ap-physics-2-equations-table

A P P h y s i c s B–C o u r s e S y l l a b u sA. COURSE OVERVIEWAdvance Placement Physics B, the third course in the accelerated science program, is designed for the student who has advanced skills in math and science and intends to pursue a post-secondary education in the fields of Science, Pre-Medical, Engineering or Mathematics. This is a first-year course in physics. Topics covered include mechanics, electricity and magnetism, sound and light. The student should be concurrently enrolled in Honors Precalculus and have the approval of the Science department. Evaluation is based upon homework, tests, quizzes, laboratory work, midyear and final exams.B. METHOD OF INSTRUCTIONClass meetings will generally take three common forms, lab/activity, interactive lecture discussions, or problem solving/review. The design as such will allow students to experience and engage the subject conceptually, actively, and analytically. Individual classes may contain multiple elements of these models to suit the topic. Classes meet each weekday for 47 minutes. Every fourth day will be a double length period allowing for longer labs/activities.Lab activities will be of two varieties: investigation or application. Investigation labs and activities will allow students to do just that – investigate a physical phenomenon, and draw conclusions from their measurements and observations. Investigation labs or activities may take place before any reading, or formal in-class discussion on the topic has begun in order to allow students to explore the subject and discover the principles via their own inquiry and collaborative group effort. Much of the course content will be initially discovered using this “workshop physics” approach.Application labs and activities will provide students the opportunity to conduct experiments that involve the concepts they are studying as well as apply understanding of physics to solve practical problems. These labs will frequently be open-ended or contain an open-ended component challenging students to solve a problem by utilizing both their understanding of the topic as well as their critical thinking skills. Individual labs may contain both application and investigation elements. Nearly all units will involve some hands-on lab component. Some activites will consist of a self-contained packet, while others will require the student take their own notes and write their own procedure, observations, data, conclusions etc. There will be at least one formal lab report per quarter. All lab materials are to be kept in a notebook for reference.Interactive lecture discussions will contain elements of a traditional lecture, where concepts are formally presented to students and problem solving is modeled. However, these sessions should also lead to a conversation between students and instructor where the observations from investigations are considered and generalized as well as considering students experience of the concepts from their lives and their interests. Classes will often begin with a starter exercise, which may be a problem or a demonstration of a discrepant event may be presented, and students will be asked to come up with a written explanation. Problem solving and review sessions may involve problems solving strategy and concepts to be reviewed by the class as a whole, or smaller group workshop sessions enabling peer interactive learning, facilitated by the instructor.C. COURSE OBJECTIVES1. To utilize real-world experience to understand physical phenomena2. To utilize controlled laboratory experience to understand physical phenomena3. To gain an understanding of the workings of our physical world and be able to express that understanding interms of:a) written/spoken languageb) graphical diagramsc) mathematical analysis4. To develop observational problem solving and critical thinking skills that will benefit you for any vocationD. TEXTBOOKS AND SOFTWAREPrimary Textbook: James S. Walker, Physics, AP* Edition, 3rd ed., Prentice Hall, Upper Saddle River New Jersey, 2007.Secondary Textbook: Douglas C. Giancoli, Physics – Principles with Applications 5th ed., Prentice Hall, Upper Saddle River New Jersey, 1998.Data Collection/Analysis Software: Logger Pro, Vernier SoftwareE. COURSE CONTENT AREAS0. The Study of Physics — Chapter 1A. Scientific Method and PhilosophyB. Measurement and MathematicsI. Newtonian mechanicsA. Kinematics1. Motion in one dimension — Chapter 22. Uses of Vectors — Chapter 33. Motion in two dimensions — Chapter 4B. Newton’s laws of motion — Chapters 5 & 61. Static equilibrium (1st law)2. Dynamics of a single particle (2nd law)3. Systems of two or more bodies (3rd law)4. Uniform Circular MotionC. Work, energy and power — Chapters 7 & 81. Work and the work-energy theorem2. Power3. Conservative forces and potential energy4. Conservation of energyD. Systems of particles, linear momentum — Chapter 91. Impulse and momentum2. Conservation of linear momentum, collisions3. Center of MassF. Circular Motion and Rotation — Chapters 10 & 111. Angular position, velocity, and acceleration2. Torque and rotational statics3. Rotational kinematics and dynamics4. Angular momentumE. Gravitation — Chapter 121. Newton’s law of gravity2. Orbits of planets and satellitesa. Circularb. GeneralII. Oscillations, Waves and SoundA. Oscillations about equilibrium — Chapter 133. Simple harmonic motion (dynamics and energy relationships)4. Mass on a spring5. Pendulum and other oscillationsB. Wave motion — Chapter 141. Traveling Waves2. Wave Propagation3. Standing Waves4. SuperpositionIII. Fluid Mechanics and Thermal PhysicsA. Fluid Mechanics — Chapter 151. Hydrostatic pressure2. Buoyancy3. Fluid flow continuity4. Bernoulli’s equationB. Temperature and heat — Chapter 161. Mechanical equivalent of heat2. Heat transfer and thermal expansionC. Kinetic Theory and Thermodynamics1. Ideal gases — Chapter 17a. Kinetic modelb. Ideal gas law2. Laws of thermodynamics — Chapter 18a. First law (PV diagrams)b. Second Law (heat engines)c. Third Law (entropy)IV. Electricity and MagnetismA. Electrostatics — Chapter 191. Charge and Coloumb’s Law2. Electric field and electric potential (including point charges)3. Gauss’s Law4. Fields and potentials for charge distributionsB. Conductors and capacitors — Chapter 201. Electrostatics with conductors2. Capacitorsa. Capacitanceb. Parallel platec. Spherical and cylindrical3. DielectricsC. Electric circuits — Chapter 211. Current, resistance, power2. Steady-state direct current circuits with batteries and resistors only3. Capacitors in circuitsa. Steady Stateb. Transients in RC circuitsD. Magnetic Fields — Chapter 221. Forces on moving charges in magnetic fields2. Forces on current carrying wires in magnetic fields3. Fields of long current carrying wires4. Biot-Savart law and Ampere’s LawE. Electromagnetism — Chapter 231. Electromagnetic induction (including Faraday’s law and Lenz’s law)2. Inductance (including LR and LC circuits)3. Maxwell’s equationsV. Electromagnetic Waves and OpticsA. Physical Optics — Chapters 25 & 281. Interference and Diffraction2. Dispersion of Light and the electromagnetic spectrumB. Geometric optics — Chapters 26 & 271. Reflection and refraction2. Mirrors3. LensesVI. Atomic and Nuclear PhysicsA. Atomic physics and quantum effects — Chapter 301. Photons and the photoelectric effect2. Atomic energy levels3. Wave particle dualityB. Nuclear physics — Chapters 31, 32, and 291. Nuclear reactions (including conservation of mass number and charge)2. Mass-energy equivalenceF. PROPOSED LAB EXPERIMENTSThe following is a list of proposed lab experiments. There may be other investigative activities, demonstrations, and virtual labs in addition to those listed below.# Lab Title Notes Type1 Experimental Accuracy and Precision Introduce good lab practice, the concepts of accuracyand precision in measurement and calculationHands-on2 Galileo’s Experiment Study uniformly accelerated motion on an inclinedplaneHands-on3 One dimensional motion Use a motion detector to observe one dimensionalmotion in terms of position, displacement, velocity and accelerationHands-on4 Acceleration due to Gravity Determine the acceleration due to gravity by examiningposition at set time intervals using a ticker tapeHands-on5 Composition and Resolution ofForcesUse a force table to graphically and analytically addand subtract force vectorsHands-on6 Two dimensional motion Use a bowling ball on a level surface with regularlymarked positions to visualize and measure twodimensional motion / Plot two dimensional motionusing video analysisWholeclasshands-on /virtual7 Bull’s Eye Predict the landing location of a projectile based on measurement and calculationHands-on8 Coefficient of Friction Determine the coefficient of static and kinetic frictionof various objects including a student’s sneakerHands-on9 Atwood’s Machine and Friends Examining Newton’s second law in several dynamicsystems involving changing direction of tension forcesusing pulleys. Friction on the system will also beinvestigatedHands-on10 Work-energy theorem and energyconservationExploring conservation of energy and work on anumber of systems including cart on an inclined plane,human motion and a “popper”Hands-on11 Collisions and Explosions Conservation of momentum in collisions andexplosions in one dimension on a motion track, and intwo dimensions using video analysisHands-on/ virtual12 Torques and Rotational Equilibriumof a Rigid BodyUsing a meter stick with lever knives to determinecenter of gravity, and determine unknown mass / videoanalysis of an irregular object in two dimensionalmotion about center of gravityHands-on/ virtual13 Simple Harmonic Motion – Mass on aSpringDynamics and conservation of energy for a mass on aspring, including damping using a motion detectorHands-on14 Simple Harmonic Motion – Pendulum Conservation of energy, period, variation of mass andlength of a simple pendulum examinedHands-on15 Properties of Sound Examination of the wave properties of various soundsusing a microphone and wave visualization software, determination of the speed of sound using resonancetubesHands-on16 Buoyancy To explore Archimedes’ Principle and the principle ofFlotation and create the lightest boat that can carry themost mass without sinkingHands-on17 Specific Heat of Metals Use of calorimetry to identify unknown metals basedon specific heatHands-on18 Linear Thermal Expansion Determination of the linear coefficient of thermalexpansion for several metals by direct measurement oftheir expansion when heatedHands-on19 The Ideal Gas Law Boyle’s law and Charles’s law investigated using ahomemade apparatus made from a plastic syringeHands-on20 Coloumb’s Law Determination of charge on objects based on indirect measurement on electrostatic forcesHands-on21 Equipotentials and Electric Fields Mapping of equipotentials around charged conducting electrodes, construction of electric field lines,quantitative evaluation of the dependence of theelectric field on distance for a line of chargeHands-on22 Circuit Challenge Construction of series and parallel circuits based onfunctional requirementsHands-on23 Ohm’s Law Exploring the relationship between voltage, current,and resistance for ohmic and non-ohmic materialsHands-on24 RC Circuits Determination of the RC time constant using avoltmeter as circuit resistance, finding an unknown capacitance, finding an unknown resistanceHands-on25 Magnetic Fields Mapping the magnetic field around a permanentmagnetHands-on26 Magnetic Induction of a currentcarrying wireDetermination of the induced emf in a coil as ameasure of the magnetic field from an alternatingcurrent in a long straight wireHands-on27 Interference – Light as a wave Determination of the wavelength of a source of light byusing a double slit, determination of grating spacingbased on a known wavelength of lightHands-on28 Reflection Establish the law of reflection, determine the focallength and radius of curvature of cylindrical mirrorsusing the ray box. Determination of focal length andradius of curvature of spherical mirrors using imageheight and object distanceHands-on29 Snell’s Law Determination of the index of refraction of a Luciteblock and gelatin. Discovery of phenomenon of totalinternal reflection as an extension of Snell’s LawHands-on30 Bohr Theory of Hydrogen Comparison of the measured values of the wavelengthsof hydrogen spectrum with Bohr theory to determinethe Rydberg constantHands-on31 Radioactive Decay and Half - life Simulation of radioactive decay using dice as ananalog, Geiger counter measurement of the half-life of137BaHands-on。

