5-9 THE FIELD CONCEPT. Answers to the Conceptual Questions. Chapter 5 Gravity 63

Size: px

Start display at page:

Download "5-9 THE FIELD CONCEPT. Answers to the Conceptual Questions. Chapter 5 Gravity 63"

Lucas Johnston
5 years ago
Views:

1 Chapt 5 Gavity 5-9 THE FIELD CONCEPT Goals Intoduc th notion of a fild. (Pobl Solvin) Calculat th Sun's avitational fild at Eath's location. Contnt Th psnc of a ass odifis spac. A valu can b assind to ach point in spac that ivs th foc on a unit of ass if it w placd th. Tachin Tips Th point of this sction is ipotant if you plan to discuss lctoantic filds in Chapt. W'v found that this sction also hlps th studnts whn w t to th idas of nal lativity in Chapt 10. Pobl Solvin 5. W calculat th Sun's fild at Eath's location and ask th studnt to do th sa fo th Eath-oon pai. Coput Aniations Activ Fiu Aniations a availabl on th ultidia ana Instucto s Rsouc CD. Thy a oanizd by txtbook chapt, and ach aniation cos within a shll that povids infoation on how to us th aniation, xploation activitis, and a shot quiz. Answs to th Concptual Qustions 1. No focs a ndd to div th plants alon thi obits.. Th avitational foc of attaction du to th Sun ovs th plants in thi (naly) cicula paths.. Accodin to Nwton's thid law, th foc Eath xts on th oon is th sa as th foc th oon xts on Eath. 4. Accodin to Nwton s thid law, th ISS ust xt th sa foc on Eath. 5. Bcaus both Eath and th oon obit th Sun at th sa ava distanc, thy ust hav th sa ava acclation.. Bcaus th acclation dos not dpnd on th ass, th acclation of th appl would b th sa as that of th oon. 7. Doublin th lnth of ach sid causs th sufac aa of ach fac to incas by a facto of 4. Thfo, th total sufac aa also quadupls. This is th sa fo a sph.. Doublin th lnth of ach sid causs th volu of a solid to incas by a facto of iht. This th sa fo th sph. 9. Skip is now twic as fa fo th cnt of th plant, which ducs th avitational foc by a facto of 4. Skip wihs 00 nwtons on SU. 10. Skip is now twic as fa fo th cnt of th plant, which would duc th avitational foc by a facto of 4. Bcaus th ass is incasd by a facto of, th nt ffct is to doubl th avitational foc. Skip wihs 100 nwtons on SU. 11. Nwton did not nd to know th ass of th oon bcaus its acclation dos not dpnd on its ass. 1. Bcaus th an of th foc of avity is infinit, th spaccaft nv "lavs" Eath s avitational foc. Th contato ant that th oon's attaction fo th spaccaft was now ston that 's attaction. 1. Sinc th acclation du to avity is twic as uch on an Eath-lik plant, th univsal

