Gravity 2002

8/13/2019 Gravity 2002

1/16

2002 Physics Chapter 6 Gravity Page 45

Chapter 6 Gravity

Newtons law of universal gravitation F = 22

r

!G!

N"#$%N&' ()# %F *N+,"-')( G-),+$)$+%N

Gravity is a force that e.ists throughout the *niverse/ +t a1es things fall own when you rop the3it 1eeps satellites in the orits3 it leas to ties on "arth3 it causes stars an lac1 holes to for anit will ultiately eterine the fate of the *niverse/

Newton eterine the gravity is a force of attraction that e.ists etween any two oies an that itvarie as the inverse of their separation suare an in irect proportion to their asses/ +t is a verywea1 force an only ecoes noticeale when at least one of the oects is e.treely assive/ $heforce acts eually on oth asses/

F = 2r

G! where F = gravitational force on each ass 7N8

G = universal gravitational constant!3 = asses 71g8- = istance etween the centres on the asses 7!3 8

$he *niversal Gravitational constant G = 6/69 0:N 2 1g:2

Gravitational fiel3 using g = 2

r

G!

G-),+$)$+%N)( F+"(;'For a oy on3 or aove3 the surface of the "arth3 the ass of the "arth ay e consiere to econcentrate at its centre/

Gravitational fielof "arth

Fiel strength is wea1er asthe fiel lines sprea out/

$he force etween the two oies = weight of sall oy

2r

G!= g g = 2r

G!

$hus the acceleration ue to gravity at then surface of the earth3 g3 is eterine y the ass of theearth an the raius of the earth3 not the si

8/13/2019 Gravity 2002

2/16


)t the surface of the "arth3 the gravitational fiel strength3 g3 is >/? N 1g:3 it ecoes wea1erfurther fro the "arth/ 400 1 aove the "arth g is ?/9 N 1g:3 the -ussian space station !ir oritsat this altitue/ )ustralia&s )*'')$ orits at 423000 13 where g is 0/22 N 1g:/

)ny oect that is falling freely through a gravitational fiel will fall with an acceleration eual to thegravitational fiel strength at the point/

g 7N@1g8

>/?

g r g 2r

"arth&s istance fro the centre of "arth 78

'urfaceEarth Application

Force between the Earth and Moon

Examples

2000

Halleys comet last passed by Earth in 1986. The path of this comet is elliptical.

Part of this ellipse is shown in Figre 1! with P! " and # representing three points

along the path. Point P is 1.$ 1$1%m from the &n.

Figure 1

2000 Question 1

'alclate the magnitde of the gra(itational field strength at point P de to the

&n.

-epro2uce2 4y per0ission of the ,ictorian Curriculu0 an2 )ssess0ent )uthority3 ,ictoria3 )ustralia/

Solution Q1

g is the gravitational fiel strength/ 'o usingA

2-

G!gF == $he cancels an we can write 2-

G!g = 'u the values in/

( )22B0

00/

00/2069/6g

=

g = /BB 0:4N1g:

Examiners comment Q1

$he agnitue of the suns gravitational fiel at point P calculates to /BB

0

:4

N1g:/ $his reuire a siple sustitution into the fiel strength euation/ #ith anaverage score of /5>@23 ost stuents unerstoo how to calculate the
http://var/www/apps/conversion/tmp/Applications/application/Gravity/Earth%20radius2.exehttp://var/www/apps/conversion/tmp/Applications/application/Gravity/Force%20Earth%20and%20Moon.exehttp://var/www/apps/conversion/tmp/Applications/application/Gravity/Earth%20radius2.exehttp://var/www/apps/conversion/tmp/Applications/application/Gravity/Force%20Earth%20and%20Moon.exe

8/13/2019 Gravity 2002

3/16


gravitational fiel strength/ $he ost coon error occurre as a result ofstuents neglecting to suare the istanceA that is3 they correctly wrote own theforula an sustitute in values3 ut then forgot to suare/ +t is also worthencouraging stuents to consier the li1eliness of answers 7forgetting to suare theistance otaine an answer that was too large8/

