Discussion Examples Chapter 10: Rotational Kinematics and Energy

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Discussion Examples Chapter 10: Rotational Kinematics and Energy"

Transcription

1 Discussion Examples Chaper : Roaional Kinemaics and Energy 9. The Crab Nebula One o he mos sudied objecs in he nigh sky is he Crab nebula, he remains o a supernova explosion observed by he Chinese in 54. In 968 i was discovered ha a pulsar a rapidly roaing neuron sar ha emis a pulse o radio waves wih each revoluion lies near he cener o he Crab nebula. The period o his pulsar is 33 ms. Wha is he angular speed (in rad/s) o he Crab nebula pulsar? Picure he Problem: The pulsar roaes abou is axis, compleing revoluion in.33 s. Sraegy: Divide one revoluion or radians by he period in seconds o ind he angular speed. Soluion: Calculae using equaion -3: rad rad 9 rad/s T.33s Insigh: The roaion rae o he pulsar can also be described as 8 rev/min.. A discus hrower sars rom res and begins o roae wih a consan angular acceleraion o. rad/s. (a) How many revoluions does i ake or he discus hrower s angular speed o reach 6.3 rad/s? (b) How much ime does his ake? Picure he Problem: The discus hrower roaes abou a verical axis hrough her cener o mass, increasing her angular velociy a a consan rae. Sraegy: Use he kinemaic equaions or roaion (equaions -8 hrough -) o ind he number o revoluions hrough which he ahlee roaes and he ime elapsed during he speciied inerval. Soluion:. (a) Solve equaion - or : Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher. 6.3 rad/s 9. rad rev rad. rad/s.4 rev 6.3 rad/s. (b) Solve equaion -8 or :.9 s. rad/s Insigh: Noice he ahlee urns nearly one and a hal imes around. Thereore, she should begin her spin wih her back urned oward he range i she plans o hrow he discus aer reaching 6.3 rad/s. I she does le go a ha poin, he linear speed o he discus will be abou 6.3 m/s (or a. m long arm) and will ravel abou 4. m i launched a 45 above level ground. No ha grea compared wih a championship hrow o over 4 m (3 ) or a college woman. 35. IP Je o he Jungle swings on a vine ha is 7. m long. Suppose ha a some poin in his swing Je has an angular speed o.85 rad/s and an angular acceleraion o.6 rad/s. Find he magniude o his cenripeal, angenial, and oal acceleraions, and he angle his oal acceleraion makes wih respec o he angenial direcion o moion. Picure he Problem: Je clings o a vine and swings along a verical arc. Sraegy: Use equaion -3 o ind Je s cenripeal acceleraion and equaion -4 o ind his angenial acceleraion. Add hese wo perpendicular vecors o ind he oal acceleraion. Soluion:. Apply equaion -3 direcly: a r 7. m.85 rad/s. Apply equaion -4 direcly: a cp 5. m/s r 7. m.6 rad/s 4.46 m/s 3. Add he wo perpendicular vecors: a a a 4. Find he angle : cp 5. m/s m/s 6.85 m/s acp 5. m/s an an 49.4 a 4.46 m/s Insigh: The angle will increase wih Je s speed i his angular acceleraion remains consan because acp depends on he square o he angenial speed.

