1 x y tanT . tan . t n a tl u s e R l a it i n i ( y ti c o l e v v) q 1 3 6 5 4 3 1 1 T s m u s m u x y . . l a t n o z ir o h e v o b a 1 3 0 , 6 . 6 6 . 6 4 . 3 6 . 5 1 1 2 2 2 2 q ? s m v s m u u v x y e g a r e v A , n o it a r e l e c c a a ( av) s m s m v 4 8 2 0 6 6 1 . . 2 2 2 7 7 4 8 2 0 2 6 6 2 u ms s v aav . . , e c r o F t e N F ( net) m s s m v g k m 4 8 2 0 6 6 5 1 0 0 1 . . . Fnet m2vs 02015026846 12N 2 2 . . . . u u f i e g n a R d e h c n u a l m 0 5 m o r f f fi l c 1 2 1 6 . 5 8 . 9 4 . 3 0 5 ' s m u s m a s m u m y x y y 0 0 5 4 . 3 9 . 4 8 . 9 2 1 4 . 3 0 5 2 1 2 2 2 ? u ' t t t t t a t u y y y m r o f e h t n i s i n o it a u q E ax2+bx+c=0. Usingt hequad.f ormula ,t i sgiven f o e u l a v e v + y b x:
m t u x s t a c a b b x x 5.6 3.6 20.1 6 . 3 9 . 2 6 . 3 9 . 4 2 0 5 9 . 4 4 4 . 3 4 . 3 2 4 2 2 u ' ? u u u r r e n o y ti c o l e V f o r e t r a u q e m it h g u o r h t t h g il f 1 1 4 . 3 8 1 . 0 4 2 7 . 0 4 6 . 5 s m u s t t s m v y v a x
l a t n o z ir o h e v o b a 6 1 0 , 8 . 5 6 1 0 6 . 5 6 . 1 n a t n a t 2 8 . 5 6 . 1 6 . 5 6 . 1 8 1 . 0 8 . 9 4 . 3 1 1 1 1 2 2 2 2 1 q ? q ¸ ¹ · ¨ © § ¸¸ ¹ · ¨¨ © § u s m v v v s m v v v s m t a u v x y y x y y y T
x Explaintheconcep to fescapeveloctiyi nt erm soft he: -grav tia itona lconstant -mas sandradiu soft heplanet : s a d e n if e d s i y ti c o l e v e p a c s E thel aunchveloctiyr equriedf o raprojectliet oescapef romt he . d l e if l a n o it a ti v a r g s ’ h tr a E c s E , y ll a c it a m e h t a M ape , y ti c o l e v where, e h t f o s s a m d n a G , t n a t s n o c l a n o it a ti v a r g e h t o t l a n o it r o p o r p e r o f e r e h t s i y ti c o l e v e p a c s e e h T y ti c o l e v e p a c s e e h t r e h g i h e h t ,t e n a l p e h t f o s s a m e h t r e t a e r g e h t . e .i t e n a l p .tIi si nversely t e n a l p e h t f o s u i d a r e h t o t l a n o it r o p o r p .ie.t hel argert heplane,tthel owert heescapeveloctiy. : e t o N Theescapeveloctiyo faplane tist hes amef o ral lobjects,i ndependen toft hei rmass . .s / m k 2 . 1 1 y l e t a m i x o r p p a s i h tr a e n o y ti c o l e v e p a c s e e h T x OutilneNewton’ sconcep to fescapeveloctiy i S rI saacNewton,t hes cienits twhodevelopedt hemathemaitc sbehindprojectliemoiton , d n a n i a t n u o m h g i h y r e v a d e b m il c n o s r e p a : t n e m ir e p x e t h g u o h t g n i w o ll o f e h t d e t a e r c b y r o t c e j a rt c il o b a r a p a s w o ll o f ll a b n o n n a c e h T . k a e p e h t m o r f ll a b n o n n a c a d e h c n u a l efore d l u o w t i ,s e it i c o l e v g n i s a e r c n i h ti w d e h c n u a l e b o t e r e w l l a b n o n n a c e h t fI . h tr a E g n it ti h . ti m o r f y a w a s e v r u c h tr a E e h t f o e r u t a v r u c e h t ,s ll a f ti s a , e s u a c e b h tr a E e h t d n u o r a l e v a rt e h d e x if a t a t i b r o r a l u c ri c a n i e v o m d l u o w e li t c e j o r p e h t ,s u h T igh tabovet heEa trh’ss urface. m o r f s e g n a h c d l u o w t i b r o s ti , s i h t n a h t r e t s a f n e v e d e h c n u a l e b o t e r e w l l a b n o n n a c e h t f I h t a p c il o b r e p y h r o c il o b a r a p a w o ll o f d l u o w t i d n a l li t s r e t s a F . e s p il l e n a o t e l c ri c a g n i e b ri t n e t i g n i p a c s e , h tr a E e h t m o r f y a w a e ly. 2 1 3 1 1 -0 1 7 6 . 6 t n a t s n o c . v a r g l a s r e v i n u G 2 u m kg s r m G V E E e h t r a E
