Experiment 6: Centripetal Force

Size: px
Start display at page:

Download "Experiment 6: Centripetal Force"

Transcription

1 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 must be foces acting on an object moving in a cicula path since it does not move off in a staight line. The second law of motion ( = ma) also indicates foces since an unbalanced foce is equied to change the motion of an object. An object moving in a cicula path is continuously being acceleated since it is continuously changing diection. This means that thee is a continuous unbalanced foce acting on the object that pulls it out of a staight-line path. The foce that pulls an object out of a staight-line path and into a cicula path is called a centipetal foce. The magnitude of the centipetal foce equied to keep an object in a cicula path depends on the inetia (o mass) and the acceleation of the object, as you know fom the second law ( = ma). The acceleation of an object moving in unifom cicula motion is a = v /, so the magnitude of the centipetal foce of an object with a mass (m) that is moving with a velocity (v) in a cicula obit of adius () can be found fom mv =. The distance (cicumfeence) aound a cicle is π. The velocity of an object moving in a cicula path can be found fom v = d/t, o v = π/t whee π is the distance aound one complete cicle and T is the peiod (time) equied to make one evolution. Substituting fo v, = m T o π = m 4π T, 4π m 1 = T m = 4π. T This is the elationship between the centipetal foce (c), the mass (m) of the object in cicula motion, the adius () of the cicle, and the time (T) equied fo one complete evolution. 65

2 Pocedue 1. The equipment setup fo this expeiment consists of weights (washes) attached to a sting, and a ubbe stoppe that swings in a hoizontal cicle. You will swing the stoppe in a cicle and adjust the speed so that the stoppe does not have a tendency to move in o out, thus balancing the centipetal foce ( c ) on the stoppe with the balancing foce ( b ), o mg, exeted by the washes on the sting. Plastic o glass tube (small diamete) Stoppe (m) Place clip hee Washes ( = mg) igue 6.1. Place some washes on the sting and pactice otating the stoppe by placing a finge next to the sting, then moving you hand in a cicula motion. You ae tying to move the stoppe with a consistent, balancing motion, just enough so the stoppe does not move in o out. Keep the stoppe moving in a faily hoizontal cicle, without the washes moving up o down. An alligato (o pape) clip placed on the sting just below the tube will help you maintain a consistent motion by poviding a point of efeence as well as helping with length measuements. Be caeful of the moving stoppe so it does not hit you in the head. 3. Afte you have leaned to move the stoppe with a constant motion in a hoizontal plane, you ae eady to take measuements. The distance fom the sting at the top of the tube to the cente of the stoppe is the adius () of the cicle of otation. The mass (m) of the stoppe is detemined with a balance. The balancing foce ( b ) of the washes is detemined fom the mass of the washes times g ( b = mg). The peiod (T) is detemined by measuing the time of a numbe of evolutions, then dividing the total time by the numbe of evolutions to obtain the time fo one evolution. o example, 0 evolutions in 10 seconds would mean that 10 0, o 0.5 seconds, is equied fo one evolution. This data is best obtained by one peson acting as a counte speaking aloud while anothe peson acts as a time. 66

3 4. Make fou o five tials by otating the stoppe with a diffeent numbe of washes on the sting each time, adding o emoving two washes (about 0 g) fo each tial. o each tial, ecod in Data Table 6.1 the mass of the washes, the adius of the cicle, and the aveage time fo a single evolution. Data Table Centipetal oce Relationships Tial Mass of washes (m) Balancing Radius Time Centipetal foce foce ( b ) () (t) (c) (kg) (N) (m) (s) (N) Mass of stoppe kg 67

4 5. Calculate and ecod the balancing foce ( b ) fo each tial fom the mass of washes times g (9.8 m/s ), o b = mg. 6. Calculate and ecod the centipetal foce ( c ) fo each tial fom m = 4π. T Consideing the balancing foce ( b ) as the accepted value, and the calculated centipetal foce ( c ) as the expeimental value, calculate you pecentage eo fo each tial of this expeiment. Analyze the pecentage eos and othe vaiables to identify some tends, if any. Tial 1 : Tial : Tial 3 : = 10% 100 = 7.% = 1.% 7 Tial 4 : = 5.% 1 Tial 5 : = 5.% 1 68

