AP Physics Gravity and Circular Motion


 Magdalene Emerald Brooks
 2 years ago
 Views:
Transcription
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 ineeque 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. Ineeque 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 tightline 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 =?
Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a eicicula 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
More informationA package travels along a conveyor belt as shown in Figure Q1(a). At the instant shown, it has a speed of 0.5 m/s and a rate of increase in speed of
pckge tels long coneyo belt s shown in Figue Q(). t the instnt shown, it hs speed of.5 /s nd te of incese in speed of t =.3 /s. (i) Deteine its speed when it ies t point (ii) Deteine the gnitude of its
More informationOrbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
More informationPHYSICS 151 Notes for Online Lecture #10
PHYSICS 5 Note for Online Lecture # Kinetic decribe the otion Dynic decribe the cue of the otion orce  Up to now, we ve been nlyzing otion, but not conidering how otion occur. Now we re redy to tke into
More informationGRAVITATION 1. BASIC FORCES IN NATURE
GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle
More informationG.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS
G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit
More informationUniversity Physics AI No. 1 Rectilinear Motion
Uniesity Physics AI No. Rectiline Motion Clss Numbe Nme I.Choose the Coect Answe. An object is moing long the is with position s function of time gien by (. Point O is t. The object is efinitely moing
More information(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
More informationVEHICLE PLANAR DYNAMICS BICYCLE MODEL
Auptions Do, VEHE PANA DYNAMS BYE MODE o tel, (esued o instntneous cente o ottion O) o Yw, (wt Globl Ais) ongitudinl elocit is ued to be constnt. Sll slip ngles, i.e. ties opete in the line egion. No
More informationChapter 4 2D and 3D Motion
Chpe 4 D nd 3D Moon I. Defnon II. Poecle oon III. Unfo ccul oon IV. Nonunfo ccul oon V. Rele oon Poon eco: eend fo he on of coodne e o he pcle. 4. k z 4. k z z I. Defnon Aee eloc: 4.3 k z Dplceen eco:
More informationPhysics 110 Spring 2006 Forces in 1 and 2Dimensions Their Solutions
Phic 110 Spring 006 orce in 1 nd Dienion heir Solution 1. wo orce 1 nd ct on 5kg. I the gnitude o 1 nd re 0 nd 15 repectivel wht re the ccelertion o ech o the e elow?.. 0; ( 0 ) + ( 15 ) 1 5kg 15 @ θ
More informationLaplace s Equation on a Disc
LECTURE 15 Lplce s Eqution on Disc Lst time we solved the Diichlet poblem fo Lplce s eqution on ectngul egion. Tody we ll look t the coesponding Diichlet poblem fo disc. Thus, we conside disc of dius 1
More informationv o a y = = * Since H < 1m, the electron does not reach to the top plate.
. The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the
More informationr Curl is associated w/rotation X F
13.5 ul nd ivegence ul is ssocited w/ottion X F ivegence is F Tody we define two opetions tht cn e pefomed on vecto fields tht ply sic ole in the pplictions of vecto clculus to fluid flow, electicity,
More informationMath 1105: Calculus II (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 5
Mth 5: Clculus II Mth/Sci mjos) MWF m / pm, Cmpion 35 Witten homewok 5 6.6, p. 458 3,33), 6.7, p. 467 8,3), 6.875), 7.58,6,6), 7.44,48) Fo pctice not to tun in): 6.6, p. 458,8,,3,4), 6.7, p. 467 4,6,8),
More information2.016 Hydrodynamics Prof. A.H. Techet
.016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting
More informationSummary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
More informationr (1+cos(θ)) sin(θ) C θ 2 r cos θ 2
icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:
More informationIntro to Circle Geometry By Raymond Cheong
Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationMAGNETIC FIELD AROUND CURRENTCARRYING WIRES. point in space due to the current in a small segment ds. a for field around long wire
MAGNETC FELD AROUND CURRENTCARRYNG WRES How will we tckle this? Pln: 1 st : Will look t contibution d to the totl mgnetic field t some point in spce due to the cuent in smll segment of wie iotsvt Lw
More informationPHYS 4110 Dynamics of Space Vehicles
PHYS 40 Dynmics of Sce Vehicles Chte 7: Obitl Mneues Eth, Moon, Ms, nd eyond D. Jinjun Shn, Pofesso of Sce Engineeing Detment of Eth nd Sce Science nd Engineeing Room 55, Petie Science nd Engineeing uilding
More informationLesson 8.1 Areas of Rectangles and Parallelograms
Leon 8.1 e of Rectngle nd Pllelogm 1. Find the e of the hded egion.. Find the e of the hded egion. 17 cm 9 cm 5 cm 8 cm 1.5 cm 13 cm cm cm 3. Rectngle D h e 684 m nd width 44 m. Find it length. 4. Find.