x Identfiywhyt het erm‘ gf orces’i susedt oexplaint hef orce sacitngonanastronau t h c n u a l g n i r u d g “ m r e t e h T -force”r eferst oamass’sapparentr atea sar aitoo fti s rtueweight . n e h w s e c n e ir e p x e s s a m s a t h g i e w e h t o t s r e f e r t h g i e w e u r T staitonary( ori nr elaitvemoiton ) t n a t s n o c t a e c a fr u s t a lf a s s o r c a y ll a t n o z ir o h g n i v o m e l c i h e v a n i g n it ti s . g . e d n u o r g e h t n o e u d e c r o f e h t s i ti e s u a c e b t l e f e b t o n n a c t h g i e w e u r T . l e v e l d n u o r g t a l li t s g n i d n a t s , y ti c o l e v f a g n i e b y ti v a r g ; y ti v a r g o t o - trcea -a-distance . n o it a r e l e c c a n a r o s e c r o f t c a t n o c o t e u d s e c n e ir e p x e s s a m a t h g i e w e h t s i t h g i e w t n e r a p p A m o r f e s ir a y e h t e s u a c e b s e c r o f l a it r e n i s a n w o n k o s l a e r a s e c r o f e s e h T . ) y ti v a r g n a h t r e h t o ( e m o m s ti g n i v a h o t e c n a t s i s e r r o a it r e n i s ’ y d o b e h t ntumchanged . g d n a s n a m u H -force: -themaximumg-forceapropelrys uppo tredhumancanwtihstandi s20g( using ifberglass g n it a e s ins pacecraf)t -mos tpeopleexpeirencet unne lvisionandl osecolou rpercepitona t4g G-forceexperiencedbyastronau tduringal aunchi ntol oworbi:t t h g i e w e u rt t h g i e w t n e r a p p a e c r o f -g 2ndstagej etitsoned ) s s a m g n i s a e r c e d ( f o n o it i n g I 2ndstage 1ststage ) s s a m g n i s a e r c e d ( e m it g-force 3 1 2 4 1ststage d e n o s it t e j
e d i r r e t s a o c r e ll o r a o t h c n u a l a f o s e c r o f f o n o s i r a p m o C : g-force Periodduringrocketl aunch Periodduringrollercoasterride > g1 Rocket sburning Acceleraitngupwards g 1 At poin tofl fi toff onho irzontals urface sandwhen tir eache speak < g1 Jus ta tferf ueli ss pent Acceleraitngdownhill x Identfiydatas ources ,gather ,analyseandpresentinforma itonont hecontribu itono f t a r o l p x e e c a p s f o t n e m p o l e v e d e h t o t g n i w o ll o f e h t f o e n o ion :Tsiolkovsky ,Oberth , tl u a n s E , d r a d d o G -Petlerie ,O‘Neli lorvonBraun d r a d d o G t r e b o R d i u q il , n r e d o m f o r e e n o i p a s a w d r a d d o G -fue lrockerty .A san undergraduate ,he wrote a n o it a z il i b a t s t e k c o r r o f s e p o c s o r y g f o e s u e h t g n i s o p o r p r e p a p .Later ,hebegan studying t he f o e s u e l b i s s o p ilquid fuel sin rocket sto i ncrease fue lefifciency .He also used calculu sto e k a m theoreitca lcalculaiton sof t he veloctiy and posiiton o frockets .Later ,hepatented t he e d i x o s u o rt i n d n a e n il o s a g y b d e l e u f t e k c o r a f o a e d i - a mliestone in rockerty .Goddard e t e l p m o c a n i m r o f r e p n a c s t e k c o r t a h t m ri f n o c o t m i h d e w o ll a t a h t t n e m ir e p x e n a d e n g i s e d , e m it e fi l s i h g n ir u D . e c a p s . e .i m u u c a v hebough tove r200patentsr elaitngt or ocke tdesign. g 1 > g 1 > g 1 < < 1g g 1 g 1
