AP Physics Electromagnetic Wrap Up


 Howard Fields
 4 years ago
 Views:
Transcription
1 AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle is the angle between the field and the elocity, q epesents the chage of the paticle. If the elocity is F Ilsin pependicula to the field, then you hae a maximum foce and it is simply equal to F q. This is the equation fo the magnitude of the foce exeted on a staight length of wie by a magnetic field. Whee F is the magnetic foce, I is the cuent, l is the length of the wie, and is the angle between the wie and the magnetic field. 0I This is the magnetic field stength aound a staight section of a cuent caying conducto. is the magnetic field stength, 0 is the pemeability of fee space, I is the cuent, and is the distance to the cente of the conducto. The alue fo the pemeability of fee space is: x10 T m A m A Acos This is the equation fo magnetic flux. m is the magnetic flux, is the magnetic field stength, A is the aea of the loop, and is the angle between and a nomal to the plane of the loop. ag m t This is the equation fo induced emf. ag is the induced emf, m is the change in magnetic flux, and t is the change in time. l This is the equation fo the induced emf in a loop of width l that is moing into o out of a magnetic field at a elocity. 430
2 Hee s what you gots to be able to do: Magnetostatics 1. Foces on Moing Chages in Magnetic Field a. You should undestand the foce expeienced by a chaged paticle in a magnetic field so you can: (1) Calculate the magnitude and diection of the foce in tems of q,, and, and explain why the magnetic foce can pefom no wok. Okay, this is simply using the old F qsin equation. The magnetic foce can pefom no wok because the diection of the magnetic foce is always pependicula to the motion of the paticle, so the wok is always zeo. () Deduce the diection of a magnetic field fom infomation about the foces expeienced by chaged paticles moing though that field. This is simply the old ight hand ule. (3) State and apply the fomula fo the adius of the cicula path of a chage that moes pependicula to a unifom magnetic field, and deie this fomula fom Newton s Second Law and the magnetic foce law. To do this, you simply deie the fomula fo the centipetal foce and set it equal to the magnetic foce. Sole fo the adius. The handout is quite happy to show you how to do this. (4) Descibe the most geneal path possible fo a chaged paticle moing in a unifom magnetic field, and descibe the motion of a paticle that entes a unifom magnetic field moing with specified initial elocity. The most geneal path is a helix spial kind of deal. If the paticle s elocity is pependicula to the field, then the paticle will follow a cicula path. (5) Descibe quantitatiely unde what conditions paticles will moe with constant elocity though cossed electic and magnetic fields. The deal hee is that the two foces, the electic and magnetic foces, must somehow add up to zeo if the paticle is to hae a constant elocity. So the foces hae to be the same magnitude and be in opposite diections. Since the electic foce is in the diection of the electic field and the magnetic foce is pependicula to the magnetic field, then the two fields hae to be pependicula to each othe.. Foces on cuentcaying Wies in Magnetic Fields a. You should undestand the foce expeienced by a cuent in a magnetic field so you can: 431
3 (1) Calculate the magnitude and diection of the foce on a staight segment of cuentcaying wie in a unifomed magnetic field Just use the equation; F Ilsin () Indicate the diection of magnetic foces on a cuentcaying loop of wie in a magnetic field, and detemine how the loop will tend to otate as a consequence of these foces. Use the good old ight hand ule. 3. Fields of Long Cuentcaying Wies a. You should undestand the magnitude field poduced by a long staight cuentcaying wie so you can: (1) Calculate the magnitude and diection of the field at a point in the icinity of such a wie. Use the equation. 0I () Use supeposition to detemine the magnetic field poduced by two long wies. Supeposition means ecto addition. Each of the wies poduces its own field. You just add them up as ectos. (3) Calculate the foce of attaction o epulsion between two long cuent caying wies. I Use the F Ilsin. Electomagnetism 1. Electomagnetic Induction 0 equation and the equation fo the foce exeted by a wie, a. You should undestand the concept of magnetic flux so you can: (1) Calculate the flux of a unifom magnetic field though a loop of abitay oientation. Simply use the equation fo magnetic flux. m A Acos b. You should undestand Faaday s Law and Lenz s Law so you can: 43
