Presentation Transcript

1. Thelaw of gravitation

   Bytheend of thistopicyoushould be ableto: appreciatethatthereisanattractiveforcebetweenanytwopointmassesthatisdirectedalongthe line joiningthetwo mases. statethedefinition of gravitationalfieldstrength.
2. Newton’slaw of gravitation Newton’ssecondlawimpliesthat, whenevera massmoveswithacceleration, a forcemust be actingonit. Anobjectfallingfreelyundergravityisaccelerating at 9.8 ms-2 and thusexperiences a net force in thedirection of theacceleration. Thisforceistheweight of themass. Similarly, a planetthatrevolvesaroundthesunalsoexperiencesacceleration and thus a forceisactingonit.
3. Newton’slaw of gravitation Newton proposedthattheattractiveforce of gravitationbetweentwopointmassesisgivenbythe formula whereM1 and M2 are themasses of theattractivebodies, r theseparationbetweenthem and G a new constant of physicscalledNewton’sconstant of universal gravitation. It has thevalueG = 6.67 x 10-11 Nm2kg-2. Thedirectionof theforceisalongthe line joiningthetwomasses.
4. Newton’slaw of gravitation Newton provedthatforbodieswhich are spherical and of uniformdensityone can assumethattheentiremass of thebodyisconcentrated at the centre – as ifthebodyis a pointmass.
5. Newton’slaw of gravitation Theweight of a mass (mg) isactuallytheforce of gravitationalattractionbetweentheearth of massMe and themass of thebody in question. Themass of theearthisassumedto be concentrated at its centre and thusthedistancethatgoes in Newton’s formula istheradius of theearth, Re.
6. Questions Findtheforcebetweenthesun and theearth(theaveragedistanceis 1.5 x 1011m, themass of theearthis 5.98 x 1024 kg and that of thesun 1.99 x 1030 kg). Ifthedistancebetweentwobodiesisdoubled, whathappenstothegravitationalforcebetweenthem? Findtheaccelerationduetogravityon a planet 10 times as massive as theearth and withradius 20 times as large. Findtheaccelerationduetogravity at a height of 300 km fromthesurface of theearth.
7. Gravitationalfieldstrength Physicistswonderedhow a mass ‘knows’ aboutthepresence of anothermassnearbythatwillatractit. Bythe 19th century, the idea of a ‘field’ wasdeveloped. A massMissaidtocreate a gravitationalfield in thespacearoundit. Thegravitationalfieldstrength at a certainpointistheforce per unitmassexperiencedby a smallpointmass m at thatpoint. Theunits of gravitationalfieldstrength are Nkg-1.
8. Gravitationalfieldstrength Thegravitationalfieldstrengthis a vector quantitywhosedirectionisgivenbythedirection of theforce a pointmasswouldexperienceif placed at thepoint of interest. Thegravitationalfieldstrengtharound a single point M is radial, whichmeansthatitisthesameforallpointsequidistantfromthemass and isdirectedtowardsthemass.
9. Questions Twostarshavethesamedensitybutstar A has doubletheradius of star B. Determine the ratio of thegravitationalfieldstrength at thesurface of eachstar. Show thatthegravitationalfieldstrength at thesurface of a planet of densityρ has a magnitud givenbyg = 4GπρR/3.