x Discusst hee ffec to ftheEarth‘ sorbtia lmo itonand ti srota itona lmo itonont he t e k c o r a f o h c n u a l d n a s i x a s ti n o h tr a E e h t f o n o it a t o r e h T theorbtia lmoitonoft heEatrharoundt hes uncanbe t s li h w l e u f s e v a s s i h T . ” t s o o b y ti c o l e v “ a h ti w t e k c o r d e h c n u a l a e d i v o r p o t d e s u givingt he . y ti c o l e v t e g r a t e h t e v e i h c a o t y g r e n e c it e n i k d e ri u q e r e h t t e k c o r d e m i a e r a s t e k c o r ,t i b r o h tr a E h c a e r o T towardst heEASTt ot akeadvantageoft heEatrh’ s n o it a t o r (abou t1700km/h ro r500m/s) .Theyr eceivet hi s1700km/hveloctiyboos twhich contirbutest ot herit arge tveloctiyo fabou t30000km/hf o ral oweatrhorb ti . d e h c n u a l T O N e r a t i b r o s h tr a E e h t d n o y e b o g o t d e n it s e d s t e k c o R untlit hedriecitonoft he r e h t f o n o it c e ri d d e ri s e d e h t h ti w s d n o p s e r r o c n u s e h t d n u o r a t i b r o s ’ h tr a E ocket. Ther ocke t w o l a o t n i d e h c n u a l t s ri f s i -Ea trhorb ti ,ass hownabove .Rocket saret henf riedt oacceleratei t . ti b r o ’ s h tr a E e h t t s a p Ther ocke tgainst heveloctiyoft heEatrhr elaitvet ot heSunwhichi s . h / m k 0 0 0 7 0 1 t u o b a n o it a t o r h t r a E m o r f e l o P h t r o N h t a p l a ti b r O y r o t c e j a r t h c n u a L E ha rt n u S y r o t c e j a r t h c n u a L
x Analysethechangingaccelera itono farocke tduringl aunchi nt erm soft he : -Lawo fConserva itono fMomentum -force sexperiencedbyastronauts 3 s ’ n o t w e N m o r f d e v ir e d r i a p e c r o f a s i n o i s l u p o r p t e k c o R rdlaw .i , e. d e v r e s n o c s i m u t n e m o M ) v m ( ) v m ( p p F F -t e k c o R s e s a g t e k c o R s e s a g t e k c o r n o s e s a g s e s a g n o t e k c o R ' ' ' ' t t h T i smeanst her ocket smomentumr emain sconstan ta tal litmes .Du irng iltfof ,ft her ocket s s e s a e r c e d s s a m asf ueli sburnt .Therefore,t omaintainConservaitono fmomentum , the s ’t e k c o r veloctiymus tconitnuet oi ncrease ..i e ther ocke’t sacceleraitonwilli ncrease. : e m i T . s v t e k c o r f o n o it a r e l e c c A e c r o f n o it c a e R t e k c o r s e h s u p s d r a w r o f n o s e h s u p e c r o f n o it c A m e h t s e t a r e l e c c a , s e s a g s d r a w k c a b n o it a r e l e c c A