Circular orits uner gravity3 using a =r

v2= 2$

r4

')$"((+$"' +N %-+$) satellite is any oect that is in a stale orit aroun another oect/ $he "arth an all the otherplanets are natural satellites of the 'un/ $he oon is the "arth&s only natural satellite ut there arethousans of artificial satellites oriting/ $hese are use for counication3 weather forecasting3geological surveying an espionage/$he oon aroun the "arth )pplicationFor a satellite in a stale circular orit3 the only force acting on a satellite is the gravitational

attraction etween it an the central oy/ $his force acting on it is always perpenicular to itsotion/ $herefore the energy of the satellite is unchange as it orits/ $he 1inetic energy angravitational potential energy oth stay the sae/

$he force of gravity hols the satellites in their orits an causes the to have an accelerationtowars the central ass/ +f the force of gravity coul e &turne off& then the satellites woul flyoff at a tangent/ $he satellites are continually falling towars the earth at the sae rate that thecurve surface of the earth is falling away fro the satellites/

'ince satellites are in a continual state of free:fall3 their acceleration will eual the gravitational fielstrength at that point/

a =-

v2*sing v =

$

-2a =

2

2

$

-4*sing F = 2-

G!an F = g 2-

G!= g

where v = spee 7@s8 - = raius of orit 78 $ = perio of orit 7s8 ! = central ass 71g8g = gravitational fiel strength 7N@1g8/Notice that the acceleration of the satellite is inepenent of the ass of the satellite/ +f a satelliteis in a geo:stationary orit3 the satellite orits the "arth every 24 hours/ $his is a &synchronous&orit an 1eeps the satellite aove the sae place all the tie/

D"P("-&' ()#' 7not on course8+n 60>3 Depler3 a Geran astronoer3 pulishe his three laws on the otion of planets/

/ $he planets ove in elliptical orits with the 'un at one focus/2/ $he line connecting a planet to the 'un sweeps out eual areas in eual tiesB/ For every planet the ratio of the cue of the average orital raius to the suare of the perio of

revolution is the sae3

i/e/2

B

$

-= constant

)s area ) = area 3 then the tie it ta1es to ove fro - to ' is the sae as to ove fro ( to !/$he ost significant conseuence of Depler&s (aws was that the planets were no longer consiere toove in perfect circles at a constant spee/ $hey ove in elliptical paths3 the close to the sun3 thefaster they travel an the further fro the sun the slower they travel/

$he constant for the thir law coes fro F = 2-

G!=

2

2

$

-E4 2E4

G!=2

B

$

-
http://var/www/apps/conversion/tmp/Applications/application/Gravity/Moon%20around%20the%20Earth.exehttp://var/www/apps/conversion/tmp/Applications/application/Gravity/Moon%20around%20the%20Earth.exe

8/13/2019 Gravity 2002

4/16

2002 Physics Chapter 6 Gravity Page 4?

Planet -

perihelion ! aphelion

(

'

$hat is3 for a given central oy of ass !3 the ratio2

B

$

-is constant an eual to 24

G!

for all its

satellites/ Note that this is not a universal constant3 ut one that is constant for each central oy3ie/ it will e ifferent for the oon oriting the earth an the earth oriting the sun/

Examples!!1

The )ir space station orbited Earth at an altitude of *9$ +m. The total mass of the space

station was 1,$ tonnes and )ir completed 8* -$$ orbits in the 1,.6 years before it

crashed to Earth on %* )arch %$$1.

Question 1

'alclate the period of )irs orbit in seconds.


Solution Q1

+f the space station coplete ?B 500 orits in 4/6 years3 then he perio is given

yorits

8s7sectie=

?B500

606024B656/4 = 5/54 0Bsecs

5/5 0Bs

Question 2

'alclate the speed of )ir while in orbit.


'un

)

8/13/2019 Gravity 2002

5/16

2002 Physics Chapter 6 Gravity Page 4>

Solution Q

ou nee to e careful with the raius of orit/ $he station is B>0 1 aove thesurface of the "arth3 so the raius of orit is -" B>0 1/ $he units are i.e3 so

you nee to e careful/ -orit= 6/B9 06

v =

t

r2=

B

B6

05/5

80B>00B9/672

+= 990B s:= 9/9 0Bs:

Question 3

'alclate the (ale of the gra(itational field strength at *9$ +m abo(e Earths srface.