2 Chapers -: Roaional Dynamics and Saic Equilibrium 5. As you drive down he road a 7 m/s, you press on he gas pedal and speed up wih a uniorm acceleraion o. m/s or.65 s. I he ires on your car have a radius o 33 cm, wha is heir angular displacemen during his period o acceleraion? Picure he Problem: Your car s ires roll wihou slipping, increasing heir velociy a a consan rae. Sraegy: Use he ac ha he ires roll wihou slipping o ind he angular acceleraion and angular velociy rom heir linear counerpars. Then use he kinemaic equaions or roaion (equaions -8 hrough -) o deermine he angle hrough which he ire roaed during he speciied inerval. Soluion:. Solve equaion - or : v 7 m/s 5 rad/s r.33 m. Solve equaion -4 or : a. m/s 3.4 rad/s r.33 m 3. Apply equaion - direcly: 5 rad/s.65 s 3.4 rad/s.65 s 35 rad 5.5 rev Insigh: Anoher way o solve his quesion is o ind he inal angular speed (54 rad/s) and hen use ind he answer. o This quesion is MUCH more diicul han you are expeced o handle in his course, bu i is very ineresing so I include i here: 63. Find he rae a which he roaional kineic energy o he Earh is decreasing. The Earh has a momen o ineria o E 6.33MER, where RE 6.38 m and ME 5.97 kg, and is roaional period increases by.3 ms wih each passing cenury. Give your answer in was. Picure he Problem: The Earh roaes on is axis, slowing down wih consan angular acceleraion. Sraegy: Deermine he dierence in roaion raes over he span o a cenury by approximaing T T T because.3 s is iny compared wih he ime (86,4 s) i akes o complee one revoluion. Then use equaion -6 o ind he average angular acceleraion over he -year ime inerval. Soluion:. Find he dierence in angular speeds: 4.94 rad/s.84 s 365 rev rad rev 365 d4 h/d36 s/h T T T T T T T T T T T. Find he sum o he angular speeds: T T T T T T T T T T T T T 3. Muliply he resuls o seps and : T 3 T T T T 4. Find he dierence Kr over a ime inerval o years: T I T Kr I I I I 3 3 T T.33M E RE T 3 T kg 6.38 m.3 s 86,4 s. J Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher.

3 Chapers -: Roaional Dynamics and Saic Equilibrium 5. Use equaion 7- o ind he energy loss rae (power): W P. J 7 y 3.6 s/y 3.5 W 3.5 TW Insigh: Your irs insinc migh be o ind he angular speed a hundred years ago assuming a period o 4. hrs ( rad/s) and igure ou he angular speed in ( rad/s), bu as you can see, aemping o subrac hese numbers requires us o ignore he rules or signiican igures. Using he approximaion oulined above allows us o avoid he subracion problem and keep wo signiican igures. The huge energy loss is due primarily o idal ricion, as he ocean ides dissipae he kineic energy o he Earh s roaion ino hea. 7. IP Awood s Machine The wo masses ( m 5. kg and m 3. kg ) in he Awood s machine shown below are released rom res, wih m a a heigh o.75 m above he loor. When m his he ground is speed is.8 m/s. Assuming ha he pulley is a uniorm disk wih a radius o cm, (a) ouline a sraegy ha allows you o ind he mass o he pulley. (b) Implemen he sraegy given in par (a) and deermine he pulley s mass. Picure he Problem: The larger mass alls and he smaller mass rises unil he larger mass his he loor. Sraegy: Use conservaion o mechanical energy, including he roaional energy o he pulley, o deermine he mass o he pulley. Because he rope does no slip on he pulley, here is a direc relaionship v r beween he roaion o he pulley and he linear speed o he rope and masses. Soluion:. (a) Equae he iniial and inal mechanical energies, hen solve or he mass o he pulley.. (b) Se Ei E and le vr p : p U K U K m gh m gh m v m v I i i p m m gh m m v m prp v rp 3. Rearrange he equaion and solve or m : p 4 m v m m gh m m v 4 p m m gh m m v mp v 4. kg 9.8 m/s.75 m 8. kg.8 m/s.8 m/s m. kg p Insigh: By he ime he masses reach.8 m/s,.8 J or % o he 5 J o oal kineic energy is sored in he kineic energy o he pulley, so he pulley plays a minor role in he energy balance o he sysem. Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher. 3