Twof orce sac tonanasrtonau tdu irngl aunch :Thedownwardweightf orceandt heupward s . e c r o f t s u r h t Newton’ s2ndlaws tatest ha t6F ma .Therefore , m g m T m F a 6 ( ) . fIt he e c r o f t s u r h t ,‘T’, remain sconstant ,bu t‘m’ keep sdecreasi ngasf ueli sburnt,t hen‘a’ mus t . e s a e r c n i o t e u n it n o c e c n e ir e p x e l li w y e h t s n a e m t I ? s t u a n o rt s a r o f n a e m s i h t s e o d t a h W increasingg-forces. Also t o n e tha tast her ocke tmove shighe,rt heatmospheret hins ,meaningt her ocke twli laccelerate ! r e t s a f n e v e However ,modernr ocket shavet heablitiyt ot hrotltebackt het hrust ,ensu irnga .s t u a n o rt s a e h t r o f t h g il f r e f a s x Analysethef orcesi nvolvedi nunfiormcircularmo itonf orarangeo fobject ,s h t r a E e h t g n it i b r o s e ti ll e t a s g n i d u l c n i e rt n e c ( l a t e p ir t n e c a o t t c e j b u s s y a w l a e r a n o it o m r a l u c ri c m r o fi n u n i s t c e j b O -seeking)f orce. s i e c r o f e h T tangentt ot hecriclea taparitculari nstan tandi salway sdriectedperpendiculart o y ti c o l e v e h t att hatinstan.t ? e c r o f l a t e p i r t n e c s e s u a c t a h W e l p m a x E Fc causedby… g n ir t s a n o t c e j b o n a g n i g n i w S Tensionf orceins t irng r e n r o c a g n i n r u t e l c i h e V F ircitonalf orcebetweent yre sandground h tr a E g n it i b r o e ti ll e t a S Gravtiaitonalf orcebetweens atelltieand h tr a E r o t o m a e d i s n i g n i n r u t r a e g A Torqueo fgearst urningoneachother m r o fi n u a o t r a l u c i d n e p r e p g n i v o m n o rt c e l E d l e if c it e n g a m Meleacgnrtoenitcf orcebetweenmagneitc ifeldand V FC
x Solveproblemsandanalyseinforma itont ocalculate centripetalf orceacitngona : g n i s u h t r a E e h t t u o b a n o it o m r a l u c r i c m r o fi n u g n i o g r e d n u e ti ll e t a s r v m F 2 s i e c r o f l a t e p ir t n e c e h t , h tr a E e h t g n it i b r o e ti ll e t a s a r o F suppiledbythegravtiaitonalf orce . h tr a E d n a e ti ll e t a s e h t n e e w t e b Hence ,u se: s e rt e m n i , e c a f r u s e v o b a t h g i e h / ti b r o f o s u i d a r g k n i , y ti c o l e v l a ti b r o v g k n i ,t c e j b o f o s s a m ) N ( s n o t w e N n i , e c r o f l a t e p ir t n e c , e r e h w 2 r m F r v m F C C f I theorb tia lveloctiyi sno tknownbutt hemasse soft het wobodies( e.g.s atelltieandEatrh ) : e c r o f l a n o it a ti v a r g e h t y b d e il p p u s s i ti e s u a c e b d n u o f e b n a c e c r o f l a t e p ir t n e c e h t , n w o n k e r a t n a t s n o c . v a r g l a s r e v i n u y d o b l a rt n e c r o s s a m y d o b g n it i b r o f o s s a m e c a f r u s e v o b a t h g i e h /t i b r o f o s u i d a r , e r e h w 2 1 22 1 G m m r r m m G FG r O btia lveloctiycanbecalculatedusingt hes amevalue sa sabove: t n a t s n o c . v a r g l a s r e v i n u e c a f r u s e v o b a t h g i e h /t i b r o f o s u i d a r t e n a l p r e h t o r o h tr a E f o s s a m , e r e h w G r m r m G v : n w o n k e r a d o ir e p d n a s u i d a r e h t fi d e t a l u c l a c e b o s l a n a c y ti c o l e v e h T s d n o c e s n i ,t i b r o e n o r o f n e k a t e m it T , e r e h w 2 T r v S e l p m a x E Problems:
) 1 TheHubblet elescopeha samas so f1200kgandorbti sa tanatltiudeo f600km . n o it o m r a l u c r i c s m r o f r e p t i s a e ti ll e t a s s i h t n o g n it c a e c r o f l a t e p i r t n e c e h t e t a l u c l a C . h t r a E e h t d n u o r a n e e w t e b e c r o f l a n o it a ti v a r g e h t s i e c r o f l a t e p ir t n e C e h T thes atelltieandEatrh .ie .FC = FG . ). f. s 3 ( 0 1 4 8 9 6 9 3 9 5 3 8 9 0 1 7 9 6 0 1 7 9 5 0 0 2 1 ) 0 1 7 6 6 0 1 7 9 6 0 1 7 3 6 0 1 0 6 0 1 7 6 6 0 1 7 9 5 0 0 2 1 3 2 6 4 2 1 1 22 1 6 6 5 2 1 3 1 1 4 2 2 1 N r m m G F m r s g k m G g k m g k m G -u # u u u u u u u u u . .. . . ) . ( ) . ( . ( . . . . . 0 1 x 4 8 . 9 s i e ti ll e t a s e h t n o g n it c a e c r o f l a t e p ir t n e c e h t , e c n e H 3N . ) 2 Acarwtihamas so f800kgt ravel sa taconstants peedo f7.5m/ sonaroundabouts o . m 6 1 f o s u i d a r a h ti w h t a p r a l u c r i c a s w o ll o f ti t a h t h t‘ : t n e m e t a t s e h t s e k a m g n i v r e s b o n o s r e p A erei sno tnetf orceacitngont hecar d a o r e h t d n a s e r y t e h t n e e w t e b n o it c i r f e h t d n a t n a t s n o c s i d e e p s e h t e s u a c e b ’. r a c e h t n o g n it c a e c r o f l a t e p i r t n e c e h t s e c n a l a b e c r o f l a t n o z i r o h e h t f o s i s y l a n a n a h ti w r e w s n a r u o y t r o p p u S . t n e m e t a t s s i h t s s e s s A t c a ingont hecar ,usingt henumerica ldataprovided. l a t e p ir t n e c e h t s i h c i h w e c r o f t e n a y b n o p u d e t c a g n i e b s i r a c e h T (cenrte-seeking)force .The r a c e h t f o n o it o m e h t o t r a l u c i d n e p r e p , e l c ri c e h t f o e rt n e c e h t o t d e t c e ri d s i e c r o f l a t e p ir t n e c s n i y n a t a tan.tThefircitoni sno tbalancingt hecentirpeta lforce;t hef ircitonI Sthecent irpeta l I . n o it o m r a l u c ri c m r o fi n u n i r a c e h t g n i p e e k s i t a h t e c r o f f therewerenocentirpetalf orce,t ha t c e h t ,) e c i s a h c u s e c a f r u s h t o o m s y r e v a n o . g . e ( n o it c ir f o n , s i a rwouldgoof fa tat angentt o . e l c ri c e h t N . r v m F s m . v m r g k m c -5 . 2 1 8 2 6 1 ) 5 7 ( 0 0 8 5 7 6 1 0 0 8 2 2 1 u N 5 . 2 1 8 2 f o e c r o f t e n l a t e p ir t n e c a y b n o d e t c a g n i e b s i r a c e h t , e c n e H
x Comparequaltia itvelyl owEarthandgeo-sta itonaryorbtis w o L -Earth G -eo sta itonary ) m k ( e d u ti tl A Abovet heEatrh’ satmospherebu t n o it a i d a r n e ll A n a v e h t w o l e b s tl e b s tl e b n e ll A n a v r e t u O ) m k 0 0 8 5 3 ( 0 5 2 1000 ) s r u o h ( d o i r e p l a ti b r O 1 .49 1 .75 23.9( aka“siderea lday”) ) s / m ( y ti c o l e v l a ti b r O 7750 7350 3070 s e s U Spy,s urveyingandweathe r s e ti ll e t a s ,r emotes ensing ,mlitiary n a m u h r o f d n a s e s o p r u p t h g il f e c a p s r e h t a e w , s n o it a c i n u m m o C s e ti ll e t a s ,s cienitifcs tudies n o it a m r o f n i l a n o it i d d A Others ub-typesi ncludepola r s ti b r o (spying)andequato irall ow -s ti b r o h tr a e e b o t s r a e p p a , h tr a E m o r F k s e h t n i d e x if y. g n ir e l g n i s a y p u c c o l l A d e n o it i s o p abovet heequator m k 0 0 8 5 3 Ghiegohsetra ,itwontiharaypoerrbiotidi ≈ 4 sm2 uh chrs . Acommunicaiton sreceiving d e m i a e b o t y l n o s d e e n h s i d l a m it p o e v i e c e r o t ti t a y lt c e r i d h t g n e r t s l a n g is - nof urther n e m t s u j d a t sareneeded. w o L -Earthorbi thass horter d o i r e p ≈1.5hours ,butf aster e l b b u H e h t y b d e s U . y ti c o l e v . e p o c s e l e t e c a p s d e w e i v , h t r a E h t r o N m o r f e l o p 0 5 2 -1000km