2 4 Chapt 5 Gavity avitational constant in this paalll univs ust b twic as at. 14. Sinc th acclation du to avity is dictly popotional to th ass of th plant, usin a la valu of sults in an ovstiat of th plant s ass. 15. Bcaus th satllit is also ovin sidways fast nouh to atch Eath's cuvatu, it nv ts any clos to Eath s sufac. 1. Th is no countin foc hin th satllit up. Th satllit is fallin towad Eath s cnt but is ovin so fast sidways that it nv ts any clos to Eath s sufac. 17. H is in f-fall towad th cnt of Eath but is ovin so fast sidways that h nv ts any clos to Eath s sufac. It is siila to th snsation of bin in an lvato in ffall. 1. Th adin on th scal os fo you noal wiht to zo. Th foc of avity dos not chan. 19. Th passns a in ffall with th plan followin th sa tajctoy. It is siila to th cas of an lvato in ffall. 0. Eath s adius of 400 k is la copad to th xta 00 k. Th avitational foc on th astonauts is only slihtly lss (about %) than on Eath s sufac. 1. No, th foc xists as if all th ass w positiond at th cnt of ass.. Th valu of did not chan bcaus th distibution was always sphically sytic and th ass and adius did not chan.. Th avitational focs, and thfo th cospondin acclations, a vy sall. 4. Bcaus th vaiation in th foc is not usually ipotant fo otion na Eath's sufac, w us th sipl fo as it ivs a vy ood appoxiation. 5. Whil th atosphic fictional focs a sall, thy a, howv, not nliibl. As Skylab lost altitud th ffcts of th ai sistanc ot at and at.. Th obital dcay is du to fiction with th tnuous atosph at that lvation. 7. W could snd a satllit to obit Vnus and asu th satllit's obital adius and piod.. W cannot dtin th ass of th oon fo its obit bcaus th poptis of its obit do not dpnd on its ass. W could snd a satllit to obit th oon and asu th satllit's obital adius and piod. 9. W would xpct th valu of to b la bcaus th uaniu has a la ass p cubic t than th ava sufac atial. 0. You wiht incass slihtly bcaus th ass p cubic t of sho atial is la than that of wat. 1. Th would b a slow dcas in th siz of th plantay obits du to th incasin cntiptal focs.. Th adius of th oon's obit would slowly dcas du to th incasin cntiptal foc.. No, bcaus a cicula obit that would kp it dictly abov Pais dos not hav its cnt at Eath s cnt. 4. All obits ust b about Eath s cnt. Gosynchonous obits ust also b abov th quato. Iaq is about 5 ds noth of th quato. 5. Bcaus a la obit would sult in a lon obital piod, th satllit would appa to ov wstwad.. Bcaus thy a obitin Eath. 7. Eath dos follow an obit, but bcaus Eath s ass is so uch la than that of th oon, it has a uch sall obit about thi coon cnt of ass.. Th foc of Eath on th Sun is qual and opposit to th foc of th Sun on Eath. Bcaus th Sun is uch o assiv than Eath, th ffct of th foc is uch lss but still causs a wobbl in th Sun s otion.

3 Chapt 5 Gavity 5 9. Bcaus tidal buls occu on opposit sids of Eath, Japan will xpinc a low tid whn th Aican wst coast xpincs a hih tid. 40. Bcaus tidal buls occu on opposit sids of Eath, both will xpinc hih tids 41. Th ti btwn tids would b half th otational piod, 4 hous 55 inuts. 4. An infinit aount of ti as th hih tids would stay in th sa locations fov (th font and back of th oon). Th would, howv, b sconday tids du to th Sun with a piod of on onth. 4. Th nw oon occus at position d. Th avitational foc of th Sun is actin in th sa diction as th avitational foc of th oon, which tnds to ak th bul la. 44. Th full oon occus at position b. Th avitational foc of th Sun, if actin alon, would caus a siila but sall bul than that causd by th oon. In this position, th two buls a alind and th ffcts add toth to poduc a la than ava bul. 45. Th oon poducs a bul that points not only towad th oon but also away fo th oon. Th Sun dos th sa. Th ffcts will infoc to poduc a la bul as lon as th individual buls a alind. This happns with th oon and th Sun ith on th sa sid of Eath o on opposit sids. 4. Th sallst diffnc btwn hih and low tids occus at fist and thid quat oons, whn Eath, oon, and Sun fo a iht anl as shown in positions a and c. 47. Th xta tidal foc du to Jupit is inuscul and should hav no ffct. 4. Th intial ass of th wat sists th chan in otion causd by th oon, and th fictional focs slow th wat's spons vn o. 49. Th stnth of Eath's avitational fild dcass with th squa of th distanc. N k /s 50. k k s 51. This is not possibl bcaus th fild psnts th nt foc actin on a tst ass and th nt foc can only point in on diction. 5. Th acclation of all objcts is th sa indpndnt of ass. Th avitational fild is th foc on a unit ass and is indpndnt of any paticula ass. Answs to th Exciss ( 10 4 s) v a 0.00 s ( 10 s) v a 0.00 s s a.5 s 4 ( k) ( ) 1 11 N s F a G k