4 (1) ecognize situations in which changing flux though a loop will cause an induced emf o cuent in the loop. Faaday s law is simply that a cuent is induced when the magnetic flux though the conducto is changing. Hae to be alet fo the idea that it is only when the flux is changing that an emf will be induced. Typical situations whee this happens would be whee a loop taels into o out of a magnetic field. Please note that once it is in a field, een though it is moing, no emf is induced because the flux is not changing. The othe situation is a loop that is otating within a magnetic field. () Calculate the magnitude and diection of the induced emf and cuent in: (a) A squae loop of wie pulled at a constant elocity into o out of a unifom magnetic field. Use the equation ule. l. To figue out the cuent diection, use the ight hand (b) A loop of wie placed in a spatially unifom magnetic field whose magnitude is changing at a constant ate. Use the equation ag m. t (c) A loop of wie that otates at a constant ate about an axis pependicula to a unifom magnetic field. This is a bit moe complicated. Thee ae some examples of how to do this in the last electomagnetic handout. Check it out. (d) A conducting ba moing pependicula to a unifom magnetic field. Just use the good old l equation. Fom 000: 7. A paticle with unknown mass and chage moes with constant speed V = 1.9 x 10 6 m/s as it passes undeflected though a pai of paallel plates, as shown aboe. The plates ae sepaated by a distance d = 6.0 x 103 m, and a constant potential diffeence V is maintained between them. A unifom magnetic field of magnitude = 0.0 T diected into the page exists both between the plates and in a egion to the ight of them as shown. Afte the paticle passes into the egion to the ight of the plates whee only the A V magnetic field exists, its tajectoy is cicula with adius = 0.10 m. 433
5 (a) What is the sign of the chage of the paticle? Check the appopiate space below. Positie _xx_ Negatie Neutal It cannot be detemined fom this infomation. If the paticle was positie, the magnetic foce would be up (ight hand ule) and the paticle would cue aboe the plates, it s motion is the opposite, so the paticle must hae a negatie chage. etween the plates, the negatie paticle is deflected downwad. Theefoe the electic field must foce the negatie paticle up, but diection of the field is the diection a positie test chage would go so the field must be down. (b) On the diagam aboe, clealy indicate the diection of the electic field between the plates. (c) Detemine the magnitude of the potential diffeence V between the plates. V The magnetic field stength is gien by: E d Magnetic foce: F qsin q F Electic Foce: E F qe q Set the electic foce and the magnetic foce equal to one anothe: V q qe q q V d d 6 m 3 3 V 1.9 x T6.0 x10 m.8 x10 V s (d) Detemine the atio of the chage to the mass ( q/m) of the paticle. This sounds bad. Okay, the paticle follows a cued path in the magnetic field. So we can set the centipetal foce = magnetic foce. m q Soling fo q/m q q m m q m x 95 x10 C 9.5 x10 C m s m T kg kg
6 Fom 1999: A ectangula conducting loop of width w, height h, and esistance is mounted etically on a nonconducting cat as shown aboe. The cat is placed on the inclined potion of a tack and eleased fom est at position P 1 at a height y o aboe the hoizontal potion of the tack. It olls with negligible fiction down the incline and though a unifom magnetic field in the egion aboe the hoizontal potion of the tack. The conducting loop is in the plane of the page, and the magnetic field is diected into the page. The loop passes completely though the field with a negligible change in speed. Expess you answes in tems of the gien quantities and fundamental constants. (a) Detemine the speed of the cat when it eaches the hoizontal potion of the tack. 1 KE ME m mgh gh gyo (b) Detemine the following fo the time at which the cat is at position P with onethid of the loop in the magnetic field. i. The magnitude of the emf induced in the conducting loop A 1 wh wh w x x 3 w t t gyo 3 gy wh 3 h gy t w 3 gy o o o ii. The magnitude of the cuent induced in the conducting loop 435
7 V I I V h gyo (c) On the following diagam of the conducting loop, indicate the diection of the cuent when it is at position P. (d) i. Using the axes below, sketch a gaph of the magnitude of the magnetic flux though the loop as a function of the hoizontal distance x taeled by the cat, letting x = 0 be the position at which the font edge of the loop just entes the field. Label appopiate alues on the etical axis. wh ii. Using the axes below, sketch a gaph of the cuent induced in the loop as a function of the hoizontal distance x taeled by the cat, letting x = 0 be the position at which the font edge of the loop just entes the field. Let counteclockwise cuent be positie and label appopiate alues on the etical axis. h gy o h gyo 436
