AP Physics Gravity and Circular Motion

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Magdalene Emerald Brooks
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1 AP Phyic Gity nd icul Motion Newton theoy i ey iple. Gity i foce of ttction between ny two object tht he. Two object itting on dektop ttct ech othe with foce tht we cll gity. They don t go flying togethe becue gity i ey wek foce nd i only ignificnt when one o the othe of the e i enoou plnet ize. Thi i why we en t ttcted to object tht we p on ou dily wndeing. The ize of the foce of gity i gien by thi eqution: G 1 Newton lw of gity! 11 N " G i the uniel gittionl contnt. G 6.67 x10 kg 1 i the of one of the bodie nd i the of the othe body. i the ditnce between the two bodie. The lue of G i the e eeywhee thoughout the uniee. On the old AP Phyic Tet the eqution i witten : G G! 1 Newton lw of gity i n inee-que Lw. Thi en tht the foce of gity get lle o lge by the que of the ditnce. The foce i diectly popotionl to the e, o if the of one of the object double, the foce of gity would double. But if the ditnce doubled, the foce of gity would decee by fcto of fou. Tht becue it decee by the que of the ditnce. Inee-que lw e ey coon in phyic. We ll ee oe of the in ou explotion. To gie the pticul of the theoy: Uniel Lw of Gittion 1. Gittionl foce i field foce between two pticle -- in ll ediu.. oce ie the inee que of the ditnce 3. oce i popotionl to of object. 4. The gity foce ct fo the cente of the two object. 5. The gittionl foce i lwy ttctie. 6. The gittionl foce cnnot be hielded o cnceled. Soling gity poble i quite iple. Let do one.

2 A gil, Bndy (4.5 kg), it 1.50 fo boy (63.0 kg), Geoge. Wht i the foce of gity between the? (Thi will tell u how ttcted they e to ech othe.) G 1 ( 4.5 kg )( 63.0 kg ) "! 11 N $ # 6.67 x10 % kg & ' ( ( 1.50 )! 11! x10 N 7.94 x10 N You cn ee tht thi i tiny foce, one o ll tht Bndy will nee notice it peence. Geoge ut genete oe othe ttctie foce if thee i to be eltionhip between the two of the. One ueful ppliction of Newton lw of gity w to weigh Eth thi llowed phyicit to ke n ccute deteintion of the eth. Let do tht. ind the of the eth. e 6.38 x We will ue 10.0 kg in ou olution (not tht it tte), the othe will be tht of the eth. 1 G E Thi i the foce of gity uing Newton lw. But we know tht the foce of gity ut lo equl g, o we et the equl to one nothe: 1 Eth 1g G The of the object cncel out: g G E g Sole fo the of the eth E G ( 6.38 x10 ) x10 kg 5.98 x10 kg E "! 11 kg $ # % x $ & ( kg ) ' kg ( x10 kg 5.98 x10 kg E

3 oce nd icul Motion - In ode fo n object to undego cicul otion, foce ut ct. Pictue n object tht h oe elocity. Wht will hppen to it if no foce ct on it? Well, ccoding to the fit lw, it will continue to oe with contnt elocity. It will follow tight-line pth. To ke it chnge diection foce ut ct on it. In ode to ke it chnge diection contntly, foce ut ct on it contntly. Wht i the diection of the foce needed to do thi? Well, when you pin oething in cicle, wht do you he to do? You jut pull it towd the cente you go ound nd ound. The object get cceleted towd the cente. We cll thi the centipetl cceletion. The eqution fo the centipetl cceletion i: c c i the centipetl cceletion, i the line o tngentil peed, nd i the diu of the cicul pth. Thi eqution will be poided to you fo the AP Phyic Tet. The foce tht bing bout thi cceletion i clled the centipetl foce. It diection i lo towd the cente of the cicul pth. entipetl en "cente eeking". The centipetl foce chnge the diection of the object elocity ecto. Without it, thee would be no cicul pth. The centipetl foce i eely conenient ne fo the net foce tht i towd the cente. It i lwy cued by oething it could be cued by the foce of gity, the ection foce between the contol ufce of n iplne with the i, &tc. When you otte bll ound you hed in cicle, the centipetl foce i upplied by the tenion in the ting. Wht i the ouce of the centipetl foce tht cue cec to tel in cicul pth on the cetck? The foce i bought bout by the tie puhing on the cetck. The fiction between the od nd the tie i ey ipotnt, o ce tie e deigned to xiize fiction. Wht i the ouce of the centipetl foce equied to ke the eth eole ound the un? Thi i whee the pple flling on Newton toy fit in. Befoe Newton no one could explin the obit of the plnet nd oon. Newton, the toy goe, w elxing unde n pple tee pondeing the poble of the oon obit. He knew tht thee hd to be foce cting on the oon to cceleting it towd the eth, but hd no ide wht w the ouce of the foce. Then he w n pple fll nd the iple olution tuck hi like the old thundebolt. Jut the eth gity eched out nd de the pple fll, o it eched out nd de the oon fll. Thu, the foce tht keep the plnet nd oon following thei obitl pth i gity.