4 Chapers -: Roaional Dynamics and Saic Equilibrium Chaper : Roaional Dynamics and Saic Equilibrium 3. A.6 kg bowling rophy is held a arm s lengh, a disance o.65 m rom he shoulder join. Wha orque does he rophy exer abou he shoulder i he arm is (a) horizonal, or (b) a an angle o.5 below he horizonal? Picure he Problem: The arm exends ou eiher horizonally or a some angle below horizonal, and he weigh o he rophy is exered sraigh downward on he hand. Sraegy: The orque equals he momen arm imes he orce according o equaion -3. In his case he momen arm is he horizonal disance beween he shoulder and he hand, and he orce is he downward weigh o he rophy. Find he horizonal disance in each case and muliply i by he weigh o he rophy o ind he orque. In par (b) he horizonal disance is r r cos.65 m cos m. Soluion:. (a) Muliply he momen arm by he weigh: r mg.65 m.6 kg 9.8 m/s 9.56 N m. (b) Muliply he momen arm by he weigh: r mg.559 m.6 kg 9.8 m/s 8.83 N m Insigh: The orque on he arm is reduced as he arm is lowered. The orque is exacly zero when he arm is verical. 4. IP A wheel on a game show is given an iniial angular speed o. rad/s. I comes o res aer roaing hrough.75 o a urn. (a) Find he average orque exered on he wheel given ha i is a disk o radius.7 m and mass 6.4 kg. (b) I he mass o he wheel is doubled and is radius is halved, will he angle hrough which i roaes beore coming o res increase, decrease, or say he same? Explain. (Assume ha he average orque exered on he wheel is unchanged.) Picure he Problem: The wheel roaes abou is axis, decreasing is angular speed a a consan rae, and comes o res. Sraegy: Use Table - o ind he momen o ineria o a uniorm disk and calculae I. Then use equaion - o ind he angular acceleraion rom he iniial angular speed and he angle hrough which he wheel roaed. Use I and ogeher in equaion -4 o ind he orque exered on he wheel. Soluion:. (a) Use Table - o ind I MR : I MR 6.4 kg.7 m.6 kg m. Solve equaion - or :. rad/s.58 rad/s.75 rev rad rev 3. Apply equaion -4 direcly: I.6 kg m.58 rad/s.5 N m 4. (b) I he mass o he wheel is doubled and is radius is halved, he momen o inerial will be cu in hal (doubled because o he mass, cu o a ourh because o he radius). Thereore he magniude o he angular acceleraion will increase i he ricional orque remains he same, and he angle hrough which he wheel roaes beore coming o res will decrease. Insigh: I he momen o ineria is cu in hal, he angular acceleraion will double o.3 rad/s and he angle hrough which he wheel roaes will be cu in hal o.38 rev. This is because he wheel has less roaional ineria bu he ricional orque remains he same. We ben he rules or signiican igures in sep o avoid rounding error in sep 3. Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher. 4