5 Results 1. Did the balancing foce ( b ) equal the centipetal foce ( c )? Do you conside them equal o not equal? Why o why not? The balancing foce and the centipetal foce ae basically equal. The balancing foce ceates the tension in the sting which keeps the stoppe moving in a cicle. The data suppots this since the eo is less than 10%.. Analyze the eos that could be made in all the measued quantities. What was pobably the geatest souce of eo and why? Discuss how these eos could be avoided and how the expeiment in geneal could be impoved. Thee ae at least two majo souces of eos: (a) time measuement, and (b) adius measuement The eos in the time measuement can be educed by timing a numbe of evolutions and finding the aveage. The eo in the adius measuement can be educed by choosing a easonable adius and making it on the sting. Then you will swing the stoppe at such a ate to make the sting stay at the mak. This also helps the student keep a constant speed thoughout the timing pocess 3. Discuss any tends that wee noted in you analysis of pecentage eo fo the diffeent tials. Analyze the meaning of any obseved tends o discuss the meaning of the lack of any tends. Thee is moe eo when the time fo a evolution is too long. This is because it is difficult to keep the stoppe moving at a constant speed. Thus, as the hanging mass inceases, and the time of evolution deceases, thee will be less eo. o the tial with a small hanging mass, it is best to make the adius small as well. This will educe the time fo a evolution and help keep the eo down. 69

6 4. Was the pupose of this lab accomplished? Why o why not? (You answe to this question should be easonable and make sense, showing thoughtful analysis and caeful, thoough thinking.) (The student should be able to explain the basics of centipetal acceleation. They should be able to explain how the centipetal acceleation (o centipetal foce) changes when the adius changes o when the time of evolution changes. They should also undestand that the tension; in the sting, o indiectly the hanging weight, supplies the foce needed to keep the stoppe moving in a cicle.) Invitation to Inquiy 1. Did you eve ty to figue out which is a cooked egg and which is a aw one without beaking the shell? One way to accomplish this is by spinning the eggs on a plate, and the wellcooked one will continue to spin while the uncooked egg will ock back and foth. The yolk is heavie than the white, but why would an uncooked egg spin moe slowly? Use you undestanding of centipetal foce to develop some ideas about why eggs should behave this way, then design a demonstation o expeiment to test you idea.. Expeiment with some things that otate, such as olling cylindes. Roll lage, small, solid, hollow, and vaious combinations of lage and solid cylindes, small and solid cylindes down an incline. Pedict ahead of time which will each the bottom of the incline fist. Then test you pedictions. 3. A hollow and solid cylinde of the same size do not have the same weight. If you oll the two cylindes down an incline slope togethe, side by side, the solid cylinde should win. Yet if you attach stings of equal lengths to make pendulums fom the same hollow and solid cylindes, then you will find that they swing togethe, side by side. Is this tue? Expeiment to find out, then be pepaed to explain you findings. 4. Exploe elationships between mass distance fom an axis and how had it is to set an object into otational motion. Conside using a baton with some kind of movable masses that can be fixed to the baton diffeent distances fom the axis of otation. A lage wooden dowel od and lumps of clay might be a good expeimental altenative to a baton. 70

12. Rolling, Torque, and Angular Momentum

12. 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 information

The Role of Gravity in Orbital Motion

The 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 information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 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 information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 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

Exam 3: Equation Summary

Exam 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 information

Gravitation. AP Physics C

Gravitation. 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 information

Determining solar characteristics using planetary data

Determining 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 information

Deflection of Electrons by Electric and Magnetic Fields

Deflection 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 information

Lab M4: The Torsional Pendulum and Moment of Inertia

Lab 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 information

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary

7 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 information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 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 information

Episode 401: Newton s law of universal gravitation

Episode 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 information

Phys 2101 Gabriela González. cos. sin. sin

Phys 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 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

(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 information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 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 information

Lab #7: Energy Conservation

Lab #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 1-4 Intoduction: Pehaps one of the most unusual

More information

Voltage ( = Electric Potential )

Voltage ( = 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 information

F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.

F 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 information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Voltage ( = Electric Potential )

Voltage ( = 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 information

Figure 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!

Figure 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 information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY 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 information

Displacement, Velocity And Acceleration

Displacement, 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 information

Thank you for participating in Teach It First!

