Lab #7: Energy Conservation


 Tabitha Roberts
 2 years ago
 Views:
Transcription
1 Lab #7: Enegy Consevation Photo by Kallin Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual and exhilaating eceational activities is the bungee jump. In this spot, a seies of intetwined elastic cods ae attached to a haness that is eithe fastened about the peson's body o attached to his/he ankles. The othe end of the cod typically is attached to a high place like a special bungee jumping stuctue, a bidge, o even a hot ai balloon. The peson leaps fom this stuctue and falls feely until the bungee cod begins to go tense. The jumpe's speed deceases until he/she momentaily comes to est and then acceleates upwads. This motion cycle continues fo a numbe of oscillations until the jumpe is bought to est. While the spot of bungee jumping in its pesent fom is quite ecent, its oigin dates back seveal centuies to the itual of "land diving in the Pacific Achipelago. Thee, the pupose of the itual was to demonstate couage and offe injuies to the gods fo a plentiful havest of yams. It wasn't until the late 1970's that this was tansfomed into a eceational activity. (See The Physics of Bungee Jumping by P.G. Menz in The Physics Teache, Nov. 1993). In this expeiment we shall conside a system, simila to the bungee jumping scenaio, in which two foces act upon a given mass. Ou goal will be to make an oveall judgment egading the consevation of enegy pinciple as it applies to this situation. The system will be compised of a mass suppoted by a sping. The mass will be made to oscillate in the vetical plane, as shown below. Notice that, while oscillating, the mass expeiences the following two foces: the (constant) foce of gavity and the (nonconstant) foce povided by the sping. Dissipative foces that ae pesent, such as ai esistance and fiction, ae small, so they will be ignoed. It is impotant to undestand the diffeences between the natue of constant and nonconstant foces. In this expeiment, the foce of gavity is consideed to be constant in both magnitude and diection, egadless of the position of the mass that is oscillating. F gavity The diection of the foce of gavity is vetically downwad. = mg The foce exeted on the mass by the sping, howeve, is not constant. Its magnitude vaies depending upon the
2 position of the oscillating mass. Hooke s Law explains that the foce exeted by the sping is popotional to the distance that the sping is stetched fom its equilibium position. In othe wods, as the stetch of the sping inceases, so does the foce with which it pulls on the mass. F sping = kx The negative sign indicates that the diection of the foce is opposite the diection of the stetch. Theefoe, since the sping is stetched downwad thoughout the oscillation, the diection of the foce exeted by the sping is always upwad in this expeiment. Note the following positions of the sping and mass system defined in the following figue: Figue A: Sping at Rest. System is consideed to be unstetched. Stating efeence point, x=0. Motion Senso eads h o. Figue B: Sping System with Mass, m, added at Rest. System is at equilibium. Refeence point of oscillation, y=0 when x= x eq. Motion Senso eads h eq. Figue C: Sping System in Oscillation at some position below equilibium. Motion Detecto eads h, x (the stetch) of the sping is lage than in Figue B, and y is downwad. Figue D: Sping System in Oscillation at some position above equilibium. Motion Detecto eads h, x (the stetch) of the sping is smalle than in Figue B, and y is upwad. Figue A Figue B Figue C Figue D x = 0 x y = 0 x eq y x y h o h eq h h h = 0
3 Notice that thee ae thee displacements defined in the above Figues: x, h, and y. Each is impotant and all ae elated to one anothe. The diections of each vecto ae also impotant: x (the stetch) is always downwad; h (the height measued by the motion detecto) is always upwad; and y (the displacement fom the equilibium position duing oscillation), is eithe upwad o downwad depending upon the moment consideed. Positive and negative values can be assigned to indicate the diection of each of these vaiables. Notice, also, in Figue B, the significance of the foces acting upon mass, m. Since this position is the equilibium position, the net foce on the mass at this moment equals zeo. Figue B x = 0 x eq F sping = kx eq y = 0 F gavity = mg h eq h = 0 Theefoe, F gavity F = 0 + sping Which can be estated as: mg kx = 0 Eq. 1 + eq Thee ae also thee types of mechanical enegy contained in the spingmass system duing oscillation: Kinetic Enegy, Gavitational Potential Enegy, and Sping (Elastic) Potential Enegy. Each ae defined as follows: Kinetic Enegy: KE = 1 mv Gavitation Potential Enegy: Sping (Elastic) Potential Enegy: GPE = mgh SPE = 1 kx If the system is ideal, then m is the mass placed upon the hange plus the mass of the hange, k is the sping constant, v is the speed of the mass, and x and h ae defined as in the figues above. An ideal system is one in which the sping is massless.