5 Chapers -: Roaional Dynamics and Saic Equilibrium 6. IP BIO A Person s Cener o Mass To deermine he locaion o her cener o mass, a physics suden lies on a lighweigh plank suppored by wo scales.5 m apar, as indicaed in Figure 6xx3. I he le scale reads 9 N, and he righ scale reads N, ind (a) he suden s mass and (b) he disance rom he suden s head o her cener o mass. Picure he Problem: The person lies on a lighweigh plank ha ress on wo scales as shown in he diagram a righ. Sraegy: Wrie Newon s Second Law in he verical direcion and Newon s Second Law or roaion o obain wo equaions wih wo unknowns, m and x cm. Solve each o ind m and x cm. Using he le side o he plank as he origin, here are wo orques o consider: he posiive orque due o he righ hand scale and he negaive orque due o he person s mass. Soluion:. (a) Wrie Newon s Second Law in he verical direcion o ind m: Fy F F mg F F 9 N m 4 kg g 9.8 m/s. (b) Wrie Newon s Second Law or r F xcmmg roaion and solve or x cm : xf.5 m N x.74 m mg cm 4 kg9.8 m/s Insigh: The equaion in sep does no depend on he axis o roaion ha we choose, bu he equaion in sep does. Neverheless, we ind exacly he same x cm i we choose he oher scale, near her ee, o be he axis o roaion. 49. IP You pull downward wih a orce o 8 N on a rope ha passes over a disk-shaped pulley o mass. kg and radius.75 m. The oher end o he rope is aached o a.67-kg mass. (a) Is he ension in he rope he same on boh sides o he pulley? I no, which side has he larges ension? (b) Find he ension in he rope on boh sides o he pulley. Picure he Problem: You pull sraigh downward on a rope ha passes over a disk-shaped pulley and hen suppors a weigh on he oher side. The orce o your pull roaes he pulley and acceleraes he mass upward. Sraegy: Wrie Newon s Second Law or he hanging mass and Newon s Second Law or orque abou he axis o he pulley, and solve he wo expressions or he ension T a he oher end o he rope. We are given in he problem ha T 5 N. Le m be he mass o he pulley, r be he radius o he pulley, and M be he hanging mass. For he diskshaped pulley he momen o ineria is I mr. Soluion:. (a) No, he ension in he rope on he oher end o he rope acceleraes he hanging mass, bu he ension on your side boh impars angular acceleraion o he pulley and acceleraes he hanging mass. Thereore, he rope on your side o he pulley has he greaer ension.. (b) As saed in he problem, T 8 N or he rope on your side o he pulley. or he pulley: 3. Se F ma or he hanging mass: Fy T Mg Ma 4. Se I 5. Subsiue he expression or a rom sep 4 ino he one rom sep 3, and solve or T (he ension on he oher side o he pulley rom you): rt rt I mr a r a T T m T Mg M T T m mt mmg MT MT M T mg T M m.67 kg 8 N. kg9.8 m/s.67 kg. kg 8 N Insigh: The ne orce on he hanging mass is hus T Mg N.4 N, enough o accelerae i upward a ar 7 m/s.75 m 3 rad/s. 7 m/s. The angular acceleraion o he pulley is hus Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher. 5

6 Chapers -: Roaional Dynamics and Saic Equilibrium 69. A disk-shaped merry-go-round o radius.63 m and mass 55 kg roaes reely wih an angular speed o.64 rev/s. A 59.4-kg person running angenial o he rim o he merry-go-round a 3.4 m/s jumps ono is rim and holds on. Beore jumping on he merry-go-round, he person was moving in he same direcion as he merry-go-round s rim. Wha is he inal angular speed o he merry-go-round? Picure he Problem: A child runs angenially o a roaing merry-go-round and hops on. Sraegy: Use conservaion o angular momenum because here is no ne orque on he sysem as long as he sysem includes boh he person and he merry-go-round. Find he momens o ineria o he disk-shaped merry-go-round, I M r, and he sysem aer he person hops on I M r mr mgr, where M is he mass o he merry-go-round, m is he mass o he person, and r is he radius o he merry-go-round. Se Li L and solve or he inal angular speed, where he iniial angular speed is: i.64 rev/s rad rev 4.3 rad/s. Soluion:. Se Li L L L L disk person inal and rearrange M r i mv r M r mr. Now solve or : M r mv r Mr mv +mr i i M r + mr M r 55 kg.63 m4.3 rad/s 59.4 kg3.4 m/s 55 kg.63 m 59.4 kg.63 m.84 rad/s Insigh: The merry-go-round has slowed down because he iniial linear speed o he person (3.4 m/s) is less han he iniial linear speed o he rim o he merry-go-round (.6 m/s). 79. A person exers a angenial orce o 36. N on he rim o a disk-shaped merry-go-round o radius.74 m and mass 67 kg. I he merry-go-round sars a res, wha is is angular speed aer he person has roaed i hrough an angle o 3.5 Picure he Problem: The merry-go-round is a uniorm disk ha is given an angular acceleraion abou is cener o mass by he applicaion o an unbalanced orque. Sraegy: The work done by he applied orque impars kineic energy o he merry-go-round. Se he orque imes he angular displacemen equal o he inal kineic energy o he merry-go-round (equaions -7 and -8) and solve or. The momen o ineria o he merry-go-round is aken o be I MR, as indicaed in Table - or a uniorm disk roaing abou is axis. Soluion:. Se W K, applying equaions -7, -3, and -7:. Solve or : rf K K I rf RF I MR i 67 kg.74 m.74 m 36. N 3.5 rev 8.43 rad/s Insigh: This roaion rae corresponds o a linear speed o only.6 m/s or he rim o he merry-go-round. The applied orce did 56. J o work o give he merry-go-round 56. J o roaional kineic energy. Copyrigh Pearson Educaion, Inc. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion o his maerial may be reproduced, in any orm or by any means, wihou permission in wriing rom he publisher. 6

