AAPT UNITED STATES PHYSICS TEAM AIP 2010

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "AAPT UNITED STATES PHYSICS TEAM AIP 2010"

Transcription

1 2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = 10 N/kg throughout this contest. You my write in this booklet of questions. However, you will not receive ny credit for nything written in this booklet. Your nswer to ech question must be mrked on the opticl mrk nswer sheet. Select the single nswer tht provides the best response to ech question. Plese be sure to use No. 2 pencil nd completely fill the box corresponding to your choice. If you chnge n nswer, the previous mrk must be completely ersed. Correct nswers will be wrded one point; incorrect nswers will result in deduction of 1 4 no penlty for leving n nswer blnk. point. There is A hnd-held clcultor my be used. Its memory must be clered of dt nd progrms. You my use only the bsic functions found on simple scientific clcultor. Clcultors my not be shred. Cell phones my not be used during the exm or while the exm ppers re present. You my not use ny tbles, books, or collections of formuls. This test contins 25 multiple choice questions. Your nswer to ech question must be mrked on the opticl mrk nswer sheet tht ccompnies the test. Only the boxes preceded by numbers 1 through 25 re to be used on the nswer sheet. All questions re eqully weighted, but re not necessrily the sme level of difficulty. In order to mintin exm security, do not communicte ny informtion bout the questions (or their nswers or solutions) on this contest until fter Februry 8, The question booklet nd nswer sheet will be collected t the end of this exm. You my not use scrtch pper. DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN

2 2010 F = m Exm 2 Questions 1 to 3 refer to the figure below which shows representtion of the motion of squirrel s it runs in stright-line long telephone wire. The letters A through E refer to the indicted times. time A B C D E 1. If the grph is grph of POSITION vs. TIME, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl(s)? (A) From A to B (B) From B to C only (C) From B to D (D) From C to D only (E) From D to E 2. If, insted, the grph is grph of VELOCITY vs. TIME, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl(s)? (A) t B (B) t C (C) t D (D) t both B nd D (E) From C to D 3. If, insted, the grph is grph of ACCELERATION vs. TIME nd the squirrel strts from rest, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl? (A) t B (B) t C (C) t D (D) t both B nd D (E) From C to D 4. Two tems of movers re lowering pino from the window of 10 floor prtment building. The rope breks when the pino is 30 meters bove the ground. The movers on the ground, lerted by the shouts of the movers bove, first notice the pino when it is 14 meters bove the ground. How long do they hve to get out of the wy before the pino hits the ground? (A) 0.66 sec (B) 0.78 sec (C) 1.67 sec (D) 1.79 sec (E) 2.45 sec

3 2010 F = m Exm 3 5. Two projectiles re lunched from 35 meter ledge s shown in the digrm. One is lunched from 37 degree ngle bove the horizontl nd the other is lunched from 37 degrees below the horizontl. Both of the lunches re given the sme initil speed of v 0 = 50 m/s. Projectile 1 35 m Projectile 2 The difference in the times of flight for these two projectiles, t 1 t 2, is closest to (A) 3 s (B) 5 s (C) 6 s (D) 8 s (E) 10 s 6. A projectile is lunched cross flt ground t n ngle θ to the horizontl nd trvels in the bsence of ir resistnce. It rises to mximum height H nd lnds horizontl distnce R wy. Wht is the rtio H/R? (A) tn θ (B) 2 tn θ (C) 2 tn θ (D) 1 2 tn θ (E) 1 4 tn θ 7. Hrry Potter is sitting 2.0 meters from the center of merry-go-round when Drco Mlfoy csts spell tht glues Hrry in plce nd then mkes the merry-go-round strt spinning on its xis. Hrry hs mss of 50.0 kg nd cn withstnd 5.0 g s of ccelertion before pssing out. Wht is the mgnitude of Hrry s ngulr momentum when he psses out? (A) 200 kg m 2 /s (B) 330 kg m 2 /s (C) 660 kg m 2 /s (D) 1000 kg m 2 /s (E) 2200 kg m 2 /s 8. A cr ttempts to ccelerte up hill t n ngle θ to the horizontl. The coefficient of sttic friction between the tires nd the hill is µ > tn θ. Wht is the mximum ccelertion the cr cn chieve (in the direction upwrds long the hill)? Neglect the rottionl inerti of the wheels. (A) g tn θ (B) g(µ cos θ sin θ) (C) g(µ sin θ) (D) gµ cos θ (E) g(µ sin θ cos θ)