4 The AP Tet eqution heet will not gie you the eqution fo centipetl foce. It doe gie you the eqution fo centipetl cceletion. It lo gie you the eqution fo the econd lw. Uing thee two eqution you cn eily deie the foul fo centipetl foce. Hee how to do it: o plug in the lue of the centipetl cceletion:! " # $ % & Tht ll thee i to it. A c i teling t contnt peed nd ke tun with diu of It peed i15.0 /. ind the iniu coefficient of fiction needed to keep the c teling long the pth. Let look t the BD: n The fictionl foce ut equl the centipetl foce. The centipetl foce i gien by: We know tht thi ut equl the fictionl foce. We lo know tht the fictionl foce i: c g f f µ N Aue the od i flt, o n g Set the two equl to ech othe nd ole fo the coefficient of fiction: µ g µ g µ! " 1 # $ % &! " # $ % &

5 A child twil yo yo. If ngle of the cod with the eticl i 30.0, find c. Look t the foce in the y diection: 0 g y 0 T co! " g 0 T co! The hoizontl coponent of T i the centipetl foce. T in! Plug into eqution fo T: g in! g tn! We know tht: co! T 0 o g tn! g tn! 9.8 tn 30.0 o 5.66 g entipetl oce nd Gity: You y he een illy deonttion inoling bucket of wte tht w pinning in eticl cicle. The wte tyed in the bucket nd did not fll out. So wht w the del? Doe pinning oething in eticl cicle oehow cncel out gity? Well, no, gity i foce tht cnnot be topped o cnceled. It i lwy thee, nytie you he the ppopite e. The wte doe fll, it fll but the bucket fll with it nd ctche it. Thi only wok if the bucket i oing ft enough to ctch the wte. If the bucket i too low, then the wte will fll out of it. The iniu line peed fo thi i clled the citicl elocity. iticl elocity iniu elocity fo n object to tel in eticl cicle nd intin it cicul pth gint the foce of gity.

6 The e thing i needed fo tellite in obit ound the eth o plnet in obit ound the un. They too ut tel t the citicl elocity. The citicl elocity foul i not poided on the AP Tet, but it i ey iple to figue out. You jut et the centipetl foce equl to the weight of the object tht i in cicul otion. If the two foce e equl, then the object won t be ble to fll out of the bucket. nd g Set the equl to ech othe: g g g So hee i the citicl elocity g Obitl Eqution: Let u ue tht the obit of tellite bout the eth (o ny othe ie body) i cicle. Mot obit e not ctully cicle but e inted ellipe. Thi w dicoeed by Johne Kepple in the But let keep it iple nd look t cicul obit. In ode to he cicul pth, centipetl foce i equied. Thi i upplied by the foce of gity between the two bodie. So we cn et the centipetl foce equl to Newton lw of gity: G 1 gity centipetl foce Set the equl to one nothe: 1 G Notice how the of the object cnceled out. 1 1 Thi gie u n eqution fo the obitl elocity: The,, in the eqution i the of the body being obited. If we e tlking bout plnet obiting the un, then the we would ue would be tht of the un. The of the tellite cncel out, o it i not inoled in the obitl elocity eqution t ll. The eqution fo the obitl elocity will not be gien you on the AP Phyic Tet. So be peped to deie it if you need it.

7 Peiod of tellite: Thi i nothe iple deition job. The peiod of tellite i T, the tie to ke one obit. Wht would be the peiod of the eth ound the un? Let deelop the eqution fo the peiod of tellite. We ll ue the eqution fo ditnce nd ole it fo the tie: x x t t d, the ditnce teled i the cicufeence of the obit. We know tht it would be: x! So we cn plug tht in to the eqution we oled fo tie:! t but i lo gien by the eqution we jut deied fo the obitl elocity: If we plug the obitl elocity into ou woking eqution, i.e., put the togethe, we get: t! Sque both ide: 4! t len up eeything up nice nd netlike uing ou potent lgeb kill: 3 4! t 4! t t 3 4! t! 3 And we end up with n eqution fo the peiod of tellite. Agin the in the thing i the of the body being obited: t! 3

Worked Examples. v max =?

Worked Examples. v max =? Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend