DYNAMICS. Kinetics of Particles: Newton s Second Law VECTOR MECHANICS FOR ENGINEERS: Ninth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
|
|
- Rose Murphy
- 5 years ago
- Views:
Transcription
1 Ninth E CHPTER VECTOR MECHNICS OR ENGINEERS: DYNMICS edinnd P. ee E. Russell Johnston, J. Lectue Notes: J. Wlt Ole Texs Tech Univesity Kinetics of Pticles: Newton s Second Lw The McGw-Hill Copnies, Inc. ll ights eseved.
2 Vecto Mechnics fo Enginees: Dynics Contents Intoduction Newton s Second Lw of Motion Line Moentu of Pticle Systes of Units Equtions of Motion Dynic Equilibiu Sple Poble. Sple Poble.3 Sple Poble.4 Sple Poble.5 Sple Poble.6 ngul Moentu of Pticle Equtions of Motion in Rdil & Tnsvese Coponents Consevtion of ngul Moentu Newton s Lw of Gvittion Sple Poble.7 Sple Poble.8 Tjectoy of Pticle Unde Centl oce ppliction to Spce Mechnics Sple Poble.9 Keple s Lws of Plnety Motion The McGw-Hill Copnies, Inc. ll ights eseved. -
3 Vecto Mechnics fo Enginees: Dynics Intoduction Newton s fist nd thid lws e sufficient fo the study of bodies t est (sttics) o bodies in otion with no cceletion. When body cceletes (chnges in velocity gnitude o diection), Newton s second lw is equied to elte the otion of the body to the foces cting on it. Newton s second lw: - pticle will hve n cceletion popotionl to the gnitude of the esultnt foce cting on it nd in the diection of the esultnt foce. - The esultnt of the foces cting on pticle is equl to the te of chnge of line oentu of the pticle. - The su of the oents bout O of the foces cting on pticle is equl to the te of chnge of ngul oentu of the pticle bout O. The McGw-Hill Copnies, Inc. ll ights eseved. - 3
4 Vecto Mechnics fo Enginees: Dynics Newton s Second Lw of Motion Newton s Second Lw: If the esultnt foce cting on pticle is not zeo, the pticle will hve n cceletion popotionl to the gnitude of esultnt nd in the diection of the esultnt. Conside pticle subjected to constnt foces, 3 constnt ss, 3 When pticle of ss is cted upon by foce, the cceletion of the pticle ust stisfy cceletion ust be evluted with espect to Newtonin fe of efeence, i.e., one tht is not cceleting o otting. If foce cting on pticle is zeo, pticle will not ccelete, i.e., it will ein sttiony o continue on stight line t constnt velocity. The McGw-Hill Copnies, Inc. ll ights eseved. - 4
5 Vecto Mechnics fo Enginees: Dynics Line Moentu of Pticle Replcing the cceletion by the deivtive of the velocity yields dv dt d dl v dt dt L line oentu of the pticle Line Moentu Consevtion Pinciple: If the esultnt foce on pticle is zeo, the line oentu of the pticle eins constnt in both gnitude nd diection. The McGw-Hill Copnies, Inc. ll ights eseved. - 5
6 Vecto Mechnics fo Enginees: Dynics Systes of Units Of the units fo the fou piy diensions (foce, ss, length, nd tie), thee y be chosen bitily. The fouth ust be coptible with Newton s nd Lw. Intentionl Syste of Units (SI Units): bse units e the units of length (), ss (kg), nd tie (second). The unit of foce is deived, N kg s kg s U.S. Custoy Units: bse units e the units of foce (lb), length (), nd tie (second). The unit of ss is deived, lb lb 3. ft s lb slug ft s lbs ft The McGw-Hill Copnies, Inc. ll ights eseved. - 6
7 Vecto Mechnics fo Enginees: Dynics Equtions of Motion Newton s second lw povides Solution fo pticle otion is fcilitted by esolving vecto eqution into scl coponent equtions, e.g., fo ectngul coponents, i j k i j k x x x y x x z y y y y x o tngentil nd nol coponents, t t t dv dt n n n v y z z z z z The McGw-Hill Copnies, Inc. ll ights eseved. - 7
8 Vecto Mechnics fo Enginees: Dynics Dynic Equilibiu The McGw-Hill Copnies, Inc. ll ights eseved. ltente expession of Newton s second lw, inetil vecto With the inclusion of the inetil vecto, the syste of foces cting on the pticle is equivlent to zeo. The pticle is in dynic equilibiu. Methods developed fo pticles in sttic equilibiu y be pplied, e.g., copln foces y be epesented with closed vecto polygon. Ineti vectos e often clled inetil foces s they esue the esistnce tht pticles offe to chnges in otion, i.e., chnges in speed o diection. Inetil foces y be conceptully useful but e not like the contct nd gvittionl foces found in sttics. - 8
9 Vecto Mechnics fo Enginees: Dynics Sple Poble. SOLUTION: Resolve the eqution of otion fo the block into two ectngul coponent equtions. -lb block ests on hoizontl plne. ind the gnitude of the foce P equied to give the block n cceletion o ft/s to the ight. The coefficient of kinetic fiction between the block nd plne is k.5. Unknowns consist of the pplied foce P nd the nol ection N fo the plne. The two equtions y be solved fo these unknowns. The McGw-Hill Copnies, Inc. ll ights eseved. - 9