Rotational Inertia of a Point Mass

Rotational Inertia of a Point Mass Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha

More information

Section 7.1 Angles and Their Measure

Section 7.1 Angles and Their Measure Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed

More information

Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr

Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i

More information

Acceleration Lab Teacher s Guide

Acceleration Lab Teacher s Guide Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

More information

Newton s Laws of Motion

Newton s Laws of Motion Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The

More information

Chapter 2 Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

More information

MOTION ALONG A STRAIGHT LINE

MOTION ALONG A STRAIGHT LINE Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,

More information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009.

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009. Name: Teacher: DO NOT OPEN THE EXMINTION PPER UNTIL YOU RE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINL EXMINTION June 2009 Value: 100% General Insrucions This examinaion consiss of wo pars. Boh pars

More information

A Curriculum Module for AP Calculus BC Curriculum Module

A Curriculum Module for AP Calculus BC Curriculum Module Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Motion Along a Straight Line

Motion Along a Straight Line Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his

More information

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing

More information

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3.

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3. SOLI MEHNIS TUTORIL GER SYSTEMS This work covers elemens of he syllabus for he Edexcel module 21722P HN/ Mechanical Principles OUTOME 3. On compleion of his shor uorial you should be able o do he following.

More information

Inductance and Transient Circuits

Inductance and Transient Circuits Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual

More information

AP Calculus AB 2010 Scoring Guidelines

AP Calculus AB 2010 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 2007 Scoring Guidelines AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

More information

The Torsion of Thin, Open Sections

The Torsion of Thin, Open Sections EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such

More information

9. Capacitor and Resistor Circuits

9. Capacitor and Resistor Circuits ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

More information

MA261-A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM

MA261-A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM MA6-A Calculus III 006 Fall Homework 4 Soluions Due 9/9/006 00AM 97 #4 Describe in words he surface 3 A half-lane in he osiive x and y erriory (See Figure in Page 67) 97 # Idenify he surface cos We see

More information

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: -Solving Exponenial Equaions (The Mehod of Common Bases) -Solving Exponenial Equaions (Using Logarihms)

More information

A = p 4 (0.05)2 = 1.9635(10-3 ) m 2. J = p 2 (0.025)4 = 0.61359(10-4 ) m 4. s = P A = 2(10 3 ) 1.9635(10-3 = 1.019 MPa. t = Tc J = 500(0.

A = p 4 (0.05)2 = 1.9635(10-3 ) m 2. J = p 2 (0.025)4 = 0.61359(10-4 ) m 4. s = P A = 2(10 3 ) 1.9635(10-3 = 1.019 MPa. t = Tc J = 500(0. 014 Pearson Educaion, Inc., Upper Saddle River, NJ. All righs reserved. This maerial is proeced under all copyrigh laws as hey currenly exis. No porion of his maerial may be reproduced, in any form or

More information

Section 5.1 The Unit Circle

Section 5.1 The Unit Circle Secion 5.1 The Uni Circle The Uni Circle EXAMPLE: Show ha he poin, ) is on he uni circle. Soluion: We need o show ha his poin saisfies he equaion of he uni circle, ha is, x +y 1. Since ) ) + 9 + 9 1 P

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot College Physics Lab RC Circuits Scott Hildreth Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

More information

Permutations and Combinations

Permutations and Combinations Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

Kinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.

Kinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard. Chaper 2 Kinemaics in 1-D From Problems and Soluions in Inroducory Mechanics (Draf ersion, Augus 2014) Daid Morin, morin@physics.harard.edu As menioned in he preface, his book should no be hough of as

More information

4.2 Trigonometric Functions; The Unit Circle

4.2 Trigonometric Functions; The Unit Circle 4. Trigonomeric Funcions; The Uni Circle Secion 4. Noes Page A uni circle is a circle cenered a he origin wih a radius of. Is equaion is as shown in he drawing below. Here he leer represens an angle measure.

More information

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails INTRODUCTION TO EMAIL MARKETING PERSONALIZATION How o increase your sales wih personalized riggered emails ECOMMERCE TRIGGERED EMAILS BEST PRACTICES Triggered emails are generaed in real ime based on each

More information

1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,

1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t, Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

More information

A Probability Density Function for Google s stocks

A Probability Density Function for Google s stocks A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009 ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

More information

m m m m m correct

m m m m m correct Version 055 Miderm 1 OConnor (05141) 1 This prin-ou should have 36 quesions. Muliple-choice quesions ma coninue on he ne column or pae find all choices before answerin. V1:1, V:1, V3:3, V4:, V5:1. 001

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

AP Physics Velocity and Linear Acceleration Unit 1 Problems:

AP Physics Velocity and Linear Acceleration Unit 1 Problems: Uni 1 Problems: Linear Velociy and Acceleraion This enire se of problems is due he day of he es. I will no accep hese for a lae grade. * = Problems we do ogeher; all oher problems are homework (bu we will

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

Part 1: White Noise and Moving Average Models

Part 1: White Noise and Moving Average Models Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

More information

Graduate Macro Theory II: Notes on Neoclassical Growth Model

Graduate Macro Theory II: Notes on Neoclassical Growth Model Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.

More information

Using RCtime to Measure Resistance

Using RCtime to Measure Resistance Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a buil-in ADC (Analog o Digial Converer)

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 0-7-380-7 Ifeachor

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Physics 111 Fall 2007 Electric Currents and DC Circuits

Physics 111 Fall 2007 Electric Currents and DC Circuits Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels

More information

Economics Honors Exam 2008 Solutions Question 5

Economics Honors Exam 2008 Solutions Question 5 Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I

More information

Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions to Nonfarm Payroll Employment: 1964 to 2011 Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

More information

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n). FW 662 Densiy-dependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Long-erm

More information

Torsion of Closed Thin Wall (CTW) Sections

Torsion of Closed Thin Wall (CTW) Sections 9 orsion of losed hin Wall (W) Secions 9 1 Lecure 9: ORSION OF LOSED HIN WALL (W) SEIONS ALE OF ONENS Page 9.1 Inroducion..................... 9 3 9.2 losed W Secions.................. 9 3 9.3 Examples......................

More information

Period 4 Activity Solutions: Transfer of Thermal Energy

Period 4 Activity Solutions: Transfer of Thermal Energy Period 4 Aciviy Soluions: Transfer of Thermal nergy 4.1 How Does Temperaure Differ from Thermal nergy? a) Temperaure Your insrucor will demonsrae molecular moion a differen emperaures. 1) Wha happens o

More information

Chapter 2: Principles of steady-state converter analysis

Chapter 2: Principles of steady-state converter analysis Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

More information

SkySails Tethered Kites for Ship Propulsion and Power Generation: Modeling and System Identification. Michael Erhard, SkySails GmbH, Hamburg, Germany

SkySails Tethered Kites for Ship Propulsion and Power Generation: Modeling and System Identification. Michael Erhard, SkySails GmbH, Hamburg, Germany SkySails Tehered Kies for Ship Propulsion and Power Generaion: Modeling and Sysem Idenificaion Michael Erhard, SkySails GmbH, Hamburg, Germany Conens Inroducion SkySails Marine and Power Simple Model Sensors

More information

IMPORTANT NOTE ABOUT WEBASSIGN:

IMPORTANT NOTE ABOUT WEBASSIGN: Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

UNIT 3 POWER TRANSMISSION DEVICES

UNIT 3 POWER TRANSMISSION DEVICES UNI 3 POWER RANSMISSION DEVIES Power ransmission Devices Srucure 3. Inroducion Objecives 3. Power ransmission Devices 3.. Bels 3.. hain 3..3 Gears 3.3 ransmission Screw 3.4 Power ransmission by Bels 3.4.