8 Fom 1996: A igid od of mass m and length is suspended fom two identical spings of negligible mass as shown in the diagam below. The uppe ends of the spings ae fixed in place and the spings stetch a distance d unde the weight of the suspended od. (a) Detemine the sping constant k of each sping in tems of the othe gien quantities and fundamental constants. F F mg 0 F mg s s but Fs kx so kx mg ut each sping holds ½ the total mass 1 mg mg kx mg k x d As shown below, the uppe end of the spings ae connected by a cicuit banch containing a battey of emf and a switch S, so that a complete cicuit is fomed with the metal od and spings. The cicuit has a total esistance, epesented by the esisto in the diagam below. The od is in a unifom magnetic field, diected pependicula to the page. The uppe ends of the spings emain fixed in place and the switch S is closed. When the system comes to equilibium, the od is loweed an additional distance d. (b) What is the diection of the magnetic field elatie to the coodinate axes shown on the ight in the peious diagam? Using the ight hand ule, the field is out of the page, along the positie z axis. The cuent is to the ight thumb points that way and the ba is pushed down, so the palm points down. The finges end up pointing out of the page. (c) Detemine the magnitude of the magnetic field in tems of m,, d, d,,, and fundamental constants. Gaity initially displaced the ba a distance d. Then the magnetic field displaced the ba an exta distance, d. Set the sping foce equal to the magnetic foce: 437
9 F S F kx I ut, thee ae two spings kx I x is d, so plug that in: kd I Sole fo : Now we need to get in tems of the items listed in (c): kd I If the intenal esistance is not mentioned, we can assume that it is zeo. So V V V I I so I Plug this into the equation we deeloped fo I: kd kd kd I Also, we aleady found a alue fo k mg d Plug this into the equation fo k: mg d kd d mgd d (d) When the switch is suddenly opened, the od oscillates. Fo these oscillations, detemine the following quantities in tems of d, d, and fundamental constants: i. The peiod. T m ut thee ae two spings. k T m Plug in the alue fo k. k T m mg d d g 438
10 ii. The maximum speed of the od. Use conseation of enegy: 1 1 US K kx m The in font of U S because thee ae two spings kd k kx kx m d and m m m k mg d mg d mg g d d d m m d d Fom 1995: In a linea acceleato, potons ae acceleated fom est though a potential diffeence to a speed of appoximately 3.1 x 10 6 metes pe second. The esulting poton beam poduces a cuent of.0 x 106 ampee. a. Detemine the potential diffeence though which the potons wee acceleated. The electic potential enegy is equal to the wok done on the paticle. This must equal its kinetic enegy. 1 qq 1 m U qv W qv qv m V 4 q 1 E 0 Note, we can look up the mass of a poton (it is 1.67 x 107 kg) kg m s 19 C m 4 V V q
11 b. If the beam is stopped in a taget, detemine the amount of themal enegy that is poduced in the taget in one minute. ecause enegy is conseed, the themal enegy poduced in the taget is simply equal to the powe of the beam of paticles. W P and P IV W Pt W IVt t 6 4 W IVt.0 x10 A 5.0 x10 V 60 s 600 x10 A 6.0 J E W 6.0 J Themal The poton beam entes a egion of unifom magnetic field, as shown aboe, that causes the beam to follow a semicicula path. c. Detemine the magnitude of the field that is equied to cause an ac of adius 0.10 mete. ac F FNet ma so FC m o F FC F qsin so qsin m sin x10 kg3.1 x10 m s m q m 0.3 T q x C m d. What is the diection of the magnetic field elatie to the axes shown aboe on the ight? Positie Z  out of the pape.. Use the ight hand ule. Thumb points in diection of elocity, palm points in diection of magnetic foce, and the finges point in the diection of the field. At the dot on the cued path of the poton, the palm points to the left towads the cente of the cicle. The thumb points down (the elocity at that point is a tangent to the cicle and is down). You finges end up pointing out of the page. Fom 1994: 440
12 A foce F is applied to a conducting od so that the od slides with constant speed oe a fictionless pai of paallel conducting ails that ae sepaated by a distance. The od and ails hae negligible esistance, but the ails ae connected by a esistance, as shown below. Thee is a unifom magnetic field pependicula to and diected out of the plane of the pape. a. On the following diagam, indicate the diection of the induced cuent in the esisto. Using the ight hand ule, the palm must point to the left (the diection of the foce which opposes the motion of the ba), the finges point in the diection of the field out of the page. This thumb then points in the diection of the cuent though the ba, which is down. Theefoe the cuent is clockwise and the cuent though the esisto is up. Detemine expessions fo the following in tems of,,, and. b. The induced emf in the od. l c. The electic field in the od. F q E F qsin F q so E E q q d. The magnitude of the induced cuent in the esisto. We know that the emf induced is: l We also know that, if the esistance in the od and ails is negligible, then the emf is equal to the oltage. So: V Now we can apply Ohm s law. 441
13 V V I I I e. The powe dissipated in the esisto as the od moes in the magnetic field. P IV P P f. The magnitude of the extenal foce F applied to the od to keep it moing with constant speed. At constant speed the net foce must equal zeo. F 0 F F 0 F F F I F F Fom 1998: The long, staight wie shown in Figue 1 below is in the plane of the page and caies a cuent I. Point P is also in the plane of the page and is a pependicula distance d fom the wie. Gaitational effects ae negligible. a. With efeence to the coodinate system in Figue 1, what is the diection of the magnetic field at point P due to the cuent in the wie? Use the ight hand ule. Into the page, in the minus z diection. A paticle of mass m and positie chage q is initially moing paallel to the wie with a speed o when it is at point P, as shown in Figue below. 44
