AP Physics Electromagnetic Wrap Up


 Howard Fields
 2 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
Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
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 informationProblems on Force Exerted by a Magnetic Fields from Ch 26 T&M
Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuentcaying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to
More informationXIIth PHYSICS (C2, G2, C, G) Solution
XIIth PHYSICS (C, G, C, G) 6 Solution. A 5 W, 0 V bulb and a 00 W, 0 V bulb ae connected in paallel acoss a 0 V line nly 00 watt bulb will fuse nly 5 watt bulb will fuse Both bulbs will fuse None of
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 informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente
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 informationSo we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)
Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing
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 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 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 information2008 QuarterFinal Exam Solutions
2008 Quatefinal Exam  Solutions 1 2008 QuateFinal Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of
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 informationGeneral Physics (PHY 2130)
Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:
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 informationmv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !
Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!
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 informationExam I. Spring 2004 Serway & Jewett, Chapters 15. Fill in the bubble for the correct answer on the answer sheet. next to the number.
Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 15 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE
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 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 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 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 informationrotation  Conservation of mechanical energy for rotation  Angular momentum  Conservation of angular momentum
Final Exam Duing class (13:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday
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 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 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 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 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 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 informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapte 5. Foce and Motion In this chapte we study causes of motion: Why does the windsufe blast acoss the wate in the way he does? The combined foces of the wind, wate, and gavity acceleate him accoding
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 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 informationChapter 26  Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field
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 informationSeventh Edition DYNAMICS 15Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University
Seenth 15Fedinand P. ee E. Russell Johnston, J. Kinematics of Lectue Notes: J. Walt Ole Texas Tech Uniesity Rigid odies CHPTER VECTOR MECHNICS FOR ENGINEERS: YNMICS 003 The McGawHill Companies, Inc. ll
More informationAPC Magnetism. APC Objectives (from College Board Learning Objectives for AP Physics)
APC Magnetism APC (fom Coege oad Leaning fo AP Physics) 1. oces on moving chages in magnetic fieds a. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic
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 informationSolutions to Homework Set #5 Phys2414 Fall 2005
Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated
More informationPoynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions
Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallelplate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing
More informationChapter F. Magnetism. Blinn College  Physics Terry Honan
Chapte F Magnetism Blinn College  Physics 46  Tey Honan F.  Magnetic Dipoles and Magnetic Fields Electomagnetic Duality Thee ae two types of "magnetic chage" o poles, Noth poles N and South poles S.
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 informationYour Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :(
You Comments Llamas, and why it is so difficult to get someone to buy me one as a pet. All ask is that it beathes fie. have simple needs people. Seiously. p.s. this lectue was had. did not undestand any
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 informationYour Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows.
You Comments lease explain the ight hand ule when thee ae two wies and ou ae ting to find the diection of the foce I am getting confused with all these ight hand ules So do ou have an ageold advice fo
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 informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
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 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 informationLearning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.
Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of
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 informationGauss Law in dielectrics
Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,
More informationMAGNETIC FIELDS AND FORCES 24
MAGNETIC FIELDS AND FORCES 24 Q24.1. Reason: When a ba magnet is bought nea the cente of anothe ba magnet as shown in Figue Q24.1, the foce between the ba magnets is zeo. The attactive foce between the
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 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 informationRotation. Problem solving strategy is the same as for problems with linear motion... Rotation
Rotation The basic quantity in otation is the angula displacement simila ole to the linea displacement studied in chapte units: adians, eolutions, degees, θ Poblem soling stategy is the same as fo poblems
More informationAlgebra and Trig. I. A point is a location or position that has no size or dimension.
Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite
More informationPhysics 107 HOMEWORK ASSIGNMENT #14
Physics 107 HOMEWORK ASSIGNMENT #14 Cutnell & Johnson, 7 th edition Chapte 17: Poblem 44, 60 Chapte 18: Poblems 14, 18, 8 **44 A tube, open at only one end, is cut into two shote (nonequal) lengths. 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 informationF = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a
.1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q q a +q a q F = kq 1q F 1 = k(q)(q) a F 13
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 informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions 1 [M] A unifom line chage that has a linea chage density l equal to.5 nc/m is on the x axis between x and x 5. m. (a) What is its total chage?
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 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 informationReview Module: Dot Product
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics 801 Fall 2009 Review Module: Dot Poduct We shall intoduce a vecto opeation, called the dot poduct o scala poduct that takes any two vectos and
More informationUNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100minute sessions
Name St.No.  Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,
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 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 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 informationSection 53 Angles and Their Measure
5 5 TRIGONOMETRIC FUNCTIONS Section 5 Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,
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 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 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 information2  ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1
 ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation
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 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 information2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90
. Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal
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 information14. Gravitation Universal Law of Gravitation (Newton):
14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1
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 informationIn this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION
MOTION IN FIELDS MOTION IN FIELDS 9 9. Pojectile motion 9. Gavitational field, potential and enegy 9.3 Electic field, potential and enegy 9. PROJECTILE MOTION 9.. State the independence of the vetical
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 informationEXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH S MAGNETIC FIELD
260 161. THEORY EXPERMENT 16 THE MAGNETC MOMENT OF A BAR MAGNET AND THE HORZONTAL COMPONENT OF THE EARTH S MAGNETC FELD The uose of this exeiment is to measue the magnetic moment μ of a ba magnet and
More informationChapter 22 Solutions
PHY49 Chapte Solutions Poblem : A +5 micoc chage is located 4 cm fom a +3 micoc chage The magnitude of the electostatic foce on the lage chage and on the smalle chage (in N) is espectively Answe: 5 5 Solution:
More informationSimple Harmonic Motion
Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium
More informationResources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics
3/4/0 Resouces Cicula Motion: Fom Moto Racing to Satellites D Jeff McCallum School of Physics http://www.gapsystem.og/~histoy/mathematicians/ Newton.html http://www.fga.com http://www.clke.com/clipat
More informationA couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance, d. F A F B (= F A
5 Moment of a Couple Ref: Hibbele 4.6, edfod & Fowle: Statics 4.4 couple is a pai of foces, equal in magnitude, oppositely diected, and displaced by pependicula distance, d. d (=  ) Since the foces ae
More informationChapter 4. Gauss s Law
Chapte 4 Gauss s Law 4.1 lectic Flux...44. Gauss s Law...43 xample 4.1: Infinitely Long Rod of Unifom Chage Density...48 xample 4.: Infinite Plane of Chage...49 xample 4.3: Spheical Shell...41 xample
More informationA) 2 B) 2 C) 2 2 D) 4 E) 8
Page 1 of 8 CTGavity1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between
More informationIn order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Radians At school we usually lean to measue an angle in degees. Howeve, thee ae othe ways of measuing an angle. One that we ae going to have a look at hee is measuing angles in units called adians. In
More informationTrigonometric Functions of Any Angle
Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An
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 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 informationSELFINDUCTANCE AND INDUCTORS
MISN0144 SELFINDUCTANCE AND INDUCTORS SELFINDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. SelfInductance L.........................................
More information