More information(d) False. The orbital period of a planet is independent of the planet s mass.
hpte Gvity onceptul Pobles ue o flse: () (b) (c) (d) o Keple s lw of equl es to be vlid, the foce of vity ust vy invesely with the sque of the distnce between iven nd the. he closest to the hs the shotest
More informationLesson 8.1 Areas of Rectangles and Parallelograms
Leon 8.1 Ae of Rectngle nd Pllelogm In Eecie 1 4, find the e of the hded egion. 1.. 1 1 cm 3. 17 cm 4. 9 cm 5 cm 1.5 cm cm 5. Rectngle ABCD h e 684 m nd width 44 m. Find it length. 6. Dw pllelogm with
More informationFormulas and Units. Transmission technical calculations Main Formulas. Size designations and units according to the SIunits.
Fomuls nd Units Tnsmission technicl clcultions Min Fomuls Size designtions nd units ccoding to the SIunits Line movement: s v = m/s t s = v t m s = t m v = m/s t P = F v W F = m N Rottion ω = π f d/s
More informationExam in physics, Elgrunder (Electromagnetism), 20140326, kl 9.0015.00
Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, Elgunde (Electomgnetism, 146, kl 9.15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue
More information10. Collisions. Before During After
10. Collisions Use conseation of momentum and enegy and the cente of mass to undestand collisions between two objects. Duing a collision, two o moe objects exet a foce on one anothe fo a shot time: F(t)
More informationOnline Homework 12 Solution
Online Homewok Solution Electic nd Mgnetic Field Vectos Conceptul Question Pt A The electic nd mgnetic field vectos t specific point in spce nd time e illustted. Bsed on this infomtion, in wht diection
More information32. The Tangency Problem of Apollonius.
. The Tngeny olem of Apollonius. Constut ll iles tngent to thee given iles. This eleted polem ws posed y Apollinius of eg (. 6070 BC), the getest mthemtiin of ntiquity fte Eulid nd Ahimedes. His mjo wok
More informationN V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 witeup. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
More informationCh. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth
Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,
More informationBasically, logarithmic transformations ask, a number, to what power equals another number?
Wht i logrithm? To nwer thi, firt try to nwer the following: wht i x in thi eqution? 9 = 3 x wht i x in thi eqution? 8 = 2 x Biclly, logrithmic trnformtion k, number, to wht power equl nother number? In
More informationPY1052 Problem Set 3 Autumn 2004 Solutions
PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationCurvature. (Com S 477/577 Notes) YanBin Jia. Oct 8, 2015
Cuvtue Com S 477/577 Notes YnBin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.
More informationAP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time.
AP QUIZ # GRAPHING MOTION ) POSITION TIME GRAPHS DISPLAEMENT Ech grph below shows the position of n object s function of time. A, B,, D, Rnk these grphs on the gretest mgnitude displcement during the time
More informationCypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
More information7 Circular Motion. 71 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary
7 Cicula Motion 71 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o
More informationChapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.11 T) i to ue a lage cuent flowing though a wie.
More informationPhys 207. Announcements. Hwk3 is posted on course website Quizzes & answers will be posted on course website Formula sheets.
Phys 07 Announcements Hwk3 is posted on course website Quizzes & nswers will be posted on course website ormul sheets Newton s 3 lws Tody s Agend How nd why do objects move? Dynmics 1 Dynmics Isc Newton
More informationMechanics 1: Motion in a Central Force Field
Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.
More informationSECTION 54 Trigonometric Functions
Tigonometic Functions 78. Engineeing. In Polem 77, though wht ngle in dins will the ck wheel tun if the font wheel tuns though dins? The c length on cicle is esy to compute if the coesponding centl ngle
More informationVersion 001 Summer Review #03 tubman (IBII20142015) 1
Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This printout should he 35 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03
More informationChapter 4 Newton s Laws
Chpte 4 Newton s Lws Conceptul Pobles While on ve sooth level tnscontinentl plne fliht, ou coffee cup sits otionless on ou t. Ae thee foces ctin on the cup? If so, how do the diffe fo the foces tht would
More informationMagnetism: a new force!