2014年5月，AP物理B考试完成了它的使命，就此退出历史舞台。

2015年，这门考试将被两门全新的考试所取代，分别为AP物理1和AP物理2。

虽然作为最后一次AP物理B考试，2014年5月的这次考题仍能给我们带来很多启发，并对之后的新考试、新题型给出非常重要的参考。

首先，本次考试的解答题部分题目数量较之前有所改变，在之前历年的考试中，AP物理B的考试一般包括6道大题，需要学生在90分钟的时间内完成，而在2014年的考试中，较少见的出了7道大题，时间仍是90分钟，这意味着两件事：1.每道题目内的小问数减少，同时题目的难度降低了；2.在解答题中考察的知识点范围更宽泛了。

在2015年即将到来的两门新考试中，在解答题的考察上会有比较明显的改变，我们来比较一下三门考试的解答题部分的异同：AP物理B：解答题共6道大题，时间90分钟，分值占50%。

对各道解答题的考试形式没有明确说明。

AP物理1：解答题共5道大题，时间90分钟，分值占50%。

明确将考察一道实验设计题，一道计算题，三道短问答题（其中一道需要学生进行辩证分析和叙述）。

AP物理2：解答题共4道大题，时间90分钟，分值占50%。

明确将考察一道实验设计题，一道计算题，两道短问答题（其中一道需要学生进行辩证分析和叙述）。

通过比较，我们可以发现，在2015年的两门新考试中，解答题部分的题目数减少了，对学生的辩证分析能力和叙述能力的要求进一步提高，解答题部分也将不再局限于对学生计算能力的考察，更将考察学生的文字叙述和书面表达能力。

