AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics)
|
|
- Annice Roberts
- 7 years ago
- Views:
Transcription
1 AP-C Magnetism AP-C (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 foce can pefom no wok. b. Deduce the diection of a magnetic fied fom infomation about the foces expeienced by chaged patices moving though that fied. c. Descibe the paths of chaged patices moving in unifom magnetic fieds. d. Deive and appy the fomua fo the adius of the cicua path of a chage that moves pependicua to a unifom magnetic fied. e. Descibe unde what conditions patices wi move with constant veocity though cossed eectic and magnetic fieds.. oces on cuent-caying wies in magnetic fieds a. Cacuate the magnitude and diection of the foce on a staight segment of cuentcaying wie in a unifom magnetic fied. b. ndicate the diection of magnetic foces on a cuent-caying of wie in a magnetic fied, and detemine how the wi tend to otate as a consequence of these foces. c. Cacuate the magnitude and diection of the toque expeienced by a ectangua of wie caying a cuent in a magnetic fied.. ieds of ong cuent-caying wies a. Cacuate the magnitude and diection of the fied at a point in the vicinity of such a wie. b. Use supeposition to detemine the magnetic fied poduced by two ong wies. c. Cacuate the foce of attaction o epusion between two ong cuent-caying wies. 4. iot-savat aw and Ampee s aw a. Students shoud undestand the iot-savat Law, so they can: i. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. ii. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. b. Students shoud undestand the statement and appication of Ampee s Law in intega fom, so they can: i. State the aw pecisey. ii. Use Ampee s aw, pus symmety aguments and the ight-hand ue, to eate magnetic fied stength to cuent fo pana o cyindica symmeties. c. Students shoud be abe to appy the supeposition pincipe so they can detemine the magnetic fied poduced by combinations of the configuations isted above. -1-
2 oces on Moving Chages in Magnetic ieds Units of Magnetic ied 1. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic foce can pefom no wok. Standad (S) units of magnetic fied ae Tesa. Deduce the diection of a magnetic fied fom infomation about the foces expeienced by chaged patices moving though that fied. 1 Tesa (1 T) 1 N s/(c m). Descibe the paths of chaged patices moving in unifom magnetic fieds. 1 Tesa is a vey stong magnetic fied 4. Deive and appy the fomua fo the adius of the cicua path of a chage that moves pependicua to a unifom magnetic fied. Moe common non-s unit is the Gauss 1 Gauss 10-4 Tesa 5. Descibe unde what conditions patices wi move with constant veocity though cossed eectic and magnetic fieds. Eath s magnetic fied stength 0.5 Gauss v Magnetic oces Cannot Pefom Wok on Moving Chages oce is aways pependicua to veocity, theefoe the magnetic foce on a moving chage is neve appied in the diection of the dispacement, theefoe a magnetic foce can do no wok on a moving +q chage (but it can change its diection). M qv M qvsin θ v oces on Moving Chages in Magnetic ieds Magnetic foce cannot pefom wok on a moving chage Magnetic foce can change its diection (moving it in a cice if M is constant.) +q θ 90 M qvsin θ sin90 1 M qv mv M C qv mv momentum q Tota oce on a Moving Chaged Patice (E fied and ied) E fied can do wok on a moving chage fied can neve do wok on a moving chage The Veocity Seecto A chaged patice in cossed E and fieds can undego constant veocity motion if v,, and E ae a seected pependicua to each othe. Then, if ve/, the patice can tave though the seecto without any defection, whie patices with any othe veocity ae diveted. -- Loentz oce TOT q E + v ( )
3 oces on cuent-caying wies in magnetic fieds 1. Cacuate the magnitude and diection of the foce on a staight segment of cuent-caying wie in a unifom magnetic fied.. ndicate the diection of magnetic foces on a cuent-caying of wie in a magnetic fied, and detemine how the wi tend to otate as a consequence of these foces.. Cacuate the magnitude and diection of the toque expeienced by a ectangua of wie caying a cuent in a magnetic fied. oces on Cuent-Caying Wies Moving chages in magnetic fieds expeience foces. Cuent in a wie is just the fow of positive chages. f chages ae moving pependicua to magnetic fieds, they expeience a foce which is appied to the wie. vd dq dq dt q( v ) d dq(vd ) dq dt vd dt d dt(vd ) v d (d ) d dt d ( ) ( ) Exampe: A staight wie of ength 1 m caies a cuent of 100A though a magnetic fied of 1 Tesa. ind the foce on the wie. Diection of oce Detemine the diection of the foce on the wie using the d ight hand ue. 100A X 1 Tesa d (d ) sinθ 100 A 1m (100 A)(1m)(1T ) 1T 100N Eectic Motos 180º ate a b a a b net 0 Net toque is evesed To keep moto moving, you need to eithe evese the cuent diection with a commutato o tun off the cuent in this stage. τ net b a + b a ab Ceates counte-cockwise otation --