10 Vecto Mechnics fo Enginees: Dynics Sple Poble. y O x W g lbs 6. ft N k.5n lb 3.ft s SOLUTION: Resolve the eqution of otion fo the block into two ectngul coponent equtions. x : y P cos3.5n : 6.lbs ft ft s 6.lb N Psin3 lb Unknowns consist of the pplied foce P nd the nol ection N fo the plne. The two equtions y be solved fo these unknowns. N Psin3 lb P cos3.5 Psin3 lb 6.lb P 5lb The McGw-Hill Copnies, Inc. ll ights eseved. -
11 Vecto Mechnics fo Enginees: Dynics Sple Poble.3 SOLUTION: Wite the kinetic eltionships fo the dependent otions nd cceletions of the blocks. Wite the equtions of otion fo the blocks nd pulley. The two blocks shown stt fo est. The hoizontl plne nd the pulley e fictionless, nd the pulley is ssued to be of negligible ss. Deteine the cceletion of ech block nd the tension in the cod. Cobine the kinetic eltionships with the equtions of otion to solve fo the cceletions nd cod tension. The McGw-Hill Copnies, Inc. ll ights eseved. -
12 Vecto Mechnics fo Enginees: Dynics Sple Poble.3 O y x SOLUTION: Wite the kinetic eltionships fo the dependent otions nd cceletions of the blocks. Wite equtions of otion fo blocks nd pulley. x T kg : y y y : 3kg 9.8 s T 3kg T T x g T 94N - C C T : 3kg The McGw-Hill Copnies, Inc. ll ights eseved. -
13 Vecto Mechnics fo Enginees: Dynics Sple Poble.3 O y x Cobine kinetic eltionships with equtions of otion to solve fo cceletions nd cod tension. y T T T x kg 94N - 3kg 94N - T T 3kg T 94 N 5kg kg 8.4 kg T s N s 84 N The McGw-Hill Copnies, Inc. ll ights eseved. - 3
14 Vecto Mechnics fo Enginees: Dynics Sple Poble.4 SOLUTION: The block is constined to slide down the wedge. Theefoe, thei otions e dependent. Expess the cceletion of block s the cceletion of wedge plus the cceletion of the block eltive to the wedge. The -lb block stts fo est nd slides on the 3-lb wedge, which is suppoted by hoizontl sufce. Wite the equtions of otion fo the wedge nd block. Solve fo the cceletions. Neglecting fiction, deteine () the cceletion of the wedge, nd (b) the cceletion of the block eltive to the wedge. The McGw-Hill Copnies, Inc. ll ights eseved. - 4
15 Vecto Mechnics fo Enginees: Dynics Sple Poble.4 y x SOLUTION: The block is constined to slide down the wedge. Theefoe, thei otions e dependent. Wite equtions of otion fo wedge nd block. : x x y N.5N sin3 W N x W sin3 y g cos3 : W g cos3 cos3 g sin3 sin3: W cos3 3 W g sin The McGw-Hill Copnies, Inc. ll ights eseved. - 5
16 Vecto Mechnics fo Enginees: Dynics Sple Poble.4 Solve fo the cceletions..5n W g N W cos3 W g sin3 W g W cos3 W g gw cos3 W W sin3 3. ft s lbcos3 3lb lbsin3 5.7ft sin3 s cos3 g sin3 5.7 ft s cos3 3. ft s sin3.5ft s The McGw-Hill Copnies, Inc. ll ights eseved. - 6
17 Vecto Mechnics fo Enginees: Dynics Sple Poble.5 SOLUTION: Resolve the eqution of otion fo the bob into tngentil nd nol coponents. Solve the coponent equtions fo the nol nd tngentil cceletions. The bob of - pendulu descibes n c of cicle in veticl plne. If the tension in the cod is.5 ties the weight of the bob fo the position shown, find the velocity nd cceletion of the bob in tht position. Solve fo the velocity in tes of the nol cceletion. The McGw-Hill Copnies, Inc. ll ights eseved. - 7
18 Vecto Mechnics fo Enginees: Dynics Sple Poble.5 SOLUTION: Resolve the eqution of otion fo the bob into tngentil nd nol coponents. Solve the coponent equtions fo the nol nd tngentil cceletions. : g sin3 t t n n : t g sin3.5g n g t t.5 cos3 4.9 g cos3 n n s 6.3 Solve fo velocity in tes of nol cceletion. n v v n 6.3 s v 5.66 s s The McGw-Hill Copnies, Inc. ll ights eseved. - 8
19 Vecto Mechnics fo Enginees: Dynics Sple Poble.6 SOLUTION: The c tvels in hoizontl cicul pth with nol coponent of cceletion diected towd the cente of the pth.the foces cting on the c e its weight nd nol ection fo the od sufce. Deteine the ted speed of highwy cuve of dius = 4 ft bnked though n ngle q = 8 o. The ted speed of bnked highwy cuve is the speed t which c should tvel if no ltel fiction foce is to be exeted t its wheels. Resolve the eqution of otion fo the c into veticl nd nol coponents. Solve fo the vehicle speed. The McGw-Hill Copnies, Inc. ll ights eseved. - 9
20 Vecto Mechnics fo Enginees: Dynics Sple Poble.6 SOLUTION: The c tvels in hoizontl cicul pth with nol coponent of cceletion diected towd the cente of the pth.the foces cting on the c e its weight nd nol ection fo the od sufce. Resolve the eqution of otion fo the c into veticl nd nol coponents. y : R cosq W W R cosq n n : Rsinq W g W sinq cosq Solve fo the vehicle speed. v g tnq n W g 3. ft s 4ft tn8 v v 64.7ft s 44.i h The McGw-Hill Copnies, Inc. ll ights eseved. -
21 Vecto Mechnics fo Enginees: Dynics ngul Moentu of Pticle The McGw-Hill Copnies, Inc. ll ights eseved. H O V oent of oentu o the ngul oentu of the pticle bout O. H O is pependicul to plne contining nd V H O V sin i j k vq HO x y z q v v v Deivtive of ngul oentu with espect to tie, H O V V V V M O It follows fo Newton s second lw tht the su of the oents bout O of the foces cting on the pticle is equl to the te of chnge of the ngul oentu of the pticle bout O. x y z -