4 Chapt 5 Gavity F nw F 540 N 0 N nw Fnw F 0 N 0 N 1 nw nw Fnw F F F ;no F nw F 50 N 1.5 N 1 1 1nw nw ath 400 k F F F 0.5 F nw 400 k k shuttl ath ath ath ath 400 k F F F 0. F shuttl 400 k k shuttl ath ath ath N k k G k 1 F 00 N h ath 1,0 k,70 k,90 k 1. Fnw F ( 00k)( 10 s ) 1N nw F G ( 0 k) N copad to 00 N k ( 0.5 ) ath 14. F G oon 4 ( 10 k) ( k) N k F.0 10 N a s ; ys k 15. ( 100 N ) / 00 N 1. F Titan k 1.4 s 70 N c 1,0 k c ath ath ath ath 10 s. s ath c ath 0. aath

5 Chapt 5 Gavity 7 1. as 0.11 ath 10 s.9 s ath as ath 0.5 ath as ath ath ath 19. d π ( ) ,000 k d 4,000 k 1 h v.0 k s 00 s t 4 hs 00 s 0. F a k 0.5 s 44. N Fnw F 1k 10 s 40N 1 nw 10 s.5 s nw 4. nw Answs to th Pobls in Pobl Solvin ( ) 4 ( ) 7 (.1 10 s) v π π a T T s Th oon obits th Sun in th sa ti as dos Eath, and at th sa ava adius. Th acclation will b th sa. 11 ( ) 4 ( ) 7 ( s) 1 ( ) 4 ( ) 9 ( s) 9 ( π ) ( ) 4 ( s) v π π a T T s v π π a T T s v a 15.7 s T T sun 5. F G vnus 0 4 ( k) ( k) N k

6 Chapt 5 Gavity. F sun as G 0 ( k 11 )(.4 10 k) N N 11 k (. 10 ) 7. F G jupit ath. jupit ath 7 4 ( k) ( k) N k Usin th valu fo th Eath-Sun foc calculatd in Exapl 4..1, 1 Fjupit ath N % F.5 10 N sun ath F G F G ath oon sun s sun oon s s k k.4 10 F a F a a F a F a1 a a F F a F F k sat ath 1 k 9. s N sat 70 k oon ( 1k) Fna G R ath 11. F F 1. oon ath ( k) ( 1 k) N k oon ( 1k) Ffa G + R oon ath ( k) ( 1 k) N k F Fath v 0.7 vnus v 1.

7 Chapt 5 Gavity 9 F Fath 1.5 as 14. jupit j 15. F tis as uch Fath j 5. ath s 1. F Fsun s, F p p (.4 10 ) 11 N s.4 10 k G G k ( 1. N)( ) F G 11 N.7 10 ( 1 k) k W 40 N.9 s 5 k ( 4s) y s t W p k 1.5 s.5 N h d d k F 11 N k G s k F d k G s d k hath ( 1 ) 70 d v 0.95 v v 4 11 N k v G s k.7 10 ( ). 11 N k v G s k

8 70 Chapt 5 Gavity T T π π G s in π π G s 10 in (.7 10 ) k k ( ) k k k. 10 s G k T ,400 k k s G k T k ( ) GT.7 10 (. 10 s) k T T T T It would obit Eath iht tis ach day k 4 F 11 N k G N k k.7 10 o 4 0 F 11 N k G N k k.9 10

GRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6

GRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6 GVITTION 1. Two satllits and o ound a plant P in cicula obits havin adii 4 and spctivly. If th spd of th satllit is V, th spd of th satllit will b 1 V 6 V 4V V. Th scap vlocity on th sufac of th ath is