Solution Q"

'ince it is in circular otion3 a = g =r

v2where g is the gravitational fiel strength/

B6

2B

0B>00B9/6

809/97

+

6

6

096/6

02>/5>g

= = ?/9? N1g:

hen )ir was in stable orbit! an ob/ect of mass %.- +g was placed on a spring balance that

was attached to the inside of the space station.

Question 4

hat wold be the weight shown on the spring balance0 Eplain yor reasoning! or show

yor wor+ing! for determining the reading of the spring balance.


Solution Q#'ince !ir is in a stale circular orit3 an a = g3 then the reaction force fro the springalance shoul e

8/13/2019 Gravity 2002

6/16



Solution Q"

+n orer to o this uestion you nee to unerstan that the net force on thespacecraft is the gravitational force3 an that it is this gravitational force is thecentripetal force reuire to 1eep the spacecraft in orit/ $herefore you can writeA

-

v-

G!F

2

2net == ivie oth sies y

-

v

-

G! 2

2 = ties oth sies y -

2v-

G!= ta1e the suare root of oth sies

efore you su the values in a1e sure they are the right ones

(ets estalish what - isA it is the istance fro the centre of ass of the "arth to thecentre of ass of the spacecraft/ 'o its the raius of the earth plus the istance thespacecraft is aove the "arths surface/

5" 0>/-- +=

56 0>/0B9/6- += 056/6- 6=

! is the ass of the earth = 1g0>?/5 24

Now you can su the values in an you get

6

24

056/6

0>?/5069/6v

=

Bs0?/9v =

Examiners comments Q"

$he par1ing orit of )pollo is an e.aple of unifor circular otion in which the netforce is provie y the gravitational force etween "arth an )pollo / $his resulte

in a spee of 9/?

0

B

s

:

/$he average ar1 of /96@B eonstrates that ust over 50I stuents ha areasonale grasp of this concept/ +n fact3 aout half of the stuents score the full Bar1s for this uestion3 ut aout B0I score

8/13/2019 Gravity 2002

7/16


Kane was correct3 an Newtons first (aw was not ro1en/ ou ust answer theuestion y a1ing stateent aout Kane an@or !aria

Examiners comment Q#

+n orer to aress whether Kane or !aria was correct stuents were e.pecte toiscuss the following pointsJ a stateent of Newtons First (awJ the velocity of )pollo was changing 7change in irection83 hence it was acceleratingJ a net force 7gravitational force8 was acting on )pollo /$he average score here was /6@B/ +t is clear that stuents are ale to recall Newtons(aws ut were unale to apply the in a particular physical situation/ Few stuentsiscusse the net force acting on )pollo or the fact that it was accelerating/

2000 Question 5

hich one of the following statements :2;

8/13/2019 Gravity 2002

8/16


2pollo 11 then lea(es its par+ing orbit and tra(els to the )oon.

2000 Question 6

hich one of the following graphs :2;F best represents the net gravitational force

acting on 2pollo 11 as it tra(els from its par+ing orbit to the )oon0


Solution Q6

Graph C est represents the net force acting on )pollo as it travels fro the par1ingorit to the oon/ $he things to 1now woul e the force is not linear3 so 3 " an F areout3 when the force fro the "arth euals the force fro the !oon3 the spacecraft

will e closer to the oon then the "arth3 an it will not occur half way etween thetwo oects/ $his rules out ) an ; therefore C is the ost reasonale answer/


Graph C est represents the variation of the net gravitational force acting on )pollo /$he force ecreases accoring to the inverse suare law as )pollo travels away fro"arth3 reaching

8/13/2019 Gravity 2002

9/16

2002 Physics Chapter 6 Gravity Page 5B

1999

7ato >>> is a commnication satellite that has a mass of *1$ +g and orbits Earth at a

constant speed at a radis of ,.%% 1$5m from the centre of Earth.

1999 Question 1

'alclate the magnitde of Earths gra(itational field at the orbit radis of 7ato >>>.