其次，在考察内容上，本次考试7道大题分别考察了：单摆，流体力学，热学，静电力学，电磁感应，光电效应，光的折射这几大知识点，同时这些内容也是历年AP物理B考察的核心知识点，在每次考试中都是重点考察的对象，那么在2015年的新考试中，重点考察的内容会有什么变化呢？我们来比较一下三门考试的重点考察知识点：AP物理B：牛顿力学，流体力学，热学，电磁学，波动学和光学，现代物理。

ap物理2公式表在学习AP物理2的过程中，熟练掌握重要的公式是至关重要的。

这些公式不仅可以帮助我们理解物理原理，还可以用于解决与该主题相关的问题。

本文将为大家提供一份AP物理2公式表，帮助大家更好地学习和掌握这门课程。

1. 电磁场与电磁波：- 库仑定律：F = k⋅(|q1 ⋅ q2|)/r^2- 电场强度：E = F/q- 电势差：V = W/q- 电位能：PE = q⋅V- 等效电容：1/Ceq = 1/C1 + 1/C2 + ...- 感应电动势：ε = -dΦ/dt- 平板电容器电容：C = ε0⋅(A/d)- 波速：v = λ⋅f2. 电路分析：- 电阻定律：V = I⋅R- 串联电阻：Rtotal = R1 + R2 + ...- 并联电阻：1/Rtotal = 1/R1 + 1/R2 + ...- 电流分流定律：I1/I2 = R2/R1- 电功率：P = I⋅V- 等效电阻：1/Req = 1/R1 + 1/R2 + ...- 电容器电荷：Q = C⋅V- 电容器电流：I = C⋅(dV/dt)3. 磁场与电磁感应：- 洛伦兹力：F = q⋅v⋅B⋅sinθ- 动生电动势：ε = B⋅v⋅l⋅sinθ- 法拉第定律：ε = -N⋅(dΦ/dt)- 比奥—萨伐尔定律：B = μ0⋅(N⋅I)/l- 感生电动势：ε = -N⋅(ΔΦ/Δt)4. 物质性质：- 折射率：n = c/v- 焦耳-汤姆逊效应：Q = m⋅c⋅ΔT- 柯西—斯蒂芬定律：n1⋅sinθ1 = n2⋅sinθ2 - 斯特藩-玻尔兹曼定律：R = ρ⋅(L/A)- 平板电容器电容：C = κ⋅ε0⋅(A/d)- 库仑摩擦力：F = μ⋅N5. 原子和核能：- 质能关系：E = mc^2- 洛伦兹变换：L = Lo⋅√(1 - v^2/c^2) - 粒子能量：E = hf- 线性空位：m = mo⋅√(1 - (v^2/c^2)) - 半衰期：N = N0⋅(1/2)^(t/t1/2)- 波长与动量：λ = h/p6. 光学：- 镜方程：1/f = 1/do + 1/di- 放大率：M = hi/ho = -di/do- 温度与颜色：I/I0 = (T/T0)^4- 干涉条纹间距：Δx = λ⋅L/d- 多普勒效应：f' = f⋅(v±vr)/(v±vs)- 扩散：I/I0 = (1/4)⋅(n^2)/(sin^2(θ/2)) - 辐射：P/(A) = σ⋅(T^4)总结：掌握这些公式对于AP物理2的学习至关重要。

lesson 2 Kinematics本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motiondescribing motions本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motionuniform acceleration motionKinema'c Equa'onsv=v 0+atx= x=v 0t+v 2=v 02+2ax 23412v 0+vt21kinematic problem solving skillsat 2本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile MotionKinema'c Equa'onsv=v 0+atx= x=v 0t+v 2=v 02+2ax 23412v 0+vt21kinematic problem solving skillsat 2always be aware that:four quantities: x, t, v, a five variables: x, t, v 0, v, a four equations: 4 variables in eachProblem Solving StepsStep1: Sketch a diagram to visually represent the problem. Step2: label the known variables or values on the diagram. Step3: Identify the unknown variable(s), and label them too. Step4: Choose the “star equation(s)”that contains all the 4 variables. Step5: Plug in the known values and solve for the unknown, or derive the unknown in terms of the known.Step 6: Feel proud in your mastery physics.kinematic problemsolving skills本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motiongraphical analysis of linear motion本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motionfree fall motion and projectile vertically F ree Fall: drop freelyfree fall motion and projectile vertically Projectile Vertically Up本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motionvector addition and relative motion vector additionParallelogram Rule and Parallelogram Methodvector addition and relative motion vector additionTail-to-tip Methodvector addition and relative motion vector additionAdding Vectors by Componentsvector addition and relative motion relative motion本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motionprojectile motion horizontally launched projectilesprojectile motion projectile launched at an angle回顾本节授课要点1 2 3Describing MotionUniform Acceleration MotionKinematics Problem Solving Strategy4567Graphical Analysis of Linear MotionFree Fall Motion and Projectile VerticallyVector Addition and Relative MotionProjectile Motion预告下节授课要点1 2 3ForcesNewton’s Laws of MotionNewton’s Laws Problem Solving Strategy Typical Problems of Applying Newton’s Laws4thank you。