22 Vecto Mechnics fo Enginees: Dynics Eqs of Motion in Rdil & Tnsvese Coponents Conside pticle t nd q, in pol coodintes, q q q q q This esult y lso be deived fo consevtion of ngul oentu, H O q q q d q dt q q q q The McGw-Hill Copnies, Inc. ll ights eseved. -
23 Vecto Mechnics fo Enginees: Dynics Consevtion of ngul Moentu When only foce cting on pticle is diected towd o wy fo fixed point O, the pticle is sid to be oving unde centl foce. Since the line of ction of the centl foce psses though O, M O H O nd V H constnt O Position vecto nd otion of pticle e in plne pependicul to. H O Mgnitude of ngul oentu, H O V sin constnt o H O H O V sin q q h constnt ngul oentu unit ss The McGw-Hill Copnies, Inc. ll ights eseved. - 3
24 Vecto Mechnics fo Enginees: Dynics Consevtion of ngul Moentu Rdius vecto OP sweeps infinitesil e d dq Define d dt dq dt q el velocity Recll, fo body oving unde centl foce, h q constnt When pticle oves unde centl foce, its el velocity is constnt. The McGw-Hill Copnies, Inc. ll ights eseved. - 4
25 Vecto Mechnics fo Enginees: Dynics Newton s Lw of Gvittion Gvittionl foce exeted by the sun on plnet o by the eth on stellite is n ipotnt exple of gvittionl foce. Newton s lw of univesl gvittion - two pticles of ss M nd ttct ech othe with equl nd opposite foce diected long the line connecting the pticles, M G G constnt of gvittion kg s ft 4 lbs o pticle of ss on the eth s sufce, W MG R g ft g s s 4 The McGw-Hill Copnies, Inc. ll ights eseved. - 5
26 Vecto Mechnics fo Enginees: Dynics Sple Poble.7 block of ss cn slide feely on fictionless O which ottes in hoizontl plne t constnt te q. Knowing tht is elesed t distnce fo O, expess s function of ) the coponent v of the velocity of long O, nd b) the gnitude of the hoizontl foce exeted on by the O. SOLUTION: Wite the dil nd tnsvese equtions of otion fo the block. Integte the dil eqution to find n expession fo the dil velocity. Substitute known infotion into the tnsvese eqution to find n expession fo the foce on the block. The McGw-Hill Copnies, Inc. ll ights eseved. - 6
27 Vecto Mechnics fo Enginees: Dynics Sple Poble.7 SOLUTION: Wite the dil nd tnsvese equtions of otion fo the block. : q : q q q q Integte the dil eqution to find n expession fo the dil velocity. v v v v dv dv dv dt v q q dv d dv dt d d d dt dv d q d v q v dv d d dt v dv d Substitute known infotion into the tnsvese eqution to find n expession fo the foce on the block. q The McGw-Hill Copnies, Inc. ll ights eseved. - 7
28 Vecto Mechnics fo Enginees: Dynics Sple Poble.8 SOLUTION: Since the stellite is oving unde centl foce, its ngul oentu is constnt. Equte the ngul oentu t nd nd solve fo the velocity t. stellite is lunched in diection pllel to the sufce of the eth with velocity of 88 i/h fo n ltitude of 4 i. Deteine the velocity of the stellite s it eches it xiu ltitude of 34 i. The dius of the eth is 396 i. The McGw-Hill Copnies, Inc. ll ights eseved. - 8
29 Vecto Mechnics fo Enginees: Dynics Sple Poble.8 SOLUTION: Since the stellite is oving unde centl foce, its ngul oentu is constnt. Equte the ngul oentu t nd nd solve fo the velocity t. vsin H v v v O v constnt i h i i v 55i h The McGw-Hill Copnies, Inc. ll ights eseved. - 9
30 Vecto Mechnics fo Enginees: Dynics Tjectoy of Pticle Unde Centl oce o pticle oving unde centl foce diected towds foce cente, q q q q Second expession is equivlent to q h h d nd dq q h constnt, fo which, fte substituting into the dil eqution of otion nd siplifying, d u u whee u dq h u If is known function of o u, then pticle tjectoy y be found by integting fo u = f(q), with constnts of integtion deteined fo initil cons. The McGw-Hill Copnies, Inc. ll ights eseved. - 3
31 Vecto Mechnics fo Enginees: Dynics ppliction to Spce Mechnics Conside eth stellites subjected to only gvittionl pull of the eth, d u u dq d u u dq h h GM u whee constnt u Solution is eqution of conic section, GM u h GM GMu cosq eccenticity Ch GM Oigin, locted t eth s cente, is focus of the conic section. Tjectoy y be ellipse, pbol, o hypebol depending on vlue of eccenticity. The McGw-Hill Copnies, Inc. ll ights eseved. - 3
32 Vecto Mechnics fo Enginees: Dynics ppliction to Spce Mechnics Tjectoy of eth stellite is defined by GM h cosq eccenticity Ch GM hypebol, > o C > GM/h. The dius vecto becoes infinite fo GM cosq q cos cos C h pbol, = o C = GM/h. The dius vecto becoes infinite fo cosq q 8 ellipse, < o C < GM/h. The dius vecto is finite fo q nd is constnt, i.e., cicle, fo <. The McGw-Hill Copnies, Inc. ll ights eseved. - 3