4 2010 F = m Exm 4 9. A point object of mss M hngs from the ceiling of cr from mssless string of length L. It is observed to mke n ngle θ from the verticl s the cr ccelertes uniformly from rest. Find the ccelertion of the cr in terms of θ, M, L, nd g. L θ (A) Mg sin θ (B) MgL tn θ (C) g tn θ (D) g cot θ (E) Mg tn θ 10. A block of mss m 1 is on top of block of mss m 2. The lower block is on horizontl surfce, nd rope cn pull horizontlly on the lower block. The coefficient of kinetic friction for ll surfces is µ. Wht is the resulting ccelertion of the lower block if force F is pplied to the rope? Assume tht F is sufficiently lrge so tht the top block slips on the lower block. 1 2 F (A) 2 = (F µg(2m 1 + m 2 ))/m 2 (B) 2 = (F µg(m 1 + m 2 ))/m 2 (C) 2 = (F µg(m 1 + 2m 2 ))/m 2 (D) 2 = (F + µg(m 1 + m 2 ))/m 2 (E) 2 = (F µg(m 2 m 1 ))/m The three msses shown in the ccompnying digrm re equl. The pulleys re smll, the string is lightweight, nd friction is negligible. Assuming the system is in equilibrium, wht is the rtio /b? The figure is not drwn to scle! b (A) 1/2 (B) 1 (C) 3 (D) 2 (E) 2 3

5 2010 F = m Exm A bll with mss m projected horizontlly off the end of tble with n initil kinetic energy K. At time t fter it leves the end of the tble it hs kinetic energy 3K. Wht is t? Neglect ir resistnce. (A) (3/g) K/m (B) (2/g) K/m (C) (1/g) 8K/m (D) (K/g) 6/m (E) (2K/g) 1/m 13. A bll of mss M nd rdius R hs moment of inerti of I = 2 5 MR2. The bll is relesed from rest nd rolls down the rmp with no frictionl loss of energy. The bll is projected verticlly upwrd off rmp s shown in the digrm, reching mximum height y mx bove the point where it leves the rmp. Determine the mximum height of the projectile y mx in terms of h. h (A) h (B) h (C) 2 5 h (D) 5 7 h (E) 7 5 h 14. A 5.0 kg block with speed of 8.0 m/s trvels 2.0 m long horizontl surfce where it mkes hed-on, perfectly elstic collision with 15.0 kg block which is t rest. The coefficient of kinetic friction between both blocks nd the surfce is How fr does the 15.0 kg block trvel before coming to rest? (A) 0.76 m (B) 1.79 m (C) 2.29 m (D) 3.04 m (E) 9.14 m

6 2010 F = m Exm 6 The following figure is used for questions 15 nd 16. m v0 M A smll block of mss m is moving on horizontl tble surfce t initil speed v 0. It then moves smoothly onto sloped big block of mss M. The big block cn lso move on the tble surfce. Assume tht everything moves without friction. 15. A smll block moving with initil speed v 0 moves smoothly onto sloped big block of mss M. After the smll block reches the height h on the slope, it slides down. Find the height h. (A) h = v2 0 2g (B) h = 1 g (C) h = 1 2g (D) h = 1 2g (E) h = v2 0 g Mv 2 0 m+m Mv 2 0 m+m mv 2 0 m+m 16. Following the previous set up, find the speed v of the smll block fter it leves the slope. (A) v = v 0 (B) v = (C) v = m m+m v 0 M m+m v 0 (D) v = M m m v 0 (E) v = M m m+m v Four msses m re rrnged t the vertices of tetrhedron of side length. Wht is the grvittionl potentil energy of this rrngement? (A) 2 Gm2 (B) 3 Gm2 (C) 4 Gm2 (D) 6 Gm2 (E) 12 Gm2

