AP Phyic Gavity Si Iaac Newton i cedited with the dicovey of gavity. Now, of coue we know that he didn t eally dicove the thing let face it, people knew about gavity fo a long a thee have been people. Gavity didn t have to be dicoveed fo cying out loud! You baic tiny little toddle figue it out in the fit few onth of life. So what i the big deal with Newton and gavity? Well, what Newton did wa to decibe gavity, extend it effect fo the uface of the eath (which eveyone undetood) out into pace to explain the behavio of the planet (which nobody upected), and to foulate a atheatical law that accuately decibed the foce of gavity between object with a. Pehap the geatet ucce of hi theoy of gavity wa to uccefully explain the otion of the heaven planet, oon, &tc. Newton theoy i vey iple. Gavity i a foce of attaction between any two object that have a. Two object itting on a dektop attact each othe with a foce that we call gavity. They don t go flying togethe becaue gavity i a vey weak foce and i only ignificant when one o the othe of the ae i enoou planet ize. Thi i why we aen t attacted to object that we pa on ou daily wandeing. The ize of the foce of gavity i given by thi equation: F G 1 Newton law of gavity 11 N G i the univeal gavitational contant. G 6.67 x10 1 i the a of one of the bodie and i the a of the othe body. i the ditance between the two bodie. The value of G i the ae eveywhee thoughout the univee. On the old AP Phyic Tet the equation i witten a: F G G 1 155
Newton law of gavity i an invee-quae Law. Thi ean that the foce of gavity get alle o lage by the quae of the ditance. The foce i diectly popotional to the ae, o if the a of one of the object double, the foce of gavity would double. But if the ditance doubled, the foce of gavity would deceae by a facto of fou. That becaue it deceae by the quae of the ditance. Invee-quae law ae vey coon in phyic. We ll ee oe of the in ou exploation. To give the paticula of the theoy: Univeal Law of Gavitation 1. Gavitational foce i a field foce between two paticle -- in all ediu.. Foce vaie a the invee quae of the ditance 3. Foce i popotional to a of object. 4. The gavity foce act fo the cente of the two object. 5. The gavitational foce i alway attactive. 6. The gavitational foce cannot be hielded o canceled. Solving gavity poble i quite iple. Let do one. A gil, Bandy (4.5 ), it 1.50 fo a boy (63.0 ), Geoge. What i the foce of gavity between the? (Thi will tell u how attacted they ae to each othe.) F G 1 F 6.67 x10 11 N 4.5 63.0 1.50 11 8 F 7940 x10 N 7.94 x10 N You can ee that thi i a tiny foce, one o all that Bandy will neve, notice it peence. Geoge ut geneate oe othe attactive foce if thee i to be a elationhip between the two of the. One ueful application of Newton law of gavity wa to weigh Eath thi allowed phyicit to ake an accuate deteination of the eath a. Let do that. Find the a of the eath. e = 6.38 x 10 6. We will ue a 10.0 a in ou olution (not that it atte), the othe a will be that of the eath. 1 F G E Thi i the foce of gavity uing Newton law. But we know that the foce of gavity ut alo equal F = g, o we et the equal to one anothe: 1 Eath 1 g G The a of the object cancel out: E g G 156
g Solve fo the a of the eath E G 6 9.8 6.38 x10 3 4 E 59.8x10 5.98x10 11 6.67 x10 10.0 3 4 59.8x10 5.98x10 E Cente of Gavity: A tone eting on the gound i acted upon by gavity. In fact, evey ato within the ock i attacted to the eath. The u of all thee foce i the thing that we call weight. Wouldn t it be a eal pain to have to add up evey ingle vecto fo evey ingle ato in an object in ode to find out what it weighed? Well fotunately, we don t have to do that. Natue ot of doe it fo u. Baically the vecto all add togethe to give u one big vecto, the weight vecto, which i diected down and which act at a point whee all the weight appea to be concentated. Thi point i called the cente of gavity. Fo an object like a unifo phee, the cente of gavity, o CG, i located at it geoetic cente. Iegula object, like, ay, you aveage baeball bat would have thei CG located cloe to the fat end of the bat athe than the cente. The dot epeent the CG of the object in the dawing below: The weight of thee object, e.g., the vecto we call weight, i applied at the CG. When a ball i thown in the ai, it follow a paabolic path. Actually, what follow thi paabolic path i the CG of the ball. Thi i alo tue fo iegula object that ae thown. If you thow a cecent wench o that it pin when you eleae it, it ee to follow a vey eatic path. It CG, howeve, tace out a nice ooth paabola. 157
All iegula object otate about thei CG when thown. Let do oe oe gavity poble. You weigh 567 N on eath. How uch would you weigh on Ma? Fit we ut calculate the a by uing the weight on eath: W g W g 1 567 57.86 9.8 Now we need only find the foce of gavity between ou peon and Ma. Fo the ditance we ue the adiu of Ma, ince the peon i on the uface of Ma and the foce of gavity act at the cente of the planet. 3 6.4 x10 57.86 N F G 6.67 x10 18 N 1 11 6 3.37 x 10 What i the acceleation of gavity on Venu? We know: F a and F G 1 a G 1 4 4.88 x10 11 1 6 a 6.67 x10 0.886 x10 8.86 6.06 x10 158
The acceleation on Venu would be lightly alle than the acceleation on eath. AP Quetion: We e eviiting one we aleady looked ove, but thi tie we can analyze it on Ma. The Sojoune ove vehicle wa ued to exploe the uface of Ma a pat of the Pathfinde iion in 1997. Ue the data in the table below to anwe the quetion that follow. Sojoune Data Ma of Sojoune vehicle: Wheel diaete: Stoed enegy available: Powe equied fo diving unde aveage condition: Land peed: 11.5 0.13 5.4 x l0 5 J 10 W 6.7 x 10-3 / Ma Data Radiu: Ma: 0.53 x Eath' adiu 0.11 x Eath' a (a) Deteine the acceleation due to gavity at the uface of Ma in te of g, the acceleation due to gavity at the uface of Eath. Foce and a ae diectly popotional to each othe. Foce i inveely popotional to the adiu quaed. We et up the popotion fo g, the acceleation of gavity on eath. g Ma g Ma Ma g Ma 0.11 9.8 3.8 0.53 159
(b) Calculate Sojoune' weight on the uface of Ma. wga 11.5 3.84 44 N (c) Aue that when leaving the Pathfinde pacecaft Sojoune oll down a ap inclined at 0 to the hoizontal. The ap ut be lightweight but tong enough to uppot Sojoune. Calculate the iniu noal foce that ut be upplied by the ap. 1. Daw a FBD: ngma co 0 n gma co n11.5 3.8 co 0.0 41 N (d) What i the net foce on Sojoune a it tavel aco the Matian uface at contant velocity? Jutify you anwe. Zeo. If it i taveling at contant velocity in the x diection then thee i no acceleation and no net foce.. The foce of gavity i cancelled by the noal foce eulting in no otion in the y diection. (e) Deteine the axiu ditance that Sojoune can tavel on a hoizontal Matian uface uing it toed enegy. W W 5 1 4 P t 5.4 x10 J 5.4 x10 t P J 10 x 3 4 v xvt 6.7 x10 5.4 x10 360 t (f). Suppoe that 0.010% of the powe fo diving i expended againt atopheic dag a Sojoune tavel on the Matian uface. Calculate the agnitude of the dag foce. P 0.00010 10W 0.001W g Ma q in q n q g Ma P Fv F P 0.001W v 3 6.7 10 0.149N 160