ap物理c练习题2012精品文档ap物理c练习题2012198Free Response QuestionsThese materials were produced by Educational Testing Service? ,which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents,2,000 high schools, and,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, eollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? . The College Board1 / 19精品文档is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1985M1. A projectile is launched from the top of a cliff above level ground. At launch the projectile ismeters above the base of the cliffand has a velocity of0 meters per second at an angle7? with the horizontal. Air resistance is negligible. Consider the following two cases and use g = 10 m/s2, sin7? =0.60, and cos7? = 0.80.Case I: The projectile follows the path shown by the curved line in the following diagram.a.b.c.2 / 19精品文档Calculate the total time from launch until the projectile hits the ground at point C. Calculate the horizontal distance R that theprojectile travels before it hits the ground. Calculate the speed of the projectile at points A, B and C.Case II: A small internal charge explodes at point B in the above diagram, causing the projectile to separate into two parts of masses kilograms and 10 kilograms. The explosive force on each part is horizontal and in the plane of the trajectory. The-kilogram mass strikes the ground at point D, located0 metersbeyond point C, where the projectile would have landed had it not exploded The 10-kilogram mass strikes the ground at point E.d. Calculate the distance x from C to E.1985M2. An apparatus to determine coefficients of friction is shown above. The box is slowly rotated counterclockwise. When the box makes an angle ? with the horizontal, the block of mass m just starts to slide, and at this instant the box is stopped from rotating. Thus at angle ?, the block slides a distance d, hits3 / 19精品文档the spring of force constant k, and compresses the spring a distance x before coming to rest.In terms of the given quantities, derive an expression for each of the following.a. ?s the coefficient of static friction.b. ?E, the loss in total mechanical energy of the block-spring system from the start of the block downthe incline to the moment at which it comes to rest on the compressed spring.c. ?k, the coefficient of kinetic friction.1985M3. A pulley of massm and radius r is mounted on frictionless bearings and supported by a standof massm at rest on a table as shown above.The moment of inertia ofthis pulley about its axis is1.5mr2.Passing over the pulley is a massless cord supporting a block ofmass m on the left and a block of massm on the right. The cord does not slip on the pulley, so after the block-pulley system is released from rest, the pulley begins to rotate.a.On the diagrams below, draw and label all the forces4 / 19精品文档acting on each block.b. Use the symbols identified in part to write each of the following.i. The equations of translational motion for each of the twoblocksii. The analogous equation for the rotational motion of the pulleyc. Solve the equations in part for the acceleration of the twoblocks.d. Determine the tension in the segment of the cord attached to the block of mass m.e. Determine the normal force exerted on the apparatus by the table while the blocks are in motion.1985E1. A capacitor consisting of conducting coaxial cylinders of radii a and b, respectively, and length Lis connected to a source of emf, as shown above.When the capacitor is charged, the inner cylinder has a charge + Q on it. Neglect end effects and assume that the region between the cylinders is filled with air. Express your answers in terms of the given quantities.a. Use Gauss's law to determine an expression for5 / 19精品文档the electric field at a distance r from the axis of thecylinder where a b. Determine the potential difference between the cylinders.c. Determine the capacitance Co of the capacitor.One third of the length of the capacitor is then filled with a dielectric of dielectric constant k =, as shownin the following diagram.d. Determine the new capacitance C in terms of Co.AP? Physics C197Free Response QuestionsThese materials were produced by Educational Testing Service? , which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service are dedicated to the principle of equalopportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to collegeand opportunity. Founded in 1900, the association is6 / 19精品文档composed of more than,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves overthree million students and their parents,2,000 high schools, and,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, eollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? . The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1979M1. A ball of mass m is released from rest at a distance h above a frictionless plane inclined at an angle of5? to the horizontal as shown above. The ball bounces elastically off the plane at point P1 and7 / 19精品文档strikes the plane again at point P2. In terms of g and h determine each of the following quantities:a. The velocity of the ball just after it first bounces off theplane at P1.b. The time the ball is in flight between points P1 and P2.c. The distance L along the plane from P1 to P2.d. The speed of the ball just before it strikes the plane at P2.1979M2. A ferryboat of mass M1 =.0 x 10kilograms moves toward a docking bumper of mass Mthat cuts off its engines to the time it first comes to rest after colliding with the bumper. At the instant it hits the bumper,t = 0 and v = meters per second.a. After colliding inelastically with the bumper, the ferryboat and bumper move together with an initialspeed of meters per second. Calculate the mass of the bumper M2.b. After colliding, the ferryboat and bumper move with a speed given by the expression v =e-4t. Although the boat never comes precisely to rest, it travels only8 / 19精品文档a finite distance. Calculate that distance.c. While the ferryboat was being slowed by water resistance before hitting the bumper, its speed was given by 1/v = 1/+ ?t, where ? is a constant. Find an expression for the retarding force of the water on the boat as a function of speed.1979M3. A mass m constrained to move on a frictionless horizontal surface is attached to a frictionless peg by a massless spring having force constant k. The unstretched length of the spring is l1, as shown in Figure 1.When the mass moves in a circle about the peg with constant angular velocity ?o.the length of the spring is las shown in Figure. Express your answers to parts a, b, and c in terms of m, k, ?o and l1. a. Determine the length l2b. Assume the total energy of the system in Figure 1 is zero. Determine the total energy of the rotating system in Figure.c. Determine the magnitude of the angular momentum of the system.d. While the mass is rotating about the peg with9 / 19精品文档angular velocity ?o, it is struck by a hammer that provides a small impulse directed inward. On the axes below, sketch graphs to indicatequalitatively the manner in which the length of the spring l and the angular velocity ? will vary with time in thesubsequent motion.1979E1. A solid conducting sphere of radius a is surrounded by a hollow conducting shell of inner radius b and outer radius c as shown above. The sphere and the shell each have a charge +Q. Express your answers to parts , and in terms of Q, a, b, c, and the Coulomb's law constant.a. Using Gauss's law, derive an expression for the electric field magnitude at a distance from the center of the solid sphere.b. Write expressions for the electric field magnitude at r > c, b given for statements of the correct expressions. It is not necessary to show your work on this part.c. the solid sphere.Ed. potential V is zero at r = ?.)V10 / 19精品文档e. Determine the Potential at r = b.1979E2. A slab of infinite length and infinite width has a thickness d.Point P1 is a point inside the slabat x = a and point Pis a point inside the slab at x = -a.For parts and consider the slab to be nonconducting with uniform charge per unit volume ? as shown.a. Sketch vectors representing the electric field E at points P1 and Pon the following diagram.b. Use Gauss's law and symmetry arguments to determine the magnitude of E at point Pl.j directed out of the page as shown below.c. Sketch vectors representing the magnetic field B at points P1 and Pon the following diagram.d. Use Ampere’s law and symmetry arguments to determine the magnitude of B at point P1.Newtonian Mechanics牛顿力学、占整个Physics C力学考试的100%其中:A.Kinematics :运动学占18%包括:矢量的概念:既有大小，又有方向;矢量代数:11 / 19精品文档矢量和的三角形法则是必须熟练掌握的，最简单的记忆方法就是花萌萌面对两段直的折线路径，她会选择直接连接出发点和终点的直线捷径，这样构成了一个矢量和三角形。