7 2010 F = m Exm 7 The following grph of potentil energy is used for questions 18 through Which of the following represents the force corresponding to the given potentil? (A) (B) (C) (D) (E)

8 2010 F = m Exm Consider the following grphs of position vs. time. I. II. III. Which of the grphs could be the motion of prticle in the given potentil? (A) I (B) III (C) I nd II (D) I nd III (E) I, II, nd III 20. Consider the following grph of position vs. time, which represents the motion of certin prticle in the given potentil. Wht is the totl energy of the prticle? (A) -5 J (B) 0 J (C) 5 J (D) 10 J (E) 15 J

9 2010 F = m Exm The grvittionl self potentil energy of solid bll of mss density ρ nd rdius R is E. Wht is the grvittionl self potentil energy of bll of mss density ρ nd rdius 2R? (A) 2E (B) 4E (C) 8E (D) 16E (E) 32E 22. A blloon filled with helium gs is tied by light string to the floor of cr; the cr is seled so tht the motion of the cr does not cuse ir from outside to ffect the blloon. If the cr is trveling with constnt speed long circulr pth, in wht direction will the blloon on the string len towrds? A B D C (A) A (B) B (C) C (D) D (E) Remins verticl 23. Two strems of wter flow through the U-shped tubes shown. The tube on the left hs cross-sectionl re A, nd the speed of the wter flowing through it is v; the tube on the right hs cross-sectionl re A = 1/2A. If the net force on the tube ssembly is zero, wht must be the speed v of the wter flowing through the tube on the right? Neglect grvity, nd ssume tht the speed of the wter in ech tube is the sme upon entry nd exit. (A) 1/2v (B) v (C) 2v (D) 2v (E) 4v

10 2010 F = m Exm A uniform circulr disk of rdius R begins with mss M; bout n xis through the center of the disk nd perpendiculr to the plne of the disk the moment of inerti is I 0 = 1 2 MR2. A hole is cut in the disk s shown in the digrm. In terms of the rdius R nd the mss M of the originl disk, wht is the moment of inerti of the resulting object bout the xis shown? R R R/2 xis of rottion (A) (15/32)MR 2 (B) (13/32)MR 2 (C) (3/8)MR 2 (D) (9/32)MR 2 (E) (15/16)MR Spcemn Fred s spceship (which hs negligible mss) is in n ellipticl orbit bout Plnet Bob. The minimum distnce between the spceship nd the plnet is R; the mximum distnce between the spceship nd the plnet is 2R. At the point of mximum distnce, Spcemn Fred is trveling t speed v 0. He then fires his thrusters so tht he enters circulr orbit of rdius 2R. Wht is his new speed? R 2R (A) 3/2v 0 (B) 5v 0 (C) 3/5v 0 (D) 2v 0 (E) 2v 0

Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:

Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period: Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A

More information

Version 001 Summer Review #03 tubman (IBII20142015) 1

Version 001 Summer Review #03 tubman (IBII20142015) 1 Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This print-out should he 35 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03

More information

Answer, Key Homework 4 David McIntyre Mar 25,

Answer, Key Homework 4 David McIntyre Mar 25, Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his print-out should hve 18 questions. Multiple-choice questions my continue on the next column or pe find ll choices before mkin your selection.