14 b. With efeence to the coodinate system in Figue, what is the diection of the magnetic foce acting on the paticle at point P? ight hand ule. Foce is down, in the minus y diection. Thumb points in diection of 0, finges point into page (diection of field), so the palm points down, the diection of the foce. c. Detemine the magnitude of the magnetic foce acting on the paticle at point P in tems of the gien quantities and fundamental constants. o I o I sin o I o o I F q q q d d d d. An electic field is applied that causes the net foce on the paticle to be zeo at point P. i. With efeence to the coodinate system in Figue, what is the diection of the electic field at point P that could accomplish this? The electic field diection is defined as the diection a positie paticle moes. The positie paticle must moe up to counte the downwad magnetic field. ii. Detemine the magnitude of the electic field in tems of the gien quantities and fundamental constants. F E F E F E q E F q oi qo d E q o oi d 443
15 Fom 199: The figue shows a coss section of a cathode ay tube. An electon in the tube initially moes hoizontally in the plane of the coss section at a speed of.0 x 10 7 metes pe second. The electon is deflected upwad by a magnetic field that has a field stength of 6.0 x 104 Tesla. a. What is the diection of the magnetic field? Out of the page. b. Detemine the magnitude of the magnetic foce acting on the electon. F q m F 1.6x10 C x10 6 x10 T 1.9 x10 N s c. Detemine the adius of cuatue of the path followed by the electon while it is in the magnetic field. ac F ma Fc m 7 m x10 31 s m 9.11 x10 kg Fc 15 kg m 1.9 x10 s 0.19 m An electic field is late established in the same egion as the magnetic field such that the electon now passes though the magnetic and electic fields without deflection. d. Detemine the magnitude of the electic field. 15 F 1.9 x10 N 444
16 F E Q x10 N N E x10 C C e. What is the diection of the electic field? The foce needs to be downwad on the electon to cancel the upwad magnetic field foce. Unlike the magnetic field which is pependicula, the electic field is paallel to its foce. The electic field is the diection a positie chage moes. Electons moe opposite the field. So if the electon needs to moe down the electic field is up. Fom 1993: A paticle of mass m and chage q is acceleated fom est in the plane of the page though a potential diffeence V between two paallel plates as shown. The paticle is injected though a hole in the ighthand plate into a egion of space containing a unifom magnetic field of magnitude oiented pependicula to the plane of the page. The paticle cues in a semicicula path and stikes a detecto. Neglect elatiistic effects thoughout this poblem. a. Detemine the following i. State whethe the sign of the chage on the paticle is positie o negatie. Positie. The ight plate is negatie and the left is positie. The paticle is attacted to the negatie plate and epelled by the positie plate so it has to be positie. ii. State whethe the diection of the magnetic field is into the page o out of the page. Out of the page. Look at the paticle at the mid point of the cue (whee the little aowhead is located). Its elocity is down, so point you thumb down. It is being foced towads the cente by the magnetic foce, so point you palm to the left. This leaes you finges pointing out of the page, which is the diection of the magnetic field. b. Detemine each of the following in tems of m, q, V, and. i. The speed of the chaged paticle as it entes the egion of the magnetic field. 1 W qv Wok Incease in KE k m 1 qv qv m m ii. The foce exeted on the chaged paticle by the magnetic field. 445
17 F qsin sin F q iii. The distance fom the point of injection to the detecto. F Fc q m o qv m m m m qv d d q q q m i. The wok done by the magnetic field on the chaged paticle duing the semicicula tip. No wok is done since the magnetic field is pependicula to the displacement. 446
Magnetic 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 informationForces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
More informationPY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ighthand end. If H 6.0 m and h 2.0 m, what
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 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 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 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 informationExam 3: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
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 information12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
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 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 informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationPhys 2101 Gabriela González. cos. sin. sin
1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe
More information8.4. Motion of Charged Particles in Magnetic Fields
Motion of Chaged Paticles in Magnetic Fields Atos and olecules ae paticles that ae the building blocks of ou uniese. How do scientists study the natue of these sall paticles? The ass spectoete shown in
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 informationChapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
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 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 informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = W/q 0 1V [Volt] =1 Nm/C
Geneal Physics  PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More information(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationUniform Rectilinear Motion
Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 111 Engineeing Mechanics : Dynamics
More informationMultiple choice questions [60 points]
1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
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 informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
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 informationChapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6
Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe
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 informationDisplacement, Velocity And Acceleration
Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationMultiple choice questions [70 points]
Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions
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 information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationPHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
More informationChapter 2. Electrostatics
Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.
More informationSolutions for Physics 1301 Course Review (Problems 10 through 18)
Solutions fo Physics 1301 Couse Review (Poblems 10 though 18) 10) a) When the bicycle wheel comes into contact with the step, thee ae fou foces acting on it at that moment: its own weight, Mg ; the nomal
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationSELFINDUCTANCE AND INDUCTORS
MISN0144 SELFINDUCTANCE AND INDUCTORS SELFINDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. SelfInductance L.........................................
More informationTORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION
MISN034 TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION shaft TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION by Kiby Mogan, Chalotte, Michigan 1. Intoduction..............................................
More informationMoment and couple. In 3D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r
Moment and couple In 3D, because the detemination of the distance can be tedious, a vecto appoach becomes advantageous. o k j i M k j i M o ) ( ) ( ) ( + + M o M + + + + M M + O A Moment about an abita
More informationPhysics Core Topic 9.2 Space
Physics 9. Space Syllabus Notes Physics Coe Topic 9. Space Summay of Contextual Outline Scientists daw on othe aeas of science to deelop iable spacecaft Launch, e enty and landing ae dangeous Huge foces
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationIntroduction to Fluid Mechanics
Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body
More informationWorked 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 informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationLesson 7 Gauss s Law and Electric Fields
Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual
More informationLab M4: The Torsional Pendulum and Moment of Inertia
M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disklike mass suspended fom a thin od o wie. When the mass is twisted about the
More informationProblems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976)
Poblems of the nd and 9 th Intenational Physics Olympiads (Budapest Hungay 968 and 976) Péte Vankó Institute of Physics Budapest Univesity of Technology and Economics Budapest Hungay Abstact Afte a shot
More informationPY106 Class13. Permanent Magnets. Magnetic Fields and Forces on Moving Charges. Interactions between magnetic north and south poles.
Permanent Magnets Magnetic ields and orces on Moing Charges 1 We encounter magnetic fields frequently in daily life from those due to a permanent magnet. Each permanent magnet has a north pole and a south
More informationTECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications
JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy
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 informationCHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL
CHATER 5 GRAVITATIONAL FIELD AND OTENTIAL 5. Intoduction. This chapte deals with the calculation of gavitational fields and potentials in the vicinity of vaious shapes and sizes of massive bodies. The
More informationA r. (Can you see that this just gives the formula we had above?)
241 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down  you can pedict (o contol) motion
More informationF G r. Don't confuse G with g: "Big G" and "little g" are totally different things.