4 ieds of ong cuent-caying wies 1. Cacuate the magnitude and diection of the fied at a point in the vicinity of a ong cuent-caying wie.. Use supeposition to detemine the magnetic fied poduced by two ong wies.. Cacuate the foce of attaction o epusion between two ong cuent-caying wies. Magnetic ieds poduced by ong staight cuent-caying wies Moving chages ceate magnetic fieds. Cuent is moving positive chages, theefoe cuent-caying wies ceate magnetic fieds. Use 1st ight Hand ue to find diection of magnetic fied. f you have two wies, detemine magnetic fied fom each and add them up using supeposition pincipe. These fieds may inteact with othe moving chages, so cuent-caying wies can ceate foces of attaction o epusion between themseves. µ 0 π 1st ight Hand ue Hod wie with you ight hand, with thumb in the diection of positive cuent fow. You finges wap aound the wie in the diection of the magnetic fied. µ0 4π 10 7 T m A oce etween Paae Cuent-Caying Wies Use ight hand ues to detemine foce between paae cuent-caying wies. ind magnetic fied due to fist wie. Daw it. ind diection of foce on nd wie due to cuent in second wie. oce on 1st wie wi be equa and opposite (Newton s d) Wies epe Each Othe Wies Attact Each Othe Gauss s Law fo Magnetism You can neve daw a cosed suface with any net magnetic fux because thee ae no magnetic monopoes. This is the basis of Gauss s Law fo Magnetism (Maxwe s nd Equation) Φ net da 0-4-
5 iot-savat Law 1. Undestand iot-savat Law a. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. b. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. iot-savat Law ute oce method of finding the magnetic fied due to a ength of cuent-caying wie µ0 ( ) µ0 ( ) d d 4π 4π d Exampe: Deive the fied due to a ong staight cuent-caying wie µ0 ( ) dx sinθ d 4π µ dx sinθ x + d 0 sinθ 4π x + x µ0 dx µ0 dx d d x 4π(x + ) 4π(x + ) P µ0 dx of ntegas Tabe 4π (x + ) µ x 0 1 4π ( + x ) d µ π ( + ) ( + ( ) ) µ0 1 µ0 1 µ0 + 4π 4π π Exampe: Deive the magnetic fied due to a cuent µ sin θ d 0 sin θ sin90 1 4π wie µ µ µ 0 0 (π ) 0 4π wie 4π -5-
6 iot-savat Law (Atenate) 1. Undestand iot-savat Law a. Deduce the magnitude and diection of the contibution to the magnetic fied made by a shot staight segment of cuent-caying wie. b. Deive and appy the expession fo the magnitude of on the axis of a cicua of cuent. Pobem Soving Steps 1. Look fo symmeties and simpifications.. Define you five quantities (note that pime mak indicates souce of magnetic fied), ',d, ",". Set up you intega. 4. ntegate (may equie compute assistance fo a but the simpest cases) ˆ µ0 d " µ0 d " d 4π " 4π " " ' Exampe: Deive the fied due to a ong staight cuent-caying wie. Note cyindica symmety, common sense tes us z ony positiona dependence wi be adia. < x,0,0 > ' < 0,0, z ' > d < 0,0, dz ' > " ' < x,0, z ' > " " x + z ' Once five items ae defined, you can integate: µ0 d " d ',0> "<0,xdz 4π " µ µ xj xdz ' j dz ' of ntegas 0 0 Tabe 4π (x + z ' ) 4π (x + z ' ) d ' ' y µ xj µ µ 0 0 j Symmety 0 4π x πx π P x Exampe: Deive the magnetic fied at the cente of a cuent of adius. ' Note: Symmeties indicate a the magnetic fied wi be in the positive z diection (towad the top of the page) d ' < 0,0,0 > ' < ',0,0 > d < 0, ',0 > " ' < ',0,0 > " " µ0 d " d "<0, ',0> < ',0,0> d "<0,0,' '>' ' k 4π " µ ' µ µ 0 k ' 0 k (π) 0 k 4π 4π Exampe: Deive the magnetic fied at some distance fom an infinite sheet of chage. Stategy: eak up sheet into infinitessimay sma squaes of aea da, each with a cuent pe pependicua ength of σv, which we can define as the aeia cuent density K. z d " ( Kdx ' dy ' iˆ) ( x ' iˆ y ' j + zk ) d " ( Kdx ' dy ' iˆ) ( y ' j ) + ( Kdx ' dy ' iˆ) (zk ) d " Kzdx ' dy ' j Ky ' dx ' dy ' k d " < 0, Kzdx ' dy ', Ky ' dx ' dy ' > P d KdA Kdx ' dy ' iˆ y x < 0,0, z > zk ' < x ', y ',0 > x ' iˆ + y ' j d < Kdx ' dy ',0,0 > Kdx ' dy ' iˆ " ' < x ', y ', z > x ' iˆ y ' j + zk " " x ' + y ' + z ˆ µ d " µ0 d " µ Kzdx ' dy ' j Ky ' dx ' dy ' k d 0 0 4π " 4π " 4π x ' + y ' + z µ0 K z µ Kzdx ' dy ' j of ntegas 0 Tabe j o Compute 4π x ' + y ' + z z -6- Note: z-component (in k diection) must be 0 since magnetic fieds must make compete s (divegence of magnetic fied is zeo)
7 Ampee s aw 1. Undestand Ampee s Law a. State the aw pecisey. b. Use Ampee s aw, pus symmety aguments and the ight-hand ue, to eate magnetic fied stength to cuent fo pana o cyindica symmeties.. Appy the supeposition pincipe to detemine the magnetic fied poduced by combinations of iot-savat and Ampee s aws configuations isted above. Ampee s Law Eegant method of finding magnetic fied in situations of symmety. cosed µ0 penetating Exampe: ind magnetic fied stength due to a cuent-caying wie Exampe: ind the magnetic fied eveywhee fo a cuent-caying wie (inside and outside the wie) Outside the Wie: cosed µ0 penetating (π ) µ0 µ0 π cosed µ0 penetating (π ) µ0 µ0 π nside the Wie: cosed µ0 penetating π µ0 (π ) µ0 π π Exampe: Cacuate the magnetic fied in the mide of a soenoid (i.e. Sinky) using Ampee s Law. Side View ist choose a ectangua cosed fo appication of Ampee s Law. Path 1 and : intega of is 0 since the ange between and is 90. Path intega is 0 with assumption is cose to 0 outside soenoid Coss-Section L pen L N d µ 0 penetating cosed Assume outside soenoid is 0. N s of wie. 1 4 ntegate though Path 4 L N µ0-7- N L µ0