4 Consideing these thee types of mechanical enegy, the Total Mechanical Enegy of the spingmass system at any time, theefoe, can be given by: Total Mechanical Enegy: E total + 1 = 1 kx mv + mgh Eq. This expession is tue as long as thee is no extenal wok added to the system by the peson who sets it into motion. Theefoe, when stating the oscillation, it is impotant to do the following pocedue: 1. Lift the mass hange so that it is at est at position x=0. (Since it is at est, v=0 and E total = mgh 0.). Release the system by quickly dopping you hand down and out of the way. In ode to make a meaningful analysis of the above Total Enegy expession, it is helpful to ewite it in tems of just one displacement vecto, y. By looking at the Figues A, B, C, and D, one can veify that the displacement vectos x and h can be defined as follows: (When veifying, emembe to assign positive and negative values to each tem.) x = x + eq y Eq. 3 h = h + eq y Eq. 4 These expessions can be substituted into Equation and then eaanged using algeba: E total = mv + mgh kx E 1 1 ) total = mv + mg( heq + y) + k( xeq + y E total eq eq eq + = 1 mv + mgh + mgy + 1 k( x + x y y ) E 1 1 total = mv + mgheq + mgy + kxeq + kxeqy + 1 ky Reaanging and combining tems esults in the following: total 1 1 mv + ky + ( mg + kxeq ) y + mgheq 1 kxeq E = + Fo analysis, conside the following thee goups of tems: total [ 1 mv + ] [ ] [ ] 1 ky + mg + kx ) y + mgh 1 kx E + = Eq.5 ( eq eq eq The leftmost backet descibes the kinetic enegy and gavitational potential enegy (as measued fom the pespective of y) of mass, m. Both of these quantities ae known to change thoughout the oscillation. The coefficient of the cente tem is descibed in Equation 1 as being equal to zeo. Howeve, this is only an appoximation because ou system is not ideal and the total mass of the system is not actually m. The behavio of this tem is detemined by the behavio of y. Since the vaiable, y, is know to oscillate, this tem descibes an oscillation whose amplitude is elatively small. (Ideally, the amplitude should be equal to zeo.) All tems contained in the ightmost backet ae constants. Theefoe, the total value contained in this backet is also a constant.
5 Consideing all of these tems togethe, the ideal case pedicts that the Total Enegy of the spingmass system should be descibed as follows: whee C is a constant. E total = mv + 1 ky + C 1 Eq. 6 The Consevation of Enegy pinciple states that, if all foms of enegy ae consideed, then E = constant Eq. 7 total If this is tue, then, ideally, the fist two tems in Equation 6 (the Kinetic Enegy of the system and the Sping Potential Enegy of the System as measued fom the pespective of y) should also add to a constant value. Check out: Lab # Enegy Consevation
6 Lab #7: Enegy Consevation Goals: Detemine the sping constant, k, of you paticula sping using a gaphical method. Compae the oscillating values of the kinetic enegy and sping potential enegy of a spingmass system. Veify the Consevation of Enegy pinciple as it applies to a spingmass system. Analyze the data fo evidence of nonideal effects and othe foms of enegy. Equipment List: Science Wokshop Motion Senso Foce Senso Sping with 50 g mass hange attached Table clamp with vetical and hoizontal posts Slotted Masses of 50 g, 100 g, & 00 g Activity 1: The Sping Constant The pupose of this activity is to detemine the sping constant, k, of you paticula sping. The equation suggests that in ode to detemine k we must measue the foce exeted on the sping and how fa the sping stetches as a esult of this foce. 1. Set up the equipment as shown in the pictue. Place the motion detecto on the floo diectly beneath the mass hange. Please, do not allow any masses to fall onto the detecto!. Using Science Wokshop set up the Motion Senso to display a gaph of Position vs. Time. Be sue that the motion detecto can see the bottom of the mass hange. Note: Since the mass will be at est fo each data ecoding, the gaph should be a hoizontal line. 3. Display the mean yvalue (Position) fo each un. (This value will effectively cancel the effects of any slight motion of the mass.) 4. Note: if desied, Steps and 3 can be eplaced by taking Position data with a Digits window. 5. While the mass hange (without any additional masses on it) is hanging feely and at est, ecod position data. This initial position (measued fom the motion detecto) will seve as a efeence point thoughout the lab. Recod this value. 6. Connect the Foce Senso to the analog channel of the Science Wokshop inteface and set it up to ead a Digits display window of the foce value. Remembe that the foce ead by the Foce Senso is equivalent in magnitude to the foce exeted by the sping. (Note: This Foce data can be taken, instead using a Foce vs. Time gaph and displaying the mean yvalue (Foce) of each data un.) h o = Lab # Enegy Consevation