AP® Physics C: Electricity and Magnetism2009 Free-Response QuestionsThe College BoardThe College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools and 3,800 colleges through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT® and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns.© 2009 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation.Permission to use copyrighted College Board materials may be requested online at:/inquiry/cbpermit.html.Visit the College Board on the Web: .AP Central is the official online home for the AP Program: .TABLE OF INFORMATION FOR 2008 and 2009meter, m mole, mol watt,W farad, F kilogram, kg hertz, Hz coulomb, C tesla, T second, s newton, N volt, V degree Celsius, C ∞ampere, A pascal, Pa ohm, Welectron-volt, eV UNIT SYMBOLSkelvin, K joule, J henry,HPREFIXESFactor Prefix Symbol910 giga G 610 mega M 310 kilo k210- centi c 310- milli m 610- micro m910-nano n 1210-pico pThe following conventions are used in this exam.I. Unless otherwise stated, the frame of reference of any problem isassumed to be inertial. II. The direction of any electric current is the direction of flow of positivecharge (conventional current).III. For any isolated electric charge, the electric potential is defined as zero atan infinite distance from the charge.ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009PHYSICS C: ELECTRICITY AND MAGNETISMSECTION II Time—45 minutes3 QuestionsDirections: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part, NOT in the green insert.E&M. 1.A spherically symmetric charge distribution has net positive charge 0Q distributed within a radius of R .Its electric potential V as a function of the distance r from the center of the sphere is given by the following.()20000()23for 4()for 4Q r V r r R R R Q V r r Rrp p È˘=-+<Í˙Î˚=>⑀⑀Express all algebraic answers in terms of the given quantities and fundamental constants.(a) For the following regions, indicate the direction of the electric field E (r ) and derive an expression for itsmagnitude.i. r R < ____ Radially inward ____ Radially outward ii. r R >____ Radially inward ____ Radially outward (b) For the following regions, derive an expression for the enclosed charge that generates the electric field in that region, expressed as a function of r .i. r R < ii. r R >(c) Is there any charge on the surface of the sphere (r = R ) ? ____ Yes ____ NoIf there is, determine the charge. In either case, explain your reasoning.(d) On the axes below, sketch a graph of the force that would act on a positive test charge in the regions r < Rand r > R. Assume that a force directed radially outward is positive.E&M. 2.A 9.0 V battery is connected to a rectangular bar of length 0.080 m, uniform cross-sectional area 625.010m ,-¥and resistivity 44.510 mW -¥i , as shown above. Electrons are the sole charge carriers in the bar. The wires have negligible resistance. The switch in the circuit is closed at time 0t =.(a) Calculate the power delivered to the circuit by the battery.(b) On the diagram below, indicate the direction of the electric field in the bar.Explain your answer.(c) Calculate the strength of the electric field in the bar.A uniform magnetic field of magnitude 0.25 T perpendicular to the bar is added to the region around the bar, as shown below.(d) Calculate the magnetic force on the bar.(e) The electrons moving through the bar are initially deflected by the external magnetic field. On the diagrambelow, indicate the direction of the additional electric field that is created in the bar by the deflected electrons.(f) The electrons eventually experience no deflection and move through the bar at an average speed of33.510m -¥. Calculate the strength of the additional electric field indicated in part (e).E&M. 3.A square conducting loop of side L contains two identical lightbulbs, 1 and 2, as shown above. There is amagnetic field directed into the page in the region inside the loop with magnitude as a function of time t given by ()=+, where a and b are positive constants. The lightbulbs each have constant resistance 0R. ExpressB t at ball answers in terms of the given quantities and fundamental constants.(a) Derive an expression for the magnitude of the emf generated in the loop.(b) i. Determine an expression for the current through bulb 2.ii. Indicate on the diagram above the direction of the current through bulb2.(c) Derive an expression for the power dissipated in bulb 1.Another identical bulb 3 is now connected in parallel with bulb 2, but it is entirely outside the magnetic field, as shown below.(d) How does the brightness of bulb 1 compare to what it was in the previous circuit?____ Brighter ____ Dimmer ____ The sameJustify your answer.Now the portion of the circuit containing bulb 3 is removed, and a wire is added to connect the midpoints of the top and bottom of the original loop, as shown below.(e) How does the brightness of bulb 1 compare to what it was in the first circuit?____ Brighter ____ Dimmer ____ The sameJustify your answer.END OF EXAM。

$3 Physics C: Mechanics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he following conventions are used in this examination.I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial.II. The direction of any electric current is the direction of flow of positive charge (conventional current).III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge.ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002PHYSICS CSection II, MECHANICSTime—45 minutes3 QuestionsDirections: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in the pink booklet in the spaces provided after each part, NOT in this green insert.Mech 1.A crash test car of mass 1,000 kg moving at constant speed of 12 m/s collides completely inelastically with anobject of mass M at time t= 0. The object was initially at rest. The speed u in m/s of the car-object system after the collision is given as a function of time t in seconds by the expressionu=8.1+5t(a) Calculate the mass M of the object.(b) Assuming an initial position of x = 0, determine an expression for the position of the car-object system afterthe collision as a function of time t.(c) Determine an expression for the resisting force on the car-object system after the collision as a function oftime t.(d) Determine the impulse delivered to the car-object system from t= 0 to t= 2.0 s.Mech 2.The cart shown above is made of a block of mass m and four solid rubber tires each of mass m/4 and radius r.Each tire may be considered to be a disk. (A disk has rotational inertia 122ML, where M is the mass and L isthe radius of the disk.) The cart is released from rest and rolls without slipping from the top of an inclined plane of height h. Express all algebraic answers in terms of the given quantities and fundamental constants.(a) Determine the total rotational inertia of all four tires.(b) Determine the speed of the cart when it reaches the bottom of the incline.(c) After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligiblemass attached to an ideal spring, which has a spring constant k. Determine the distance x m the spring is compressed before the cart and bumper come to rest.(d) Now assume that the bumper has a non-neglible mass. After the collision with the bumper, the springis compressed to a maximum distance of about 90% of the value of x m in part (c). Give a reasonableexplanation for this decrease.Mech 3.An object of mass 0.5 kg experiences a force that is associated with the potential energy functionU x x()..=+4020, where U is in joules and x is in meters.(a) On the axes below, sketch the graph of U (x ) versus x .(b) Determine the force associated with the potential energy function given above.(c) Suppose that the object is released from rest at the origin. Determine the speed of the particle at x = 2 m.In the laboratory, you are given a glider of mass 0.5 kg on an air track. The glider is acted on by the forcedetermined in part (b). Your goal is to determine experimentally the validity of your theoretical calculation in part (c).(d) From the list below, select the additional equipment you will need from the laboratory to do your experimentby checking the line next to each item. If you need more than one of an item, place the number you need on the line. ___ Meterstick ___ Stopwatch ___ Photogate timer___ String___ Spring___ Balance___ Wood block___ Set of objects of different masses(e) Briefly outline the procedure you will use, being explicit about what measurements you need to makein order to determine the speed. You may include a labeled diagram of your setup if it will clarify your procedure.END OF SECTION II, MECHANICS。