x Deifnethet ermorbtia lveloctiyandt hequanttia itveandqualtia itverela itonship s s a m , y d o b l a r t n e c e h t f o s s a m , t n a t s n o c l a n o it a ti v a r g e h t , y ti c o l e v l a ti b r o n e e w t e b s d o i r e P f o w a L s ' r e l p e K g n i s u t i b r o e h t f o s u i d a r e h t d n a e ti ll e t a s e h t f o s i y ti c o l e v l a ti b r O d neif edas :theinstantaneouss peed(magntiude)i nt hedriecitonindicated w o r r a n a y b (d riecitonal )drawna satangentt oaparitcula rpoin tont heorbtia lpat . h e h t n e e w t e b p i h s n o it a l e r l a c it a m e h t a m e h t d e r e v o c s i d r e l p e K s e n n a h o J peirodo fanorbi tand s ti radius: t n a t s n o c . e .i 2 3 2 3 v T R T R F , e ti ll e t a s g n it i b r o n a r o f t a h t w o n k e W C = FG,s o: y d o b l a rt n e c f o s s a m t n a t s n o c . v a r g l a s r e v i n u ti b r o f o d o ir e p e c a f r u s e v o b a t h g i e h /t i b r o f o s u i d a r , e r e h w 4 4 2 , y ti c o l e v l a ti b r o t u b 2 2 3 2 2 2 2 2 2 1 ? M G T R M G T R e c n e H r M G T r o S T r v r M G v r M m G r v m S S S , , l p o t s e il p p a o s l a s d o ir e p f o w a l s ’ r e l p e K anets .When compairnganynumbe ro fplanetsint he m e t s y s r a l o s , 23 TR wli lalway sgiveaconstan.t
x Solveproblem sandanalyseinforma itonusing: 23 2 4S M G T R : s m e l b o r P e l p m a x E n u o r a l e v a r t , Y d n a X , s t e n a l p o w T ) 1 das tari nt hes amedireciton,i ncircularorbtis . e m it n i r a t s e h t d n u o r a n o it u l o v e r e n o s e t e l p m o c X t e n a l P T .Theradi ioft heorbti sare . 4 : 1 o it a r e h t n i e m it e m a s e h t n i r a t s e h t t u o b a e k a m Y t e n a l p s e o d s n o it u l o v e r y n a m w o H T? s n o it u l o v e r 8 1 e k a m t s u m Y , e c n e H . s n o it u l o v e r 8 s e k a m X , n o it u l o v e r e n o e k a m o t Y s e k a t ti e m it e m a s e h t n I . e .i 8 4 6 4 1 4 4 d n a ,t n a t s n o c g n i s U 2 2 2 3 2 2 3 2 3 2 3 2 3 2 3 X Y X Y Y X Y X X X X Y Y Y X X T T T T T T T R T R R R T R T R T R ? ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( d e ti b r o d r a o b n o s n il l o C l e a h c i M h ti w e l u d o M d n a m m o C 1 1 o ll o p A e h t 9 6 9 1 e n u J n I ) 2 f o s s a m e h T . e c a f r u s s ’ n o o M e h t m o r f n r u t e r o t e l u d o M t n e c s a e h t r o f g n it i a w n o o m e h t 0 1 x 8 9 . 9 s a w e l u d o m d n a m m o C e h t 3kg , ti speriodwa s119minute sandt heradiu so fti s 0 1 x 5 8 . 1 s a w n o o m e h t m o r f ti b r o 6metres ) a Assumingt hecommandmodulewasi ncircularorb ti ,calculate )i Themas soft hemoon