33 Vecto Mechnics fo Enginees: Dynics ppliction to Spce Mechnics Integtion constnt C is deteined by cons t beginning of fee flight, q =, =, GM Ch h GM GM C h cos GM v Stellite escpes eth obit fo v esc o v C GM GM h GM Tjectoy is elliptic fo v < v esc nd becoes cicul fo = o C =, v cic GM v The McGw-Hill Copnies, Inc. ll ights eseved. - 33
34 Vecto Mechnics fo Enginees: Dynics ppliction to Spce Mechnics Recll tht fo pticle oving unde centl foce, the el velocity is constnt, i.e., d q h constnt dt Peiodic tie o tie equied fo stellite to coplete n obit is equl to e within the obit divided by el velocity, b b h h whee b The McGw-Hill Copnies, Inc. ll ights eseved. - 34
35 Vecto Mechnics fo Enginees: Dynics Sple Poble.9 stellite is lunched in diection pllel to the sufce of the eth with velocity of 36,9 k/h t n ltitude of 5 k. Deteine: ) the xiu ltitude eched by the stellite, nd b) the peiodic tie of the stellite. SOLUTION: Tjectoy of the stellite is descibed by GM h C cosq Evlute C using the initil cons t q =. Deteine the xiu ltitude by finding t q = 8 o. With the ltitudes t the peigee nd pogee known, the peiodic tie cn be evluted. The McGw-Hill Copnies, Inc. ll ights eseved. - 35
36 Vecto Mechnics fo Enginees: Dynics Sple Poble.9 v GM s s s k k /k 369 h 36s/h h v gr 3 s s SOLUTION: Tjectoy of the stellite is descibed by GM C cosq h Evlute C using the initil cons t q =. GM C h s 3 s The McGw-Hill Copnies, Inc. ll ights eseved. - 36
37 Vecto Mechnics fo Enginees: Dynics Sple Poble.9 Deteine the xiu ltitude by finding t q = 8 o. GM h C s k x ltitude s k 63 k With the ltitudes t the peigee nd pogee known, the peiodic tie cn be evluted. b b h s 9h 3in 6 s The McGw-Hill Copnies, Inc. ll ights eseved. - 37
38 Vecto Mechnics fo Enginees: Dynics Keple s Lws of Plnety Motion Results obtined fo tjectoies of stellites ound eth y lso be pplied to tjectoies of plnets ound the sun. Popeties of plnety obits ound the sun wee deteined stonoicl obsevtions by Johnn Keple (57-63) befoe Newton hd developed his fundentl theoy. ) Ech plnet descibes n ellipse, with the sun locted t one of its foci. ) The dius vecto dwn fo the sun to plnet sweeps equl es in equl ties. 3) The sques of the peiodic ties of the plnets e popotionl to the cubes of the seijo xes of thei obits. The McGw-Hill Copnies, Inc. ll ights eseved. - 38
ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law
ME 141 Engineering Mechnics Lecture 10: Kinetics of prticles: Newton s nd Lw Ahmd Shhedi Shkil Lecturer, Dept. of Mechnicl Engg, BUET E-mil: sshkil@me.buet.c.bd, shkil6791@gmil.com Website: techer.buet.c.bd/sshkil
More information6. Gravitation. 6.1 Newton's law of Gravitation
Gvittion / 1 6.1 Newton's lw of Gvittion 6. Gvittion Newton's lw of gvittion sttes tht evey body in this univese ttcts evey othe body with foce, which is diectly popotionl to the poduct of thei msses nd
More information10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =
Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon
More informationE S dition event Vector Mechanics for Engineers: Dynamics h Due, next Wednesday, 07/19/2006! 1-30
Vector Mechnics for Engineers: Dynmics nnouncement Reminders Wednesdy s clss will strt t 1:00PM. Summry of the chpter 11 ws posted on website nd ws sent you by emil. For the students, who needs hrdcopy,
More informationPicking Coordinate Axes
Picing Coodinte Axes If the object you e inteested in Is cceleting Choose one xis long the cceletion Su of Foce coponents long tht xis equls Su of Foce coponents long ny othe xis equls 0 Clcultions e esie
More informationSOLUTIONS TO CONCEPTS CHAPTER 11
SLUTINS T NEPTS HPTE. Gvittionl fce of ttction, F.7 0 0 0.7 0 7 N (0.). To clculte the gvittionl fce on t unline due to othe ouse. F D G 4 ( / ) 8G E F I F G ( / ) G ( / ) G 4G 4 D F F G ( / ) G esultnt
More informationChapter 2. Review of Newton's Laws, Units and Dimensions, and Basic Physics
Chpte. Review of Newton's Lws, Units nd Diensions, nd Bsic Physics You e ll fili with these ipotnt lws. But which e bsed on expeients nd which e ttes of definition? FIRST LAW n object oves unifoly (o eins
More informationEquations from the Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk
Equtions fo the illenniu heoy of Ineti nd vity Copyight 004 Joseph A. Rybzyk ollowing is oplete list of ll of the equtions used o deived in the illenniu heoy of Ineti nd vity. o ese of efeene the equtions
More informationRadial geodesics in Schwarzschild spacetime
Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using
More informationAlgebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016
Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw
More informationAnswers to test yourself questions
Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E
More informationChapter 12. Kinetics of Particles: Newton s Second Law