COURSE DESCRIPTIONThe New York State course in Regents Physics is an excellent introduction to physics for the college bound senior. Many students embark on their university career without knowing exactly what they want to study. Taking physics in high school can open many doors for students who find that they want to major in a technical area. Students who take high school physics can obviously expect to do far better in university physics courses than those students who have not.Taking a course in physics gives the student a stronger foundation in problem-solving strategies and critical thinking. These are exactly the areas in which many universities and employers are complaining that candidates are not skilled enough!The Regents course is comprehensive in scope with each subject is treated with the proper depth for the average student. Students are prepared for, and expected to take, the Regents Physics exam in June.There are two prerequisites for this course. First, students should have completed Regents Biology, Regents Earth Science and Regents Chemistry. Without previous science experience, it will be difficult to do well in this class. Second, students should have completed two Regents Math exams. This course requires the understanding of algebra and fundamental knowledge of geometry that you gain from your math class.We meet every day for 40 minutes with an additional 40 minute lab period every-other day. At the completion of this course students should have a strong conceptual understanding of required topic and be able to complete all required physics laboratory experiments.COURSE TOPICS1. The science of physics2. Kinematics and Mechanics3. Energy and Momentum4. Electricity and Magnetism5. Vibration and Waves6. Modern PhysicsRESOURCES AND HELPFUL LINKSTextbook - Holt Physics, by Raymond A Servway and Jerry Faughn,/physics//.au/online/sciences/physics/t utes1.html/en/simulations/category/physics //Domain/248/physics/http://hyperphysics.phy-/hbase/hph.html#mechcon/physlet_resources/bu_ semester1/index.html/mathphysics.htmlhttp://www.walter-fendt.de/ph14e/stwaverefl.htmGRADING POLICYCategory 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Tests & Exams 60% 40% 60% 60% Lab 5% 5% 5% 5% Project/formal lab 5% 5% 5% 5% Class work/ Participation 10% 10% 10% 10% Homework 20% 20% 20% 20%Midterm Exam 20%Course GradeStudents will receive a course grade that is an average of their grade for each of the four quarters and their score on the Regents Exam. Thus, each quarter and the Final Exam will comprise 20% of the final course grade.MidtermThe physics department administers a district-wide midterm exam during "Midterm Week" in January. This exam includes Regents level questions and will count for 20% of the student's second quarter grade.Tests and ExamsA test is a 25 point assessment with a blend of multiple choice and extended response questions. Tests are typically given in the middle of a large unit of instruction. An exam is given at the end of each unit and is a two part assessment. Part One of the assessment will consist of 30 multiple choice questions. Part Two of the assessment will consist of 20 points worth of extended response questions. All tests and exams are built using questions from past Regents exams and/or questions based directly on Regents exam questions.LabAll labs will be documented in a personal lab-notebook which will be kept in the classroom. Students will be required to complete at least 1200 minutes of lab (about 30 labs) time with a complete lab report in order to pass the course.Project/Formal LabOne lab per quarter will be designated as a "formal lab". This lab will be subjected to strict grading criteria and will be important in teaching students how to produce high quality lab reports.One project is also assigned every quarter. This project is for students to construct some type of device after school and write a report about the project.Class work / ParticipationClass work includes any formal or informal assessment of student work or preparedness for class. Most of the class work grades will consist of "Do Now's", "Exit Slips", and "Activities". Participation includes attendance, attentiveness to tasks during class and ability to work well with others. Participation grade heavily rewards effort on the part of the student.HomeworkHomework is assigned every day; it will take an average student about half an hour to complete. Homework will be collected and graded daily. According to research, completion of homework in high school produces a gain of about 24 percentile points.REQUIRED SUPPLIES▪Lab notebook▪Binder for class notes and homework▪Protractor with ruler▪CalculatorTENTATIVE SCHEDULE。