More information

v T R x m Version PREVIEW Practice 7 carroll (11108) 1

v T R x m Version PREVIEW Practice 7 carroll (11108) 1 Version PEVIEW Prctice 7 crroll (08) his print-out should he 5 questions. Multiple-choice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

SOLUTIONS TO CONCEPTS CHAPTER 5

SOLUTIONS TO CONCEPTS CHAPTER 5 1. m k S 10m Let, ccelertion, Initil velocity u 0. S ut + 1/ t 10 ½ ( ) 10 5 m/s orce: m 5 10N (ns) 40000. u 40 km/hr 11.11 m/s. 3600 m 000 k ; v 0 ; s 4m v u ccelertion s SOLUIONS O CONCEPS CHPE 5 0 11.11

More information

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1 PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.

More information

Review Problems for the Final of Math 121, Fall 2014

Review Problems for the Final of Math 121, Fall 2014 Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since

More information

PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions

PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Week 11 - Inductance

Week 11 - Inductance Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n

More information

Applications to Physics and Engineering

Applications to Physics and Engineering Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics

More information

Newton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt

Newton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt Newton s Three Lws For couple centuries before Einstein, Newton s Lws were the bsic principles of Physics. These lws re still vlid nd they re the bsis for much engineering nlysis tody. Forml sttements

More information

t 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam

t 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam Cndin Assocition of Physicists 1999 Prize Exm This is three hour exm. Ntionl rnking nd prizes will be bsed on student s performnce on both sections A nd B of the exm. However, performnce on the multiple

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions MSSCHUSES INSIUE OF ECHNOLOGY Deprtment of hysics 8.0 W02D3_0 Group roblem: ulleys nd Ropes Constrint Conditions Consider the rrngement of pulleys nd blocks shown in the figure. he pulleys re ssumed mssless

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

Lesson 12.1 Trigonometric Ratios

Lesson 12.1 Trigonometric Ratios Lesson 12.1 rigonometric Rtios Nme eriod Dte In Eercises 1 6, give ech nswer s frction in terms of p, q, nd r. 1. sin 2. cos 3. tn 4. sin Q 5. cos Q 6. tn Q p In Eercises 7 12, give ech nswer s deciml

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

AREA OF A SURFACE OF REVOLUTION

AREA OF A SURFACE OF REVOLUTION AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.

More information

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply? Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the

More information

NCERT INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS. Trigonometric Ratios of the angle A in a triangle ABC right angled at B are defined as:

NCERT INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS. Trigonometric Ratios of the angle A in a triangle ABC right angled at B are defined as: INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS (A) Min Concepts nd Results Trigonometric Rtios of the ngle A in tringle ABC right ngled t B re defined s: side opposite to A BC sine of A = sin A = hypotenuse

More information

Understanding 22. 23. The frictional force acting to the left is missing. It is equal in magnitude to the applied force acting to the right.

Understanding 22. 23. The frictional force acting to the left is missing. It is equal in magnitude to the applied force acting to the right. Chpter 3 Review, pges 154 159 Knowledge 1. (c) 2. () 3. (d) 4. (d) 5. (d) 6. (c) 7. (b) 8. (c) 9. Flse. One newton is equl to 1 kg /s 2. 10. Flse. A norl force is perpendiculr force cting on n object tht

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow. Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge

More information

COMPONENTS: COMBINED LOADING

COMPONENTS: COMBINED LOADING LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of

More information

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,

More information

Double Integrals over General Regions

Double Integrals over General Regions Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

Euler Euler Everywhere Using the Euler-Lagrange Equation to Solve Calculus of Variation Problems

Euler Euler Everywhere Using the Euler-Lagrange Equation to Solve Calculus of Variation Problems Euler Euler Everywhere Using the Euler-Lgrnge Eqution to Solve Clculus of Vrition Problems Jenine Smllwood Principles of Anlysis Professor Flschk My 12, 1998 1 1. Introduction Clculus of vritions is brnch

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Review guide for the final exam in Math 233

Review guide for the final exam in Math 233 Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered

More information

Mathematics Higher Level

Mathematics Higher Level Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:

More information

SAT PHYSICS SUBJECT TEST 1

SAT PHYSICS SUBJECT TEST 1 SAT PHYSICS SUBJECT TEST TEST Your responses to the Physics Subject Test questions should be filled in on Test of your nswer sheet (t the bck of the book). PHYSICS SUBJECT TEST 75 Questions Time limit

More information

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter

More information

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2 7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

Lecture 5. Inner Product

Lecture 5. Inner Product Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right

More information

PHY 140A: Solid State Physics. Solution to Homework #2

PHY 140A: Solid State Physics. Solution to Homework #2 PHY 140A: Solid Stte Physics Solution to Homework # TA: Xun Ji 1 October 14, 006 1 Emil: jixun@physics.ucl.edu Problem #1 Prove tht the reciprocl lttice for the reciprocl lttice is the originl lttice.

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

Geometry and Measure. 12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm

Geometry and Measure. 12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm Reding Scles There re two things to do when reding scle. 1. Mke sure you know wht ech division on the scle represents. 2. Mke sure you red in the right direction. Mesure Length metres (m), kilometres (km),

More information

Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006

Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006 dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.

More information

Integration. 148 Chapter 7 Integration

Integration. 148 Chapter 7 Integration 48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but

More information

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

Physics 2102 Lecture 2. Physics 2102

Physics 2102 Lecture 2. Physics 2102 Physics 10 Jonthn Dowling Physics 10 Lecture Electric Fields Chrles-Augustin de Coulomb (1736-1806) Jnury 17, 07 Version: 1/17/07 Wht re we going to lern? A rod mp Electric chrge Electric force on other

More information

10.6 Applications of Quadratic Equations

10.6 Applications of Quadratic Equations 10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding 1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde

More information

Plotting and Graphing

Plotting and Graphing Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Homework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.

Homework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule. Text questions, Chpter 5, problems 1-5: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed

More information

6 Energy Methods And The Energy of Waves MATH 22C

6 Energy Methods And The Energy of Waves MATH 22C 6 Energy Methods And The Energy of Wves MATH 22C. Conservtion of Energy We discuss the principle of conservtion of energy for ODE s, derive the energy ssocited with the hrmonic oscilltor, nd then use this

More information

Picture Match Words Fusion Density Isotope Neutron Atomic Number Structure Components Function Atomic Mass Orbit

Picture Match Words Fusion Density Isotope Neutron Atomic Number Structure Components Function Atomic Mass Orbit Picture Mtch Words Fusion Density Isotope Neutron Atomic Number Structure Components Function Atomic Mss Orbit Mterils copyrighted by the University of Louisville. Eductors re free to use these mterils

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t).

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t). 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

Surface Area and Volume

Surface Area and Volume Surfce Are nd Volume Student Book - Series J- Mthletics Instnt Workooks Copyright Surfce re nd volume Student Book - Series J Contents Topics Topic - Surfce re of right prism Topic 2 - Surfce re of right

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

More information

The Laws of Motion. chapter

The Laws of Motion. chapter chpter The Lws of Motion 5 5.1 The Concept of Force 5.2 Newton s First Lw nd Inertil Frmes 5.3 Mss 5.4 Newton s econd Lw 5.5 The Grvittionl Force nd Weight 5.6 Newton s Third Lw 5.7 Anlysis Models Using

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

Curve Sketching. 96 Chapter 5 Curve Sketching

Curve Sketching. 96 Chapter 5 Curve Sketching 96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of

More information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

More information

Version 001 CIRCUITS holland (1290) 1

Version 001 CIRCUITS holland (1290) 1 Version CRCUTS hollnd (9) This print-out should hve questions Multiple-choice questions my continue on the next column or pge find ll choices efore nswering AP M 99 MC points The power dissipted in wire

More information

AP Physics 1 Midterm Exam Review

AP Physics 1 Midterm Exam Review AP Physics 1 Midterm Exam Review 1. The graph above shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is

More information

PHY231 Section 1, Form B March 22, 2012

PHY231 Section 1, Form B March 22, 2012 1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate

More information

B) 286 m C) 325 m D) 367 m Answer: B

B) 286 m C) 325 m D) 367 m Answer: B Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

OPTIMA QUADRANT / OFFSET QUADRANT

OPTIMA QUADRANT / OFFSET QUADRANT OPTIMA QUADRANT / OFFSET QUADRANT 71799 00 / Issue 1 / 15 Y Z DIMENSIONS Check the enclosure size in the tle elow mtches the showertry instlltion. = Widths: 800 Door = 780-805mm 900 Door = 880-905mm Y

More information

1 Numerical Solution to Quadratic Equations

1 Numerical Solution to Quadratic Equations cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll

More information

AP Physics C. Oscillations/SHM Review Packet

AP Physics C. Oscillations/SHM Review Packet AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

More information

PSW-4-Motion Worksheet Name:. Class #:

PSW-4-Motion Worksheet Name:. Class #: Speed, Velocity, nd Accelertion PSW-4-1 Vocbulry Distnce: Displcement: Speed: Velocity: Accelertion: How fr something trvels. How fr something trvels in given direction. How fst something is moving. How

More information

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00 COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided

More information

B Conic Sections. B.1 Conic Sections. Introduction to Conic Sections. Appendix B.1 Conic Sections B1

B Conic Sections. B.1 Conic Sections. Introduction to Conic Sections. Appendix B.1 Conic Sections B1 Appendi B. Conic Sections B B Conic Sections B. Conic Sections Recognize the four bsic conics: circles, prbols, ellipses, nd hperbols. Recognize, grph, nd write equtions of prbols (verte t origin). Recognize,

More information

addition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.

addition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix. APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The

More information

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Harvard College. Math 21a: Multivariable Calculus Formula and Theorem Review

Harvard College. Math 21a: Multivariable Calculus Formula and Theorem Review Hrvrd College Mth 21: Multivrible Clculus Formul nd Theorem Review Tommy McWillim, 13 tmcwillim@college.hrvrd.edu December 15, 2009 1 Contents Tble of Contents 4 9 Vectors nd the Geometry of Spce 5 9.1

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of

More information

Sensorless Force Estimation for Robots with Friction

Sensorless Force Estimation for Robots with Friction Proc. Austrlsin Conference on Rootics nd Automtion Aucklnd, 7-9 Novemer Sensorless orce Estimtion for Roots with riction John W.L Simpson, Chris D Cook, Zheng Li School of Electricl, Computer nd Telecommunictions

More information

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013 PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be

More information

MerCarb 2 bbl Carburetor

MerCarb 2 bbl Carburetor TO: SERVICE MANAGER TECHNICIANS PARTS MANAGER No. 97-8 Revised June 1999. Informtion underlined is new. MerCr 2 l Cruretor 8 Point Cruretor Check List To ensure tht the cruretor is the cuse of the engine

More information

Geometry 7-1 Geometric Mean and the Pythagorean Theorem

Geometry 7-1 Geometric Mean and the Pythagorean Theorem Geometry 7-1 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the

More information

Slow roll inflation. 1 What is inflation? 2 Equations of motions for a homogeneous scalar field in an FRW metric

Slow roll inflation. 1 What is inflation? 2 Equations of motions for a homogeneous scalar field in an FRW metric Slow roll infltion Pscl udrevnge pscl@vudrevnge.com October 6, 00 Wht is infltion? Infltion is period of ccelerted expnsion of the universe. Historiclly, it ws invented to solve severl problems: Homogeneity:

More information

PROBLEM 4.1 SOLUTION. Knowing that the couple shown acts in a vertical plane, determine the stress at (a) point A, (b) point B.

PROBLEM 4.1 SOLUTION. Knowing that the couple shown acts in a vertical plane, determine the stress at (a) point A, (b) point B. PROBLEM.1 Knowing tht the couple shown cts in verticl plne, determine the stress t () point A, (b) point B. SOLUTON () (b) For rectngle: For cross sectionl re: 1 = bh 1 1 = 1 + + = ()(1.5) + ()(5.5) +

More information