Chapte 1. Kinetics of Paticles: Newton s Second Law Intoduction Newton s Second Law of Motion Linea Momentum of a Paticle Systems of Units Equations of Motion Dynamic Equilibium Angula Momentum of a Paticle
More informationUNIT VII Central Force: Review Key
UNIT VII Centl oce: Review Key. Which of the following tteent e tue of n object oving in cicle t contnt peed? Include ll tht pply.. The object expeience foce which h coponent diected pllel to the diection
More informationOn the Eötvös effect
On the Eötvös effect Mugu B. Răuţ The im of this ppe is to popose new theoy bout the Eötvös effect. We develop mthemticl model which loud us bette undestnding of this effect. Fom the eqution of motion
More information13.5. Torsion of a curve Tangential and Normal Components of Acceleration
13.5 osion of cuve ngentil nd oml Components of Acceletion Recll: Length of cuve '( t) Ac length function s( t) b t u du '( t) Ac length pmetiztion ( s) with '( s) 1 '( t) Unit tngent vecto '( t) Cuvtue:
More information1. A man pulls himself up the 15 incline by the method shown. If the combined mass of the man and cart is 100 kg, determine the acceleration of the
1. n pulls hiself up the 15 incline b the ethod shown. If the cobined ss of the n nd ct is 100 g deteine the cceletion of the ct if the n eets pull of 50 on the ope. eglect ll fiction nd the ss of the
More informationU>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
More informationr a + r b a + ( r b + r c)
AP Phsics C Unit 2 2.1 Nme Vectos Vectos e used to epesent quntities tht e chcteized b mgnitude ( numeicl vlue with ppopite units) nd diection. The usul emple is the displcement vecto. A quntit with onl
More informationSection 35 SHM and Circular Motion
Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.
More informationSolutions to Midterm Physics 201
Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of
More information( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept.
Physics Lectue 3 (Wlke: Ch. 6.4-5) Connected Objects Cicul Motion Centipetl Acceletion Centipetl Foce Sept. 30, 009 Exmple: Connected Blocks Block of mss m slides on fictionless tbletop. It is connected
More informationB 20 kg. 60 kg A. m s, m k
1. he sste is elesed o est with the cble tut. o the iction coeicients s =.5 nd =. clculte the cceletion o ech bod nd the tension in the cble. eglect the sll ss nd iction o the pulles.(3/9) s 6 g 3 g W
More information(a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information
m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque
More informationπ,π is the angle FROM a! TO b
Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two
More informationEnergy Dissipation Gravitational Potential Energy Power
Lectue 4 Chpte 8 Physics I 0.8.03 negy Dissiption Gvittionl Potentil negy Powe Couse wesite: http://fculty.uml.edu/andiy_dnylov/teching/physicsi Lectue Cptue: http://echo360.uml.edu/dnylov03/physicsfll.html
More informationPhysics 1502: Lecture 2 Today s Agenda
1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics
More informationPhysics 111 Lecture 04. Force and Motion I: The Laws of Motion. SJ 8th Ed.: Ch Newton s First Law: zero net force
Phsics Lectue 04 oce nd Motion I: he Lws of Motion SJ 8th Ed.: Ch. 5. 5.7 Dnics - Soe histo oce Cuses Acceletion ewton s ist Lw: zeo net foce Mss ewton s Second Lw ee Bod Digs Gvittion ewton s hid Lw Appliction
More informationFriedmannien equations
..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions
More informationGet Solution of These Packages & Learn by Video Tutorials on EXERCISE-1
FEE Downlod Study Pckge fom website: www.tekoclsses.com & www.mthsbysuhg.com Get Solution of These Pckges & Len by Video Tutoils on www.mthsbysuhg.com EXECISE- * MAK IS MOE THAN ONE COECT QUESTIONS. SECTION
More informationChapter 4 Kinematics in Two Dimensions
D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Kinemtics in Two Dimensions D Motion Pemble In this chpte, we ll tnsplnt the
More informationChapter 4 Two-Dimensional Motion
D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Two-Dimensionl Motion D Motion Pemble In this chpte, we ll tnsplnt the conceptul
More informationPhysics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468
ics Announcements dy, embe 28, 2004 Ch 6: Cicul Motion - centipetl cceletion Fiction Tension - the mssless sting Help this week: Wednesdy, 8-9 pm in NSC 128/119 Sundy, 6:30-8 pm in CCLIR 468 Announcements
More informationAQA Maths M2. Topic Questions from Papers. Circular Motion. Answers
AQA Mths M Topic Questions fom Ppes Cicul Motion Answes PhysicsAndMthsTuto.com PhysicsAndMthsTuto.com Totl 6 () T cos30 = 9.8 Resolving veticlly with two tems Coect eqution 9.8 T = cos30 T =.6 N AG 3 Coect
More informationMATHEMATICS IV 2 MARKS. 5 2 = e 3, 4
