AAPT UNITED STATES PHYSICS TEAM AIP 2010
|
|
- Madeleine Howard
- 8 years ago
- Views:
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:
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 informationVersion 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 informationv 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 informationExperiment 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 informationSOLUTIONS 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 informationPROBLEMS 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 informationReview 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 informationWarm-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 informationPolynomial 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 informationWeek 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 informationApplications 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 informationt 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 information5.2. 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 informationHelicopter 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 informationGraphs 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 informationMathematics. 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 informationOperations 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 informationPractice 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 informationA.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 informationModule 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 informationAREA 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 information1. 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, 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 informationCOMPONENTS: 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 informationPHY 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 informationSection 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 informationPROF. 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 informationEuler 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. 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 informationSection 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 informationReview 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 informationPhysics 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 informationUnit 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 informationPHY 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 informationBasic 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 informationLecture 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 informationRadius 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 informationIntegration. 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 informationVectors 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 information9.3. 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 informationVector 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 information10.6 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 informationC 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 informationExample 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 informationUse 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 informationFactoring 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 informationPhysics 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 information1. 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 informationAnswer, 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 informationEcon 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 information6 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 informationMidterm 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 informationTreatment 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 informationPHY231 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 informationIntegration 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 informationThe 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 informationOPTIMA 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 informationEQUATIONS 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 informationAP 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 informationPSW-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 informationHarvard 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 informationPROBLEM 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 informationTwo 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 informationB 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 informationAP 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 informationPHY231 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 informationPhysics 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 information6.2 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 informationSensorless 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 informationLecture 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 informationB) 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 informationGeometry 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 information15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationAP STATISTICS SUMMER MATH PACKET
AP STATISTICS SUMMER MATH PACKET This pcket is review of Algebr I, Algebr II, nd bsic probbility/counting. The problems re designed to help you review topics tht re importnt to your success in the clss.
More informationaddition, 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 informationc b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00
Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume
More informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More informationLecture 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 informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationExam 1 Study Guide. Differentiation and Anti-differentiation Rules from Calculus I
Exm Stuy Guie Mth 2020 - Clculus II, Winter 204 The following is list of importnt concepts from ech section tht will be teste on exm. This is not complete list of the mteril tht you shoul know for the
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More informationPure C4. Revision Notes
Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd
More informationPHYSICS 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 informationVectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics
Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium
More informationUNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES
UNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES Solution to exm in: FYS30, Quntum mechnics Dy of exm: Nov. 30. 05 Permitted mteril: Approved clcultor, D.J. Griffiths: Introduction to Quntum
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationVectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics
Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd
More information1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam
1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211 - Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationProject 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
More informationChapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.
Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed
More informationHow To Network A Smll Business
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More information