28th International Physics OlympiadSudbury, CanadaTHEORETICAL COMPETITIONThursday, July 17th, 1997Time Available: 5 hoursRead This First:1. Use only the pen provided.2. Use only the front side of the answer sheets and paper.3. In your answers please use as little text as possible; express yourself primarily inequations, numbers and figures. Summarize your results on the answer sheet.4. Please indicate on the first page the total number of pages you used.5. At the end of the exam please put your answer sheets, pages and graphs in order.This set of problems consists of 11 pages.Examination prepared at: University of British ColumbiaDepartment of Physics and AstronomyCommittee Chair: Chris WalthamHosted by: Laurentian UniversityTheory Question No.1Scaling(a) A small mass hangs on the end of a massless ideal spring and oscillates up and downat its natural frequency f. If the spring is cut in half and the mass reattached at the end,what is the new frequency? (1.5 mark s)′f(b) The radius of a hydrogen atom in its ground state is a0= 0.0529 nm (the “Bohr radius”). What is the radius of a “muonic-hydrogen” atom in which the electron is′areplaced by an identically charged muon, with mass 207 times that of the electron?Assume the proton mass is much larger than that of the muon and electron. (2 marks)(c) The mean temperature of the earth is T = 287 K. What would the new mean temperature ′T be if the mean distance between the earth and the sun was reduced by1%?(2 marks)(d) On a given day, the air is dry and has a density ρ= 1.2500 kg/m3. The next day the humidity has increased and the air is 2% by mass water vapour. The pressure and temperature are the same as the day before. What is the air density′ρnow? (2 marks)Mean molecular weight of dry air: 28.8 (g/mol)Molecular weight of water: 18 (g/mol)Assume ideal-gas behaviour.(e) A type of helicopter can hover if the mechanical power output of its engine is P. If another helicopter is made which is an exact ½-scale replica (in all linear dimensions) ofthe first, what mechanical power′P is required for it to hover? (2.5 marks)Theory Question 1: Answer Sheet STUDENT CODE: (a) Frequency : ′f(b) R adius : ′a(c) Temperature ′T:(d) Density ′ρ:(e) Power : ′PTheory Question No.2Nuclear Masses and StabilityAll energies in this question are expressed in MeV - millions of electron volts. One MeV = 1.6 × 10-13 J, but it is not necessary to know this to solve the problem.The mass M of an atomic nucleus with Z protons and N neutrons (i.e. the mass number A = N + Z ) is the sum of masses of the free constituent nucleons (protons and neutrons) minus the binding energy B/c 2.M c Zm c Nm c B p n 222=+−The graph shown below plots the maximum value of B/A for a given value of A , vs. A. The greater the value of B/A , in general, the more stable is the nucleus.Binding Energy per Nucleon(a) Above a certain mass number A α , nuclei have binding energies which are always small enough to allow the emission of alpha-particles (A=4). Use a linear approximation to this curve above A = 100 to estimate A α . (3 marks )For this model, assume the following:• Both initial and final nuclei are represented on this curve.• The total binding energy of the alpha-particle is given by B 4 = 25.0 MeV (this cannot be read off the graph!).(b) The binding energy of an atomic nucleus with Z protons and N neutrons (A=N+Z ) is given by a semi-empirical formula:B a A a A a Z A a N Z A v s c a =−−−−−−232132()δThe value of δ is given by:+ a p A -3/4 for odd-N/odd-Z nuclei0 for even-N/odd-Z or odd-N/even-Z nuclei- a p A -3/4 for even-N/even-Z nucleiThe values of the coefficients are:a v = 15.8 MeV; a s = 16.8 MeV; a c = 0.72 MeV; a a = 23.5 MeV; a p = 33.5 MeV.(i) Derive an expression for the proton number Z max of the nucleus with the largest binding energy for a given mass number A . Ignore the δ-term for this part only. (2 marks )(ii) What is the value of Z for the A = 200 nucleus with the largest B/A ? Include the effect of the δ-term. (2 marks )(iii) Consider the three nuclei with A = 128 listed in the table on the answer sheet. Determine which ones are energetically stable and which ones have sufficient energy to decay by the processes listed below. Determine Z max as defined in part (i) and fill out the table on your answer sheet.In filling out the table, please:•Mark processes which are energetically allowed thus: √•Mark processes which are NOT energetically allowed thus: 0•Consider only transitions between these three nuclei.Decay processes:(1) β -- decay; emission from the nucleus of an electron(2) β+- decay; emission from the nucleus of a positron(3)β-β- - decay; emission from the nucleus of two electrons simultaneously(4) Electron capture; capture of an atomic electron by the nucleus.The rest mass energy of an electron (and positron) is m e c2 = 0.51 MeV; that of a proton is m p c2 = 938.27 MeV; that of a neutron is m n c2 = 939.57 MeV.(3 marks)Question 2: Answer Sheet STUDENT CODE:(a) Numerical value for :Aα(b) (i) Expression for Z max:(b) (ii) Numerical value of Z :(b) (iii)Nucleus/Process β−- decay β+- decay Electron-capture ββ−−- decay128I53128Xe54128Cs55A XNotation :ZX = Chemical SymbolTheory Question No.3Solar-Powered AircraftWe wish to design an aircraft which will stay aloft using solar power alone. The mostefficient type of layout is one with a wing whose top surface is completely covered insolar cells. The cells supply electrical power with which the motor drives the propeller. Consider a wing of rectangular plan-form with span l, chord (width) c; the wing area isS = cl, and the wing aspect ratio A = l / c. We can get an approximate idea of the wing’sperformance by considering a slice of air of height x and length l being deflected downward at a small angle ε with only a very small change in speed. Control surfacescan be used to select an optimal value of ε for flight. This simple model correspondsclosely to reality if x = π l /4, and we can assume this to be the case. The total mass of ther v relative to the surrounding air. In aircraft is M and it flies horizontally with velocitythe following calculations consider only the air flow around the wing.Top view of aircraft (in its own frame of reference):incident airclSide view of wing (in a frame of reference moving with the aircraft):xr vincident air wing section air leaving wing vertical(up)Ignore the modification of the airflow due to the propeller.(a) Consider the change in momentum of the air moving past the wing, with no change in speed while it does so. Derive expressions for the vertical lift force L and the horizontal drag force D 1 on the wing in terms of wing dimensions , v, ε, and the air density ρ.Assume the direction of air flow is always parallel to the plane of the side-view diagram. (3 marks )(b) T here is an additional horizontal drag force D 2 caused by the friction of air flowing over the surface of the wing. The air slows slightly, with a change of speed ∆v (<< 1% of v ) given by:∆v v f A=The value of f is independent of ε.Find an expression (in terms of M , f , A , S , ρ and g - the acceleration due to gravity) for the flight speed v 0 corresponding to a minimum power being needed to maintain thisaircraft in flight at constant altitude and velocity. Neglect terms of order (ε 2 f ) or higher. (3 marks )You may find the following small angle approximation useful:122−≈cos sin εε(c) On the answer sheet, sketch a graph of power P versus flight speed v . Show the separate contributions to the power needed from the two sources of drag. Find anexpression (in terms of M , f , A , S , ρ and g ) for the minimum power, P min . (2 marks )(d) If the solar cells can supply sufficient energy so that the electric motors and propellers generate mechanical power of I = 10 watts per square metre of wing area, calculate the maximum wing loading Mg/S (N/m2) for this power and flight speed v0 (m/s). Assume ρ = 1.25 kg/m3, f = 0.004, A = 10. (2 marks)Question 3: Answer Sheet STUDENT CODE: (a) Expression for L :(a) Expression for D1 :(b) Expression for D2 :(b) Expression for v0 :(c)P v P minv 0(c) Expression for P min : (d) M aximum value of Mg/S : (d) Numerical value of v 0 :。

2024年AP Calculus AB历年真题精选辑随着时间的推移，越来越多的学生对于高考考试已经过去了，他们开始考虑其他更具挑战性的考试，其中一个备受关注的就是AP（高级学术课程）考试。