7 7. Push the TARE button on the side of the Foce Senso to eset the pobe to zeo while just the sping is suspended fom it. This will calibate the senso to only ead additional foce ceated by adding moe mass. Note: Remembe to ecalibate the foce senso often thoughout the lab. 8. Stating with 50 gams, hang successively highe masses (not to exceed 350 gm) to the hange while ecoding the magnitude of the stetch of the sping. Remembe: the motion detecto does not measue the stetch, x, of the sping. With 50 gams added With 100 gams added With 150 gams added With 00 gams added With 50 gams added With 300 gams added With 350 gams added h (metes) X (metes) Foce (Newtons)n Using Excel, ceate a gaph of F vs. x (Foce vs. stetch). (It is pemissible to gaph only the magnitudes.) 10. Based upon you gaph, what is the value of k that you obtain fo you sping? (Including units.) Explain how this value was obtained. (Also ecod it fo use in the Post Lab.) k = 11. Theoetical Question: (Do not take any data.) How much would you sping stetch if a mass of 15 kg was attached? Show you wok. Activity : Compaing Sping Potential Enegy and Kinetic Enegy of a SpingMass System The pupose of this activity is to measue and compae the sping potential enegy and the kinetic enegy of the spingmass system. 1. It is acceptable to delete all data uns, gaphing windows, and digital window displays fom Activity 1.. Choose one of the mass amounts used in Activity 1 and place it upon the hange. Please do not allow the mass to fall onto the motion detecto. Recod this mass value. m = 3. While the mass is hanging feely and at est, begin ecoding position data. This initial position, h eq, will seve as ou equilibium efeence point (y=0) thoughout this lab. Also detemine the value fo x eq. (Note: This data was aleady ecoded in Activity 1. Theefoe it is not necessay to etake it.) h eq = x eq = Lab #6 Enegy Consevation
8 4. Use the Science Wokshop Expeiment Calculato to calculate the position, y. (See Equation 4 in the Intoduction of the Lab. This effectively shifts ou coodinate system to the at est position of the hanging mass.) [Hint: You can check the coectness of you calculation by gaphing y vs. Time. When the mass is at equilibium, y = 0. ] 5. Use the Expeiment Calculato to define a calculation called Sping Potential Enegy. This calculation should be equal to (0.5*k*y*y). (See Equation 5 in the Intoduction of the Lab.) 6. Use the Expeiment Calculato to define a calculation called Kinetic Enegy. This calculation should be equal to (0.5*m*v*v). (See Equation 5 in the Intoduction of the Lab.) Remembe that m should be expessed in units of kilogams. 7. Ceate a gaphing window of Sping Potential Enegy vs. y and then use the Add Plot button to add a gaph of Kinetic Enegy vs. y to the same window. 8. Ceate a new gaphing window of y vs. Time, and then use the Add Plot button to add gaphs of Sping Potential Enegy vs. Time and Kinetic Enegy vs. Time to the same window. 9. Lift the mass upwad until the spingmass system is appoximately at position x = 0. Pess Recod and elease the mass. Recod data fo 5 to 10 complete oscillations. 10. Resize and impot these gaphing windows into you template. 11. Answe the following questions: Sping Potential Enegy a. At what position(s) in the oscillation does the sping have the geatest sping potential enegy? b. At what position(s) in the oscillation does the sping have the geatest sping potential enegy? c. What is the maximum sping potential enegy value ecoded in this pat of the lab? SPE max = d. What is the minimum sping potential enegy value ecoded in this pat of the lab? SPE min = Kinetic Enegy a. At what position(s) is the Kinetic Enegy of the mass the geatest? b. At what position(s) is the Kinetic Enegy of the mass the least? c. What is the maximum amount of Kinetic Enegy ecoded in this pat of the lab? KE max = d. What is the minimum amount of Kinetic Enegy ecoded in this pat of the lab? KE min =