More information

Transient Analysis of First Order RC and RL circuits

Transient Analysis of First Order RC and RL circuits Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage

More information

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are

More information

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations. Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given

More information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convolution. Recommended Problems. x2[n] 1 2[n] 4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

A Mathematical Description of MOSFET Behavior

A Mathematical Description of MOSFET Behavior 10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical

More information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 Introduction to Mathematical Finance Lesson 5 26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

More information

Chapter 4: Exponential and Logarithmic Functions

Chapter 4: Exponential and Logarithmic Functions Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

More information

Form measurement systems from Hommel-Etamic Geometrical tolerancing in practice DKD-K-02401. Precision is our business.

Form measurement systems from Hommel-Etamic Geometrical tolerancing in practice DKD-K-02401. Precision is our business. Form measuremen sysems from Hommel-Eamic Geomerical olerancing in pracice DKD-K-02401 Precision is our business. Drawing enries Tolerance frame 0.01 0.01 Daum leer Tolerance value in mm Symbol for he oleranced

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

Basic Description for PCL Series

Basic Description for PCL Series Insrucion documens Pulse Conrol LSIs Basic Descripion or PCL Series Nippon Pulse Moor Co., Ld. Table o conens I. Ouline 1 1. PCL-240 amily 1 2. PCL50oo series 1 3. PCL61oo series / 60oo series 1 II. Dierences

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

Voltage level shifting

Voltage level shifting rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bi-polar

More information

Circuit Types. () i( t) ( )

Circuit Types. () i( t) ( ) Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance. 5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()

More information

EXERCISES AND PROBLEMS

EXERCISES AND PROBLEMS Exercises and Problems 71 EXERCISES AND PROBLEMS The icon in fron of a problem indicaes ha he problem can be done on a Dnamics Workshee. Dnamics Workshees are found a he back of he Suden Workbook. If ou

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67 - FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1 - RANIEN Uni conen 2 Undersand he ransien behaviour of resisor-capacior (R) and resisor-inducor (RL) D circuis

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k

= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k Week 5 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions o these problems, various details have been changed, so that the answers will come out dierently. The method to ind the solution

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes

6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes Modelling Exercises 6.5 Inroducion This Secion provides examples and asks employing exponenial funcions and logarihmic funcions, such as growh and decay models which are imporan hroughou science and engineering.

More information

SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS

SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS Noe: Two DOE Handbooks are used in conjuncion wih he pracice quesions and problems below o provide preparaory maerial for he NPS

More information

Pulse-Width Modulation Inverters

Pulse-Width Modulation Inverters SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol

More information

Diagnostic Examination

Diagnostic Examination Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)

More information

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July

More information

RC Circuit and Time Constant

RC Circuit and Time Constant ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisor-capacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he

More information

Nuclear Magnetic Resonance Principles. Nagarajan Murali Rutgers, The State University of New Jersey

Nuclear Magnetic Resonance Principles. Nagarajan Murali Rutgers, The State University of New Jersey Nuclear Magneic Resonance Principles Nagarajan Murali Rugers, The ae Universi of New Jerse References Undersanding NMR pecroscop James Keeler John Wile & ons (006,007 pin Dnamics Basics of Nuclear Magneic

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Signal Processing and Linear Systems I

Signal Processing and Linear Systems I Sanford Universiy Summer 214-215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 14-15, Gibbons

More information

PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test

PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed.

More information

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true? 1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always

More information