07 Gravitation Notes

P a g e 1 4 of 1 9 T he resultant field strength at a point due to m ore than one m ass can be found by the T he gravitational field strength at a point is the acceleration of free fall at that point. created it. G r av itat ion a l fiel d stren gt h is a vec tor qu a n tity an d it po i nts tow a r ds the ma s s wh i ch N ote Sh. II : e g. A lH fut ' "lwomMp(ht. ' " lsglm by ¡Æ ¡¤ ªÆ产 国ì×国 ¡£ * N x a©¥\h ߣ诈 uniform with a m agnitude of 9 . 8 1 N kg - 1 . H ence, n e a r the surface of the E aM , w e c a n c o n sider the gravitationa©¥ tield to be Ù³to be parallel to one another as shown in the figure on the right. lts centre. If we zoom In to a region near the surface of tFre E arth, the field linea e e T he figure on the left show s the field lines around E arth, w hich are directed towarda centre. F or a po©¥nt m ass or a uniform apherica©¥ m ass. The field ©¥ines are directed toward©¥ ll©¥ gravitational fie©¥d atrength wil©¥ have do©¥er or denaer field lines, a n d vice versa. T he dene©¥tv of Êö ©¥e neid linea indica©¥es ©¥t& l . A region with a ©¥©¥ronger T he direction of the neid línea ©¥ndicales the ģ clion Q t M Q i o n a ©¥ ©¥iau , gravitational force. F©¥e©¥d L ©¥nes fie©¥d ©¥lnea ©¥n which the tangent at a point on a tield ©¥ine ©¥ct©¥ ©¥n the direction ol the G rav©¥tat©¥onal A reg©¥on of gravitational neld can be vi©¥uali©¥ed as con©¥i©¥©¥lng of an ©¥rr ¡¤ y of Im ©¥glnary , - ~ " J» : Į r enceB a gravi©¥allona©¥ force ©¥là w av©¥tat©¥ona©¥ neid ©¥©¥' region of ©¥p©¥ce ©¥n w hich . M ass p©¥aced ©¥n that reglon©¥F©¥eld G rayltational 7 . 2 G ravitational F l ¡¤ ©¥d S trength g Y E A R S - ©¬ pH Y S ©¥C S D E P A R T M E N T R A FFL E S ©¥N ST ©¥TU T©¥O N

P a g e ©¥6 of 1 9 Q uestion W hat happens if the E arth spins faster about its axis of rotation? object m oving in a uniform circular m otion. A t the E quator, part of the gravitationa©¥ force provides for the centripetal force to keep the value is know n as the apparent w eight. T h e spr ing ba l an c e indi cates a value les s tha n the true we i gh t of the ob ject. T hisa T herefore, T = F . - F c . S in ce th e o bject undergoes circu©¥ar m otion, F R - F c - F . - T A pplying N ewton ' s s e c o n d law , Fn - F . - T R esultant force F n at the E q u ato r T h e sp r ing ba l an c e indi cates F. . wh ich is the true we ight of the object. T herefore, T = F , S ince there is no circular m otion, Fn - O: $ Ply" g N ewton ' " " ' " law , F n - F * - T R esultant force F at the polar region m otion at the E quator. and po©¥ar regions. H owever, T wil©¥ be di¨¤erent because the m ass undergoes circular lf the E arth is taken to be a unworm sphere, then F ©¥i the sam e at both the equator©¥a©¥ ror o \ :Ť L ) R otation w eight) and force T due to the apring . due to E arth ' = ©¥n b o th c a s e s ©¥h e re a re ©¥w o fo rce ©¥ a clln g o n m a s s - gravi©¥ationa©¥ force F , (true F ield S trength G ravltat©¥o