MATHEMATICS IV MARKS. If + + 6 + c epesents cicle with dius 6, find the vlue of c. R 9 f c ; g, f 6 9 c 6 c c. Find the eccenticit of the hpeol Eqution of the hpeol Hee, nd + e + e 5 e 5 e. Find the distnce
More information1 Using Integration to Find Arc Lengths and Surface Areas
Novembe 9, 8 MAT86 Week Justin Ko Using Integtion to Find Ac Lengths nd Sufce Aes. Ac Length Fomul: If f () is continuous on [, b], then the c length of the cuve = f() on the intevl [, b] is given b s
More informationChapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
More informationChapter 28 Sources of Magnetic Field
Chpte 8 Souces of Mgnetic Field - Mgnetic Field of Moving Chge - Mgnetic Field of Cuent Element - Mgnetic Field of Stight Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent
More information1. The sphere P travels in a straight line with speed
1. The sphee P tels in stight line with speed = 10 m/s. Fo the instnt depicted, detemine the coesponding lues of,,,,, s mesued eltie to the fixed Oxy coodinte system. (/134) + 38.66 1.34 51.34 10sin 3.639
More information( ) ( ) ( ) ( ) ( ) # B x ( ˆ i ) ( ) # B y ( ˆ j ) ( ) # B y ("ˆ ( ) ( ) ( (( ) # ("ˆ ( ) ( ) ( ) # B ˆ z ( k )
Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i
More information(A) 6.32 (B) 9.49 (C) (D) (E) 18.97
Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10
More informationElectric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
More informationFluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoil-like thn poblem nd leds you though conceptul development of Benoulli s eqution using the ides of Newton s 2 nd lw nd enegy. You e going
More information+ r Position Velocity
1. The phee P tel in tight line with contnt peed of =100 m/. Fo the intnt hown, detemine the coeponding lue of,,,,, eltie to the fixed Ox coodinte tem. meued + + Poition Velocit e 80 e 45 o 113. 137 d
More informationCHAPTER 5: Circular Motion; Gravitation
CHAPER 5: Cicula Motion; Gavitation Solution Guide to WebAssign Pobles 5.1 [1] (a) Find the centipetal acceleation fo Eq. 5-1.. a R v ( 1.5 s) 1.10 1.4 s (b) he net hoizontal foce is causing the centipetal
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
More informationCHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD
ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons
More informationEWTO S LAWS OF MOTIO ewton 1 st lw o Lw of Ineti Evey body continues to be in its stte of est o of unifom motion until nd unless nd until it is compelled by n extenl foce to chnge its stte of est o of
More informationSatellite Orbits. Orbital Mechanics. Circular Satellite Orbits
Obitl Mechnic tellite Obit Let u tt by king the quetion, Wht keep tellite in n obit ound eth?. Why doen t tellite go diectly towd th, nd why doen t it ecpe th? The nwe i tht thee e two min foce tht ct
More informationRELATIVE KINEMATICS. q 2 R 12. u 1 O 2 S 2 S 1. r 1 O 1. Figure 1
RELAIVE KINEMAICS he equtions of motion fo point P will be nlyzed in two diffeent efeence systems. One efeence system is inetil, fixed to the gound, the second system is moving in the physicl spce nd the
More informationTwo dimensional polar coordinate system in airy stress functions
I J C T A, 9(9), 6, pp. 433-44 Intentionl Science Pess Two dimensionl pol coodinte system in iy stess functions S. Senthil nd P. Sek ABSTRACT Stisfy the given equtions, boundy conditions nd bihmonic eqution.in
More informationComparative Studies of Law of Gravity and General Relativity. No.1 of Comparative Physics Series Papers
Comptive Studies of Lw of Gvity nd Genel Reltivity No. of Comptive hysics Seies pes Fu Yuhu (CNOOC Resech Institute, E-mil:fuyh945@sin.com) Abstct: As No. of comptive physics seies ppes, this ppe discusses
More informationThe Formulas of Vector Calculus John Cullinan
The Fomuls of Vecto lculus John ullinn Anlytic Geomety A vecto v is n n-tuple of el numbes: v = (v 1,..., v n ). Given two vectos v, w n, ddition nd multipliction with scl t e defined by Hee is bief list
More informationSURFACE TENSION. e-edge Education Classes 1 of 7 website: , ,
SURFACE TENSION Definition Sufce tension is popety of liquid by which the fee sufce of liquid behves like stetched elstic membne, hving contctive tendency. The sufce tension is mesued by the foce cting
More informationSpring-Pendulum Dynamic System
Sping-endulum Dynmic System echtonics Sping-endulum Dynmic System 1 esuements, Clcultions, nufctue's Specifictions odel mete ID Which metes to Identify? Wht Tests to efom? hysicl System hysicl odel th
More informationAssistant Professor: Zhou Yufeng. N , ,
Aitnt Pofeo: Zhou Yufeng N3.-0-5, 6790-448, yfzhou@ntu.edu.g http://www3.ntu.edu.g/home/yfzhou/coue.html . A pojectile i fied t flling tget hown. The pojectile lee the gun t the me intnt tht the tget dopped