Forces & 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 informationAP Physics Electromagnetic Wrap Up
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
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 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 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 (.1-1 T) i to ue a lage cuent flowing though a wie.
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 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 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. 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 plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
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 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 informationVoltage ( = Electric Potential )
V-1 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 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 informationGauss Law. Physics 231 Lecture 2-1
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 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 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 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 informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuent-caying conducto is basic to evey electic moto -- tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
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 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 information9.3 Surface Area of Pyramids
Page 1 of 9 9.3 Suface Aea of Pyamids and Cones Goa Find the suface aeas of pyamids and cones. Key Wods pyamid height of a pyamid sant height of a pyamid cone height of a cone sant height of a cone The
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 informationVoltage ( = Electric Potential )
V-1 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 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 informationSELF-INDUCTANCE AND INDUCTORS
MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................
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 ight-hand end. If H 6.0 m and h 2.0 m, what
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 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 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 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 informationwww.sakshieducation.com
Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased
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 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 informationF G r. Don't confuse G with g: "Big G" and "little g" are totally different things.
G-1 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 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 informationMoment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r
Moment and couple In 3-D, 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 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 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 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 2-D, this velocit
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 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 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?)
24-1 (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 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 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 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 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 isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom
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 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 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 informationGraphs of Equations. A coordinate system is a way to graphically show the relationship between 2 quantities.
Gaphs of Equations CHAT Pe-Calculus 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 informationTORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION
MISN-0-34 TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION shaft TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION by Kiby Mogan, Chalotte, Michigan 1. Intoduction..............................................
More informationVISCOSITY OF BIO-DIESEL FUELS
VISCOSITY OF BIO-DIESEL 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 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 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 informationGAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN-0-133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University
MISN-0-133 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 information7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary
7 Cicula Motion 7-1 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 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 11-1 Engineeing Mechanics : Dynamics
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 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 informationDefine What Type of Trader Are you?
Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this
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 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 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 disk-like mass suspended fom a thin od o wie. When the mass is twisted about the
More informationINVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE
1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of
More informationCarter-Penrose diagrams and black holes
Cate-Penose 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 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 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 informationbilliards: Augmented Reality System with wearable Force-Feedback device 1
biiards: Augmented Reaity System with weaabe Foce-Feedback device Usman Sagaana, Woontack Woo Hossein S. Faahani, Jeha Ryu Jongweon Lee GIST U-VR Lab. Gwangju 500-72, S. Koea {sagaana, wwoo}@gist.ac.k
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 information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero 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 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 informationdz + η 1 r r 2 + c 1 ln r + c 2 subject to the boundary conditions of no-slip side walls and finite force over the fluid length u z at r = 0
Poiseuille Flow Jean Louis Maie Poiseuille, a Fench physicist and physiologist, was inteested in human blood flow and aound 1840 he expeimentally deived a law fo flow though cylindical pipes. It s extemely
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 informationIBM Research Smarter Transportation Analytics
IBM Reseach Smate Tanspotation Analytics Laua Wynte PhD, Senio Reseach Scientist, IBM Watson Reseach Cente lwynte@us.ibm.com INSTRUMENTED We now have the ability to measue, sense and see the exact condition
More informationClassical Mechanics (CM):
Classical Mechanics (CM): We ought to have some backgound to aeciate that QM eally does just use CM and makes one slight modification that then changes the natue of the oblem we need to solve but much
More informationWorked Examples. v max =?
Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend
More information2. Orbital dynamics and tides
2. Obital dynamics and tides 2.1 The two-body 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 informationAutomated Hydraulic Drilling Rigs. HHSeries
Automated Hydaulic Dilling Rigs HHSeies The Shape of Things to Come CUSTOMSOLUTIONS HH600 Rig The HH Hydaulic Hoist Seies Eveything about the HH Seies is designed fo speed, safety and efficiency. You can
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 informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
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 informationEnergy Density / Energy Flux / Total Energy in 3D
Lecture 5 Phys 75 Energy Density / Energy Fux / Tota Energy in D Overview and Motivation: In this ecture we extend the discussion of the energy associated with wave otion to waves described by the D wave
More informationOptical Fibers: History, Structure and the Weakly Guided Solution. May 30, 2008 Physics 464 Dr. La Rosa Portland State University.
Optica Fibes: Histoy, Stuctue and the Weaky Guided Soution May 30, 008 Physics 464 D. La Rosa Potand State Univesity by Tayo Biyeu Abstact In this pape, I wi tak about the histoy and deveopment of fibe
More informationChapter 4: Fluid Kinematics
Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian
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 informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495-499, 2013 ISSN 1818-4952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationHow to recover your Exchange 2003/2007 mailboxes and emails if all you have available are your PRIV1.EDB and PRIV1.STM Information Store database
AnswesThatWok TM Recoveing Emails and Mailboxes fom a PRIV1.EDB Exchange 2003 IS database How to ecove you Exchange 2003/2007 mailboxes and emails if all you have available ae you PRIV1.EDB and PRIV1.STM
More informationAnalytical Proof of Newton's Force Laws
Analytical Poof of Newton s Foce Laws Page 1 1 Intouction Analytical Poof of Newton's Foce Laws Many stuents intuitively assume that Newton's inetial an gavitational foce laws, F = ma an Mm F = G, ae tue
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More information883 Brochure A5 GENE ss vernis.indd 1-2
ess x a eu / u e a. p o.eu c e / :/ http EURAXESS Reseaches in Motion is the gateway to attactive eseach caees in Euope and to a pool of wold-class eseach talent. By suppoting the mobility of eseaches,
More informationGravitation. Definition of Weight Revisited. Newton s Law of Universal Gravitation. Newton s Law of Universal Gravitation. Gravitational Field
Defnton of Weght evsted Gavtaton The weght of an object on o above the eath s the gavtatonal foce that the eath exets on the object. The weght always ponts towad the cente of mass of the eath. On o above
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 informationHow To Find The Optimal Stategy For Buying Life Insuance
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
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 informationHow to SYSPREP a Windows 7 Pro corporate PC setup so you can image it for use on future PCs
AnswesThatWok TM How to SYSPREP a Windows 7 Po copoate PC setup so you can image it fo use on futue PCs In a copoate envionment most PCs will usually have identical setups, with the same pogams installed
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 informationDo Vibrations Make Sound?
Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact
More information