1 Magnetism: a new foce! o fa, we'e leaned about two foces: gaity and the electic field foce. F E = E, FE = E Definition of Efield kq Efields ae ceated by chages: E = 2 Efield exets a foce on othe
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationSolution to Problem Set 1
CSE 5: Introduction to the Theory o Computtion, Winter A. Hevi nd J. Mo Solution to Prolem Set Jnury, Solution to Prolem Set.4 ). L = {w w egin with nd end with }. q q q q, d). L = {w w h length t let
More informationHomework Solutions Unit 4: Chapter 22 CMPSC 465
Homeok Solution Unit : Chapte CMPSC 65 Diclaime: Thi i a daft of olution that ha been pepaed b the TA and the intucto make no guaantee that olution peented hee contain the leel of detail that ould be expected
More informationPHYSICS 218 Honors EXAM 2 Retest. Choose 5 of the following 6 problems. Indicate which problem is not to be graded.
PHYSICS 18 Honos EXAM Retest Choose 5 of the following 6 pobles. Indicate which poble is not to be gaded. 1. A ope is affixed at one end to the i of a pulley, and wapped five tuns aound the pulley. The
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationASTR 170! 2010 S1 " Daniel Zucker! E7A 317 Mathematics as a tool for understanding physics
A New Scientific Er Grity nd Tides ASTR 170! 2010 S1 " Dniel Zucker! E7A 317 Mthemtics s tool for understnding physics zucker@science.mq.edu.u! 1 2 Velocity nd Accelertion Isc Newton (16431727)! Building
More informationMath 22B Solutions Homework 1 Spring 2008
Mth 22B Solutions Homework 1 Spring 2008 Section 1.1 22. A sphericl rindrop evportes t rte proportionl to its surfce re. Write differentil eqution for the volume of the rindrop s function of time. Solution
More information1. CIRCULAR MOTION. ω =
1. CIRCULAR MOION 1. Calculate the angula elocity and linea elocity of a tip of minute hand of length 1 cm. 6 min. 6 6 s 36 s l 1 cm.1 m ω?? Fomula : ω π ω ω π 3.14 36 ω 1.744 1 3 ad/s ω.1 1.74 1 3 1.74
More informationChapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43
Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.
More informationChapter 23 Electrical Potential
hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is
More informationVectors. Graphical Representation of a Vector
Vector There i a great teptation to put ector tailtotail when ou go to add the. Ma all the battle that ou wage in our war againt that teptation end with our gloriou triuph. Vector add headtotail. We
More informationTwo special Righttriangles 1. The
Mth Right Tringle Trigonometry Hndout B (length of )  c  (length of side ) (Length of side to ) Pythgoren s Theorem: for tringles with right ngle ( side + side = ) + = c Two specil Righttringles. The
More informationv T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his printout should he 5 questions. Multiplechoice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationExponents base exponent power exponentiation
Exonents We hve seen counting s reeted successors ddition s reeted counting multiliction s reeted ddition so it is nturl to sk wht we would get by reeting multiliction. For exmle, suose we reetedly multily
More informationCircles and Tangents with Geometry Expressions
icles nd Tngents with eomety xpessions IRLS N TNNTS WITH OMTRY XPRSSIONS... INTROUTION... 2 icle common tngents... 3 xmple : Loction of intesection of common tngents... 4 xmple 2: yclic Tpezium defined
More informationWell say we were dealing with a weak acid K a = 1x10, and had a formal concentration of.1m. What is the % dissociation of the acid?
Chpter 9 Buffers Problems 2, 5, 7, 8, 9, 12, 15, 17,19 A Buffer is solution tht resists chnges in ph when cids or bses re dded or when the solution is diluted. Buffers re importnt in Biochemistry becuse
More informationTRAJECTORIES AND TRAJECTORIES AND MISN072 RADIUS, VELOCITY, ACCELERATION. by James M. Tanner, Georgia Institute of Technology
MIS72 TRAJECTORIES AD RADIUS, VELOCITY, ACCELERATIO TRAJECTORIES AD RADIUS, VELOCITY, ACCELERATIO by Jmes M. Tnne, Geogi Institute of Technology 1. Kinemtics nd Its Uses. Motion is Eeywhee...................................
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More informationGravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
More informationMechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
More informationSHAPES AND SHAPE WORDS!