Thank you for participating in Teach It First! Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Suppot Coach, Foundational Mathematics teache lesson followed by the coesponding student lesson. We ae confident

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 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 information

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy

More information

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field

Physics 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 information

Experiment MF Magnetic Force

Experiment 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 information

Multiple choice questions [70 points]

Multiple 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 information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate 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 information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 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 information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The 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 information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 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 information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & 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 information

Multiple choice questions [60 points]

Multiple 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 information

AP Physics Electromagnetic Wrap Up

AP 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 information

Solution Derivations for Capa #8

Solution 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 information

Model Question Paper Mathematics Class XII

Model 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 information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector 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 information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 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 information

Define What Type of Trader Are you?

Define 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 information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information

Forces & Magnetic Dipoles. r r τ = μ B r

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 information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT 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 information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! 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 information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

UNIT CIRCLE TRIGONOMETRY

UNIT 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 information

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

More information

TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION

TORQUE 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 information

Chapter 30: Magnetic Fields Due to Currents

Chapter 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 information

est 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.

est 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 information

Do Vibrations Make Sound?

Do 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

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Financing Terms in the EOQ Model

Financing 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 information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 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 information

Gauss Law. Physics 231 Lecture 2-1

Gauss 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 information

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions.

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions. Facts about the LS Design LATIN SQUARE DESIGN (LS) -With the Latin Squae design you ae able to contol vaiation in two diections. -Teatments ae aanged in ows and columns -Each ow contains evey teatment.

More information

10. Collisions. Before During After

10. 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

Worked Examples. v max =?

Worked 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 information

Introduction to Fluid Mechanics

Introduction 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 information

Converting knowledge Into Practice

Converting knowledge Into Practice Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading

More information

Chapter 4: Fluid Kinematics

Chapter 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 information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

SELF-INDUCTANCE AND INDUCTORS

SELF-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 information

2. Orbital dynamics and tides

2. 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 information

Ignorance is not bliss when it comes to knowing credit score

Ignorance is not bliss when it comes to knowing credit score NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

An Introduction to Omega

An 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 information

Semipartial (Part) and Partial Correlation

Semipartial (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 information

4a 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

4a 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 information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR 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 information

Carter-Penrose diagrams and black holes

Carter-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 information

The Detection of Obstacles Using Features by the Horizon View Camera

The Detection of Obstacles Using Features by the Horizon View Camera The Detection of Obstacles Using Featues b the Hoizon View Camea Aami Iwata, Kunihito Kato, Kazuhiko Yamamoto Depatment of Infomation Science, Facult of Engineeing, Gifu Univesit aa@am.info.gifu-u.ac.jp

More information

Problems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976)

Problems 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 information

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 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 information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The 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

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011 The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 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 information

Analytical Proof of Newton's Force Laws

Analytical 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 information

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w 1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a

More information

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

INVESTIGATION 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 information

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg

More information

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.

Gravity. 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 information

Solutions for Physics 1301 Course Review (Problems 10 through 18)

Solutions 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 information

Skills Needed for Success in Calculus 1

Skills 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

Timing Synchronization in High Mobility OFDM Systems

Timing Synchronization in High Mobility OFDM Systems Timing Synchonization in High Mobility OFDM Systems Yasamin Mostofi Depatment of Electical Engineeing Stanfod Univesity Stanfod, CA 94305, USA Email: yasi@wieless.stanfod.edu Donald C. Cox Depatment of

More information

Controlling the Money Supply: Bond Purchases in the Open Market

Controlling the Money Supply: Bond Purchases in the Open Market Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises

More information

Uncertainty Associated with Microbiological Analysis

Uncertainty Associated with Microbiological Analysis Appendix J STWG Pat 3 Uncetainty 7-8-06 Page 1 of 31 Uncetainty Associated with Micobiological Analysis 1. Intoduction 1.1. Thee ae only two absolute cetainties in life: death and taxes! Whateve task we

More information

How to recover your Exchange 2003/2007 mailboxes and emails if all you have available are your PRIV1.EDB and PRIV1.STM Information Store database

How 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 information

Software Engineering and Development

Software Engineering and Development I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining

More information

Faithful Comptroller s Handbook

Faithful Comptroller s Handbook Faithful Comptolle s Handbook Faithful Comptolle s Handbook Selection of Faithful Comptolle The Laws govening the Fouth Degee povide that the faithful comptolle be elected, along with the othe offices

More information

Office of Family Assistance. Evaluation Resource Guide for Responsible Fatherhood Programs

Office of Family Assistance. Evaluation Resource Guide for Responsible Fatherhood Programs Office of Family Assistance Evaluation Resouce Guide fo Responsible Fathehood Pogams Contents Intoduction........................................................ 4 Backgound..........................................................

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information