9 Compaison of SPE and KE a. Compae the positions of the maximum and minimum enegy values. Descibe what appeas to be happening to the enegy ove the couse of one oscillation. Does this obsevation suppot the Consevation of Enegy pinciple stated in Equations 6 and 7 in the Intoduction to the Lab? Explain. b. Compae the minimum enegy values obtained fom you data. What conclusions can you daw fom this? c. Compae the maximum enegy values obtained fom you data. What conclusions can you daw fom this? (Why ae they not the same?) Peiod of Oscillation a. Fom you gaphs, detemine the time it took the masssping system to complete one oscillation. T measued = Activity 3: Total Enegy 1. Use the Expeiment Calculato to define a calculation called Total Enegy (Kinetic Enegy + Sping Potential Enegy).. Ceate a new gaphing window of Total Enegy vs. Time. 3. Lift the mass to position x = 0, as befoe, and ecod data fo 0 to 5 oscillations. Impot this gaph to you template. Detemine the slope and yintecept of the Total Enegy vs. Time gaph. Slope = Yintecept =
10 7. Answe the following questions: (Hint: Refe to Equations 5, 6, & 7 in the Intoduction of the Lab.) a. Does the Total Enegy vs. Time gaph suppot the Consevation of Enegy pinciple? Why o why not? b. Compae the Total Enegy vs. Time gaph to Equation 5 in the Intoduction of the lab. Why does you data appea to oscillate slightly? Explain. c. Is the initial (when eleased) Total Enegy value of the system (calculated on you gaph) actually equal to mgh 0 as claimed in the Intoduction of the Lab? Veify by calculation. Explain you findings. Lab # Enegy Consevation
mv2. 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationSamples 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 informationChapter 6. GraduallyVaried Flow in Open Channels
Chapte 6 GaduallyVaied Flow in Open Channels 6.. Intoduction A stea nonunifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gaduallyvaied flow (GVF). The backwate
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 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 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 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 informationPhysics 202, Lecture 4. Gauss s Law: Review
Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential
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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationL19 Geomagnetic Field Part I
Intoduction to Geophysics L191 L19 Geomagnetic Field Pat I 1. Intoduction We now stat the last majo topic o this class which is magnetic ields and measuing the magnetic popeties o mateials. As a way o
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 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 informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationProblems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)
Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems
More informationTheory and measurement
Gavity: Theoy and measuement Reading: Today: p11  Theoy of gavity Use two of Newton s laws: 1) Univesal law of gavitation: ) Second law of motion: Gm1m F = F = mg We can combine them to obtain the gavitational
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 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 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 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 informationConcept and Experiences on using a Wikibased System for Softwarerelated Seminar Papers
Concept and Expeiences on using a Wikibased System fo Softwaeelated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wthaachen.de,
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 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 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 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 informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049001 Lisboa Email: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB30 AIRCRAFT  PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
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 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 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 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 informationClassical Lifetime of a Bohr Atom
1 Poblem Classical Lifetime of a Boh Atom James D. Olsen and Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 85 (Mach 7, 5) In the Boh model of the hydogen atom s gound state,
More informationReview of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction.
Appendi A Review of Vectos This appendi is a summa of the mathematical aspects of vectos used in electicit and magnetism. Fo a moe detailed intoduction to vectos, see Chapte 1. A.1 DESCRIBING THE 3D WORLD:
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
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 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 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 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 information