1 Pintbl Activity Pg 1 SAPES AND SAPE WORDS! (bst fo 1 o plys) Fo ch child (o pi of childn), you will nd: wo copis of pgs nd Cyons Scissos Glu stick 10 indx cds Colo nd Mk Shp Cds! Giv ch child o pi of
More informationGeometry 71 Geometric Mean and the Pythagorean Theorem
Geometry 71 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the
More informationAnswer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1
Answe, Key Homewok 6 vid McInye 4513 M 5, 004 1 This pinou should hve 0 quesions. Muliplechoice quesions my coninue on he nex column o pge find ll choices befoe mking you selecion. The due ime is Cenl
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More information10.5 Graphing Quadratic Functions
0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions
MSSCHUSES INSIUE OF ECHNOLOGY Deprtment of hysics 8.0 W02D3_0 Group roblem: ulleys nd Ropes Constrint Conditions Consider the rrngement of pulleys nd blocks shown in the figure. he pulleys re ssumed mssless
More informationPhysics 111 Fall 2007 Electrostatic Forces and the Electric Field  Solutions
Physics 111 Fall 007 Electostatic Foces an the Electic Fiel  Solutions 1. Two point chages, 5 µc an 8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationExponentiation: Theorems, Proofs, Problems Pre/Calculus 11, Veritas Prep.
Exponentition: Theorems, Proofs, Problems Pre/Clculus, Verits Prep. Our Exponentition Theorems Theorem A: n+m = n m Theorem B: ( n ) m = nm Theorem C: (b) n = n b n ( ) n n Theorem D: = b b n Theorem E:
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More information. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2
7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6
More informationPhysics 110 Spring 2006 Rotational Dynamics Their Solutions
Phyc 0 Spng 006 Roonl Dync The Soluon. An objec o e nd oe couneclockwe wh conn ngul cceleon nd eche n ngul peed o / n. Wh he ngul cceleon o he wheel? Wh he ngle (n n hough whch he objec oe n h e? α α θ
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationNewton s Shell Theorem
Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheicallyymmetic maive bodie (like planet,
More informationLesson 12.1 Trigonometric Ratios
Lesson 12.1 rigonometric Rtios Nme eriod Dte In Eercises 1 6, give ech nswer s frction in terms of p, q, nd r. 1. sin 2. cos 3. tn 4. sin Q 5. cos Q 6. tn Q p In Eercises 7 12, give ech nswer s deciml
More informationSolution Derivations for Capa #8
Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationThe Quadratic Formula and the Discriminant
99 The Qudrtic Formul nd the Discriminnt Objectives Solve qudrtic equtions by using the Qudrtic Formul. Determine the number of solutions of qudrtic eqution by using the discriminnt. Vocbulry discriminnt
More informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
More information1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s
Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 1 This printout should he 30 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. The due time
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More information4.0 5Minute Review: Rational Functions
mth 130 dy 4: working with limits 1 40 5Minute Review: Rtionl Functions DEFINITION A rtionl function 1 is function of the form y = r(x) = p(x) q(x), 1 Here the term rtionl mens rtio s in the rtio of two
More informationNumerical Solutions of Linear Systems of Equations
EE 6 Clss Notes Numericl Solutions of Liner Systems of Equtions Liner Dependence nd Independence An eqution in set of equtions is linerly independent if it cnnot e generted y ny liner comintion of the
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationChapter 9: Quadratic Equations
Chpter 9: Qudrtic Equtions QUADRATIC EQUATIONS DEFINITION + + c = 0,, c re constnts (generlly integers) ROOTS Synonyms: Solutions or Zeros Cn hve 0, 1, or rel roots Consider the grph of qudrtic equtions.
More informationMon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,34 Magnetic Force
Mon., 3/9 Tues., 3/10 Wed., 3/11 Thus., 3/12 Fi., 3/ 13 Mon., 3/16 Tues., 3/17 Wed., 3/18 Thus., 3/19 Fi., 3/20 20.1,34 Magnetic Foce 20.2,5 Cuent and Motional Emf Quiz Ch 19, Lab 8 Cycloton & Electon
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationThe Chain Rule. rf dx. t t lim " (x) dt " (0) dx. df dt = df. dt dt. f (r) = rf v (1) df dx
The Chin Rule The Chin Rule In this section, we generlize the chin rule to functions of more thn one vrible. In prticulr, we will show tht the product in the singlevrible chin rule extends to n inner
More informationThe Casino Experience. Let us entertain you
The Csio Expeiee Let us eteti you The Csio Expeiee If you e lookig fo get ight out, Csio Expeiee is just fo you. 10 The Stight Flush Expeiee 25 pe peso This is get itodutio to gmig tht sves you moey Kik
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More information