?i(e yor answer totree significant figure

s. @o!ust

show yor wor+ing.

Figure 1-epro2uce2 4y per0ission of the ,ictorian Curriculu0 an2 )ssess0ent )uthority3 ,ictoria3 )ustralia/

Solution Q1

$he gravitational fiel strength is given y

'ustituting gives g = 29

24:

8022/47

05/>?06/69

=

0/22B>96 g = 0/224 s:2


$he agnitue of "arths gravitational fiel calculates out to 0/224 N 1g:/ $hisreuire a siple sustitution into the fiel strength euation an with an averagescore of /5@2 a aority of the stuents were ale to o this/ $he vast aority ofstuents recognise the correct forula to use an any errors were ue to using theincorrect value for the ass or eing unale to correctly anipulate the ata whenusing the calculator/ ) nuer of caniates faile to answer to three significantfigures as reueste in the uestion/

1999 Question 2

hat is the speed of 7ato >>> in its orbit0


Solution Q

$he gravitational fiel strength euals the acceleration of the satellite/ $hus

2

e

-

G!g =

B2

s009/Bv224/0-

v ==

8/13/2019 Gravity 2002

10/16


Examiners comment Q

$he spee of Nato +++ calculates to B/ . 0B s:/ $his coul have een achieve ysiply coining the forulas of *niversal Gravitation an unifor circular otion/$he average ar1 for this uestion was />@B inicating that the aority of caniatesunerstoo how to erive the necessary euation an then correctly calculate thespee/ $he euation for the spee can e erive irectly an any stuents i so/Lowever3 it was isappointing to note the nuer of stuents who starte ycalculating the perio of the orit an then eterining the spee in what was a two:step process/ $his latter etho not only waste valuale e.a tie ut increase theli1elihoo of an arithetic error as well/$his uestion also highlighte the continuing prole that any stuents have whenusing the calculator to eterine the value of e.pressions with inices/

1999 Question 3

hich one of the following statements :2;>> is correct0

A. The net force acting on 7ato >>> is Aero and therefore it does not accelerate.B. The speed is constant and therefore the net force acting on 7ato >>> is Aero.

C. There is a net force acting on 7ato >>> and therefore it is accelerating.

D. There is a net force acting on 7ato >>>! bt it has Aero acceleration.


Solution Q"

C+f there was no net force on the satellite it woul travel in a straight line rather thanorit/

Examiners comment Q"

Nato +++ is travelling in unifor circular otion an hence there is a net force3provie y the gravitational attraction to "arth3 acting towars the centre of theorit 7"arth8/ $hus3 stateent C was correct/ $he average ar1 of /0@2 eonstratesthat only 50I of caniates correctly unerstoo this concept/

"nergy transfers3 using area uner force:istance graph only

G-),+$)$+%N)( P%$"N$+)( "N"-G)s a oy gets further fro the earth3 &g& ecreases an the e.pression *g= gh is no longer

aeuate/ +f F = 2r

G!then the force isplaceent graph is Force

+f the raius of the earth is re3 then the wor1 one inraising a ass && fro the surface is given y theshae area/

er

2r

G!0r =

er

G!

re istance fro earth

8/13/2019 Gravity 2002

11/16


$he potential energy at is aritrarily ta1en as

8/13/2019 Gravity 2002

12/16


weight3 apparent weightA ass an weightA apparent weight as easure ynoral reaction N3 e.perience of weightlessness when N = 0

#"+GL$ )N; )PP)-"N$ #"+GL$

;oule:clic1 to activate/#eightless#eightless2

#eightlessB#eightless4Mass and %ei&ht

Massan wei&ht are ifferent uantities/ !ass is efine as the aount of atter in a oy3 it iseasure in 1ilogras/ +t is soeties referre to as inertia3 which is the tenency for an oect toresist acceleration/ 'ince F= a3 a larger force is neee to give a larger ass the saeacceleration/

#eight is not the sae as ass/ #eight is the force of gravity on an oect/ $he acceleration ue togravity is &g&3 so the weight of a ass && is given y F= &7newtons8/ $he aount of atter in anoect oes not change3 hence the ass of an oect is always the sae/ Lowever3 &g& varies fro

place to place on the earth&s surface epening on the istance fro the centre of the earth3 soweight oes change/

Apparent %ei&ht

#hen you are accelerating vertically3 the noral reaction force on you will not eual &g&3 this willalter your perception of your weight3 you will feel either lighter or heavier/ +f you are travelling at aconstant velocity you will feel your usual weight/ $he apparent weight of a person is eual in agnitueto the noral force &N& that the supporting surface e.erts/

N

# = g aF =

+n this case3 the person is accelerating own3 F = g :NN = g : a

$he Noral reaction force is less than g3 so the person feels lighter/+f a = g3 then the person feels &weightless&/ $his happens when the person is in &free fall& unerthe influence of gravity/
http://var/www/apps/conversion/tmp/Applications/weightless.movhttp://var/www/apps/conversion/tmp/Applications/Weightlessness%203.movhttp://var/www/apps/conversion/tmp/Applications/Weightlessness.movhttp://var/www/apps/conversion/tmp/Applications/weightlessness2.movhttp://var/www/apps/conversion/tmp/Applications/weightless.movhttp://var/www/apps/conversion/tmp/Applications/Weightlessness%203.movhttp://var/www/apps/conversion/tmp/Applications/Weightlessness.movhttp://var/www/apps/conversion/tmp/Applications/weightlessness2.mov

8/13/2019 Gravity 2002

13/16


Apparent %ei&htlessness

$rue weightlessness is only possile where the strength of the gravitational fiel is

8/13/2019 Gravity 2002

14/16

2002 Physics Chapter 6 Gravity Page 5?

Solution Q6

$he satellite was in a stale circular orit/

2r

G!=r

v2'ince v = 2r@$3 then

r

v2ecoes

2

2

r$

rE4= 2$

rE4

2r

G!=

2$

rE4! =

2

B

G$

rE4 =

24

BB

80>/57069/6

80507E4

= 6/9 05

1g

Question "

Bn the diagram below! draw one or more labelled arrows to show any force:s acting on the

spacecraft as it orbits Eros. @o can ignore any other astronomical bodies.


Solution Q'

'ince the spacecraft was in a stale orit3 the net force ust e acting raiallyinwars/ $his is the only force acting/

1999

The #ssian space station! )># :#ssian meaning!peace! is in a circlar orbit

arond Earth at a height where the gra(itational field strength is 8.5 7 +g1

.1999 Question 4

'alclate the magnitde of the gra(itational force eerted by Earth on an astronat of

mass 68 +g on board )>#.


Solution Q#

5>2 NForce = 0gso the force is 6? . ?/9 = 5>2 N O5/> . 02N in other wors3 theastronaut&s weightQ!a1e sure that you use the value for g 7given as ?/9 N 1g :3 not >/? N 1g:8

8/13/2019 Gravity 2002

15/16

2002 Physics Chapter 6 Gravity Page 5>

Examiners comment Q#

)pplication of the forula F = g resulte in a gravitational force of 5>2 N/ $heaverage score here was /4@23 ut it was isappointing to note that B0I of caniatesscore /? N 1g:rather than thegiven value of ?/9 N 1g:/

hen the astronat wishes to rest he has to lie down and strap himself into bed.

1999 Question 5

hat is the magnitde of the force that the bed eerts on the astronat before he

begins to fasten the strap0


Solutions Q$0 NForce will e @2 inicates that aout only 45I of caniatescorrectly unerstoo this concept/

7ewspaper articles abot astronats in orbit sometimes spea+ abot Aero gra(ity

when describing weightlessness.

1999 Question 6

Eplain why the astronat in the orbiting )># is not really weightless.


Solution Q6

$he astronaut is not weightless ecause the "arth is still attracting hi@her/ $heastronaut still has weight3 since # = g is the gravitational force applie to the

astronaut y the "arth/ +n this situation g is not

8/13/2019 Gravity 2002

16/16


$he average ar1 here was /5@B3 an the ain prole note was the nuer ofstuents who evote their answer to a iscussion of RweightlessnessS rather thansiply aressing why the astronaut oes have weight/

Documents

Gravity 2002