More informationOptimization. x = 22 corresponds to local maximum by second derivative test
Optimiztion Lectue 17 discussed the exteme vlues of functions. This lectue will pply the lesson fom Lectue 17 to wod poblems. In this section, it is impotnt to emembe we e in Clculus I nd e deling one-vible
More informationCh. 4: FOC 9, 13, 16, 18. Problems 20, 24, 38, 48, 77, 83 & 115;
WEEK-3 Recitation PHYS 3 eb 4, 09 Ch. 4: OC 9, 3,, 8. Pobles 0, 4, 38, 48, 77, 83 & 5; Ch. 4: OC Questions 9, 3,, 8. 9. (e) Newton s law of gavitation gives the answe diectl. ccoding to this law the weight
More informationMAGNETIC EFFECT OF CURRENT & MAGNETISM
TODUCTO MAGETC EFFECT OF CUET & MAGETM The molecul theo of mgnetism ws given b Webe nd modified lte b Ewing. Oested, in 18 obseved tht mgnetic field is ssocited with n electic cuent. ince, cuent is due
More informationLecture 10. Solution of Nonlinear Equations - II
Fied point Poblems Lectue Solution o Nonline Equtions - II Given unction g : R R, vlue such tht gis clled ied point o the unction g, since is unchnged when g is pplied to it. Whees with nonline eqution
More informationChapter 2: Electric Field
P 6 Genel Phsics II Lectue Outline. The Definition of lectic ield. lectic ield Lines 3. The lectic ield Due to Point Chges 4. The lectic ield Due to Continuous Chge Distibutions 5. The oce on Chges in
More informationGEOMETRY Properties of lines
www.sscexmtuto.com GEOMETRY Popeties of lines Intesecting Lines nd ngles If two lines intesect t point, ten opposite ngles e clled veticl ngles nd tey ve te sme mesue. Pependicul Lines n ngle tt mesues
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationHomework: 5, 9, 19, 25, 31, 34, 39 (p )
Hoework: 5, 9, 19, 5, 31, 34, 39 (p 130-134) 5. A 3.0 kg block is initilly t rest on horizontl surfce. A force of gnitude 6.0 nd erticl force P re then pplied to the block. The coefficients of friction
More informationPX3008 Problem Sheet 1
PX38 Poblem Sheet 1 1) A sphee of dius (m) contins chge of unifom density ρ (Cm -3 ). Using Guss' theoem, obtin expessions fo the mgnitude of the electic field (t distnce fom the cente of the sphee) in
More informationGeneral Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface
Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to
More informationN for static friction and N
Fiction: Epeimentll the following fetues e obseed to be tue of the foce of fiction: ) Fiction lws opposes the motion. The foce is dissiptie nd its diection is pllel to the sufce of the object in motion.
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationHomework: Study 6.2 #1, 3, 5, 7, 11, 15, 55, 57
Gols: 1. Undestnd volume s the sum of the es of n infinite nume of sufces. 2. Be le to identify: the ounded egion the efeence ectngle the sufce tht esults fom evolution of the ectngle ound n xis o foms
More informationPhys101 Lecture 4,5 Dynamics: Newton s Laws of Motion
Phys101 Lecture 4,5 Dynics: ewton s Lws of Motion Key points: ewton s second lw is vector eqution ction nd rection re cting on different objects ree-ody Digrs riction Inclines Ref: 4-1,2,3,4,5,6,7,8,9.
More informationWork, Potential Energy, Conservation of Energy. the electric forces are conservative: ur r
Wok, Potentil Enegy, Consevtion of Enegy the electic foces e consevtive: u Fd = Wok, Potentil Enegy, Consevtion of Enegy b b W = u b b Fdl = F()[ d + $ $ dl ] = F() d u Fdl = the electic foces e consevtive
More informationB.A. (PROGRAMME) 1 YEAR MATHEMATICS
Gdute Couse B.A. (PROGRAMME) YEAR MATHEMATICS ALGEBRA & CALCULUS PART B : CALCULUS SM 4 CONTENTS Lesson Lesson Lesson Lesson Lesson Lesson Lesson : Tngents nd Nomls : Tngents nd Nomls (Pol Co-odintes)
More informationCHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES
HPTER ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy So,. foce between chges 4 So, foce between chges.6 weight of
More informationr = (0.250 m) + (0.250 m) r = m = = ( N m / C )
ELECTIC POTENTIAL IDENTIFY: Apply Eq() to clculte the wok The electic potentil enegy of pi of point chges is given y Eq(9) SET UP: Let the initil position of q e point nd the finl position e point, s shown
More informationPhysics 111 Lecture 5 Circular Motion
Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight
More informationLecture 23: Central Force Motion
Lectue 3: Cental Foce Motion Many of the foces we encounte in natue act between two paticles along the line connecting the Gavity, electicity, and the stong nuclea foce ae exaples These types of foces
More informationCHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton
Downloe fo HPTER? ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy.5 So, foce between chges 4 So, foce between chges
More informationForce can be exerted by direct contact between bodies: Contact Force.