G1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just
More informationCharges, Coulomb s Law, and Electric Fields
Q&E 1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and ( ). An atom consists of a heavy (+) chaged nucleus suounded
More informationQuantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w
1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a
More informationPhysics HSC Course Stage 6. Space. Part 1: Earth s gravitational field
Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe
More informationLesson 8 Ampère s Law and Differential Operators
Lesson 8 Ampèe s Law and Diffeential Opeatos Lawence Rees 7 You ma make a single cop of this document fo pesonal use without witten pemission 8 Intoduction Thee ae significant diffeences between the electic
More information2. Orbital dynamics and tides
2. Obital dynamics and tides 2.1 The twobody poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
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 informationGravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.
Physics: Mechanics 1 Gavity D. Bill Pezzaglia A. The Law of Gavity Gavity B. Gavitational Field C. Tides Updated: 01Jul09 A. Law of Gavity 3 1a. Invese Squae Law 4 1. Invese Squae Law. Newton s 4 th law
More informationFluids Lecture 15 Notes
Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2D, this velocit
More informationFigure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
More informationModel Question Paper Mathematics Class XII
Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495499, 2013 ISSN 18184952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationChapter 2 Coulomb s Law
Chapte Coulomb s Law.1 lectic Chage...3. Coulomb's Law...3 Animation.1: Van de Gaaff Geneato...4.3 Pinciple of Supeposition...5 xample.1: Thee Chages...5.4 lectic Field...7 Animation.: lectic Field
More informationElectrostatic properties of conductors and dielectrics
Unit Electostatic popeties of conductos and dielectics. Intoduction. Dielectic beaking. onducto in electostatic equilibium..3 Gound connection.4 Phenomena of electostatic influence. Electostatic shields.5
More information4.1  Trigonometric Functions of Acute Angles
4.1  Tigonometic Functions of cute ngles a is a halfline that begins at a point and etends indefinitel in some diection. Two as that shae a common endpoint (o vete) fom an angle. If we designate one
More informationGAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN0133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University
MISN0133 GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS by Pete Signell, Michigan State Univesity 1. Intoduction..............................................
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationChapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom
Chapte 7 The Keple Poblem: Planetay Mechanics and the Boh Atom Keple s Laws: Each planet moves in an ellipse with the sun at one focus. The adius vecto fom the sun to a planet sweeps out equal aeas in
More informationChapter 29: Magnetic Fields
Chapter 29: Magnetic Fields Magnetism has been known as early as 800C when people realized that certain stones could be used to attract bits of iron. Experiments using magnets hae shown the following:
More information12.1. FÖRSTER RESONANCE ENERGY TRANSFER
ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 11 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to
More informationThank you for participating in Teach It First!
Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Suppot Coach, Foundational Mathematics teache lesson followed by the coesponding student lesson. We ae confident
More informationNUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
More informationLecture 7 Force and Motion. Practice with Freebody Diagrams and Newton s Laws
Lecture 7 Force and Motion Practice with Freebody Diagrams and Newton s Laws oday we ll just work through as many examples as we can utilizing Newton s Laws and freebody diagrams. Example 1: An eleator
More informationPearson Physics Level 30 Unit VI Forces and Fields: Chapter 10 Solutions
Peason Physics Level 30 Unit VI Foces and Fields: hapte 10 Solutions Student Book page 518 oncept heck 1. It is easie fo ebonite to eove electons fo fu than fo silk.. Ebonite acquies a negative chage when
More informationGraphs of Equations. A coordinate system is a way to graphically show the relationship between 2 quantities.
Gaphs of Equations CHAT PeCalculus A coodinate sstem is a wa to gaphicall show the elationship between quantities. Definition: A solution of an equation in two vaiables and is an odeed pai (a, b) such
More informationStructure and evolution of circumstellar disks during the early phase of accretion from a parent cloud
Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationFunctions of a Random Variable: Density. Math 425 Intro to Probability Lecture 30. Definition Nice Transformations. Problem
Intoduction One Function of Random Vaiables Functions of a Random Vaiable: Density Math 45 Into to Pobability Lectue 30 Let gx) = y be a onetoone function whose deiatie is nonzeo on some egion A of the
More informationTHERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS
THERMAL OLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS E.K.G. Boateng, P.J. Schubel, N.A. Waio Polyme Composites Goup Division of Mateials, Mechanics and Stuctues Faculty of Engineeing
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More information