Chapte 4, Newton s Laws of Motion Chapte IV NEWTON S LAWS OF MOTION Study of Dynamics: cause of motion (foces) and the esistance of objects to motion (mass), also called inetia. The fundamental Pinciples
More informationJEE(Advanced) 2018 TEST PAPER WITH SOLUTION PHYSICS. (HELD ON SUNDAY 20 th MAY, 2018) PART-1 : PHYSICS. (C) L = mkr ALLEN
JEE(Advnced) 08 TEST PAPE WITH SOUTION (HED ON SUNDAY 0 th MAY, 08) PAT- : JEE(Advnced) 08/Ppe-. The potentil enegy of pticle of mss m t distnce fom fixed point O is given by V () k /, whee k is positive
More information1121 T Question 1
1121 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, tavelling on the sae path in the sae diection as you, at a constant speed
More informationChap 5. Circular Motion: Gravitation
Chap 5. Cicula Motion: Gavitation Sec. 5.1 - Unifom Cicula Motion A body moves in unifom cicula motion, if the magnitude of the velocity vecto is constant and the diection changes at evey point and is
More informationVECTOR MECHANICS FOR ENGINEERS: STATICS
4 Equilibium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Fedinand P. Bee E. Russell Johnston, J. of Rigid Bodies Lectue Notes: J. Walt Ole Texas Tech Univesity Contents Intoduction Fee-Body Diagam
More informationSTD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0
STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed
More informationMark Scheme (Results) January 2008
Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question
More informationElectric Field F E. q Q R Q. ˆ 4 r r - - Electric field intensity depends on the medium! origin
1 1 Electic Field + + q F Q R oigin E 0 0 F E ˆ E 4 4 R q Q R Q - - Electic field intensity depends on the medium! Electic Flux Density We intoduce new vecto field D independent of medium. D E So, electic
More informationTopics for Review for Final Exam in Calculus 16A
Topics fo Review fo Finl Em in Clculus 16A Instucto: Zvezdelin Stnkov Contents 1. Definitions 1. Theoems nd Poblem Solving Techniques 1 3. Eecises to Review 5 4. Chet Sheet 5 1. Definitions Undestnd the
More informationChapter 6 Thermoelasticity
Chpte 6 Themoelsticity Intoduction When theml enegy is dded to n elstic mteil it expnds. Fo the simple unidimensionl cse of b of length L, initilly t unifom tempetue T 0 which is then heted to nonunifom
More informationPhysics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
More informationELECTRO - MAGNETIC INDUCTION
NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s
More informationCollection of Formulas
Collection of Fomuls Electomgnetic Fields EITF8 Deptment of Electicl nd Infomtion Technology Lund Univesity, Sweden August 8 / ELECTOSTATICS field point '' ' Oigin ' Souce point Coulomb s Lw The foce F
More information6. Numbers. The line of numbers: Important subsets of IR:
6. Nubes We do not give n xiotic definition of the el nubes hee. Intuitive ening: Ech point on the (infinite) line of nubes coesponds to el nube, i.e., n eleent of IR. The line of nubes: Ipotnt subsets
More informationEN40: Dynamics and Vibrations. Midterm Examination Tuesday March
EN4: Dynaics and Vibations Midte Exaination Tuesday Mach 8 16 School of Engineeing Bown Univesity NME: Geneal Instuctions No collaboation of any kind is peitted on this exaination. You ay bing double sided
More informationNewton s Laws, Kepler s Laws, and Planetary Orbits
Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion
More informationME 236 Engineering Mechanics I Test #4 Solution
ME 36 Enineein Mechnics I est #4 Slutin Dte: id, M 14, 4 ie: 8:-1: inutes Instuctins: vein hptes 1-13 f the tetbk, clsed-bk test, clcults llwed. 1 (4% blck ves utwd ln the slt in the pltf with speed f
More informationF 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation
Physics 201, Lectue 22 Review Today s Topics n Univesal Gavitation (Chapte 13.1-13.3) n Newton s Law of Univesal Gavitation n Popeties of Gavitational Foce n Planet Obits; Keple s Laws by Newton s Law
More informationPhys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j.
7. We denote the two foces F A + F B = ma,sof B = ma F A. (a) In unit vecto notation F A = ( 20.0 N)ˆ i and Theefoe, Phys 201A Homewok 6 Solutions F A and F B. Accoding to Newton s second law, a = [ (
More informationChapter 1. Model Theory
Chte odel heo.. Intoduction Phsicl siultion of hdulic henoenon, such s the flow ove sillw, in the lboto is clled hsicl odel o onl odel. Potote is the hdulic henoen in the ntue like the sillw ove d. odels
More informationThis immediately suggests an inverse-square law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
More information1.4 Using Newton s laws, show that r satisfies the differential equation 2 2
EN40: Dnmics nd Vibtions Homewok 3: Solving equtions of motion fo pticles School of Engineeing Bown Univesit. The figue shows smll mss m on igid od. The sstem stts t est with 0 nd =0, nd then the od begins
More information