AP课程为学生提供了高水平的学术教育，尤其是在数学领域。

AP Calculus AB考试是其中之一，它涉及微积分的基础知识和应用。

为了更好地帮助考生准备AP Calculus AB考试，本文将为你提供2024年的历年真题精选辑。

以下是几个种类的题目，包括选择题、填空题和解答题。

无论你是正在备考AP Calculus AB考试，还是希望了解更多关于这一考试的信息，本文都将为你提供帮助。

选择题1. 在曲线y = x^3 - 3x^2 + 2x的区间（-∞，∞）上，当x = 1时，曲线的斜率是多少？A. -1B. 0C. 1D. 2E. 32. 函数y = ln(x^2 + 4)在x = 2处的导数是多少？A. 0B. 1/6C. 1/4D. 1/2E. 6填空题1. ∫(2x + 5) dx = _______2. 如果函数f(x)和g(x)都是可微函数，那么(f(x) + g(x))' = _______解答题1. 证明：对于函数f(x) = 2x + 3，f'(x) = 2。

这些题目展示了AP Calculus AB考试所涵盖的各种题型和难度级别。

通过做这些题目，你可以更好地了解数学问题的解决方法，以及如何运用微积分的知识进行计算和推理。

无论你是通过自学还是参加相关课程来备考AP Calculus AB考试，以下几点建议可以帮助你更好地应对考试：1. 理解基础知识：AP Calculus AB考试基础考查学生对微积分的基本概念和技巧的理解。

确保你掌握了函数的导数、积分和微分方程等基础知识，并能够灵活运用。

2. 多做练习题：做更多的练习题可以提高你的数学思维和解题能力。

不仅要做历年AP考试真题，还可以寻找其他相关题库进行练习。

ap物理2学教材以下是一些可供参考的AP物理2学教材：1. "AP Physics 2 Essentials: An APlusPhysics Guide" by Dan Fullerton这本书是一本非常实用的教材，涵盖了所有AP物理2课程的主题，包括电学、光学、原子和核物理、热力学和流体力学。

该书还包括丰富的练习题和答案，以帮助学生深入理解这些概念。

2. "Physics for Scientists and Engineers with Modern Physics" by Douglas C. Giancoli这本教材是一本经典的物理教材，已经使用了多年。

它不仅涵盖了AP物理2课程的主题，还包括了现代物理的最新发展。

这本书包含大量的练习题和答案，以及详细的解释和图表，以帮助学生掌握复杂的概念。

3. "Physics: Principles with Applications" by Douglas C. Giancoli这本教材是AP物理2课程的分级教材，旨在为学生提供一个全面的物理知识体系，并帮助他们解决实际问题。

该书使用生动的插图和实例，以帮助学生理解最复杂的概念，并包含了许多练习题和答案，以帮助他们检验自己的理解。

4. "University Physics with Modern Physics" by Hugh D. Young and Roger A. Freedman这本教材是一本非常全面的书籍，涵盖了物理学的各个方面，包括AP物理2课程中的所有主题。

该书突出了物理学的现代化和应用性，包含大量的图表、图像和练习题，以帮助学生深入理解概念和解决问题。

5. "Serway and Jewett's Physics for Scientists and Engineers with Modern Physics" by Raymond A. Serway and John W. Jewett这本教材也是一本经典的物理教材，已经使用多年。

AP® Physics B2010 Free-Response QuestionsThe College BoardThe College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment. Among its widely recognized programs are the SAT®, the PSAT/NMSQT®, the Advanced Placement Program® (AP®), SpringBoard® and ACCUPLACER®. The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns.© 2010 The College Board. College Board, ACCUPLACER, Advanced Placement Program, AP, AP Central, SAT, SpringBoard and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service is a trademark owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: /inquiry/cbpermit.html.Visit the College Board on the Web: .AP Central is the official online home for the AP Program: .TABLE OF INFORMATION FOR 2010 and 2011meter, m mole, mol watt, W farad, F kilogram, kg hertz, Hz coulomb, C tesla, Tsecond, s newton, N volt, V degree Celsius, C ∞ampere, A pascal, Pa ohm, Welectron-volt, eV UNITSYMBOLSkelvin, K joule, J henry, HPREFIXESFactor Prefix Symbol 910giga G 610 mega M 310 kilo k210- centi c 310- milli m 610- micro m910- nano n1210-pico pThe following conventions are used in this exam.I. Unless otherwise stated, the frame of reference of any problem isassumed to be inertial. II. The direction of any electric current is the direction of flow of positivecharge (conventional current).III. For any isolated electric charge, the electric potential is defined as zero atan infinite distance from the charge. IV. For mechanics and thermodynamics equations, W represents the work done on a system.ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2010 and 2011ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2010 and 2011PHYSICS BSECTION IITime—90 minutes7 QuestionsDirections: Answer all seven questions, which are weighted according to the points indicated. The suggested times are about 17 minutes for answering each of Questions 1-2 and about 11 minutes for answering each of Questions3-7. The parts within a question may not have equal weight. Show all your work in the pink booklet in the spaces provided after each part, NOT in this green insert.1. (15 points)Block A of mass 4.0 kg is on a horizontal, frictionless tabletop and is placed against a spring of negligible mass and spring constant 650 N m. The other end of the spring is attached to a wall. The block is pushed toward the wall until the spring has been compressed a distance x, as shown above. The block is released and follows the trajectory shown, falling 0.80 m vertically and striking a target on the floor that is a horizontal distance of 1.2 m from the edge of the table. Air resistance is negligible.(a) Calculate the time elapsed from the instant block A leaves the table to the instant it strikes the floor.(b) Calculate the speed of the block as it leaves the table.(c) Calculate the distance x the spring was compressed.Block B, also of mass 4.0 kg, is now placed at the edge of the table. The spring is again compressed a distance x, and block A is released. As it nears the end of the table, it instantaneously collides with and sticks to block B.The blocks follow the trajectory shown in the figure below and strike the floor at a horizontal distance d from the edge of the table.(d) Calculate d if x is equal to the value determined in part (c).(e) Consider the system consisting of the spring, the blocks, and the table. How does the total mechanical energy2E of the system just before the blocks leave the table compare to the total mechanical energy 1E of the system just before block A is released? ____ 21E E < ____ 21E E =____ 21E E >Justify your answer.2. (15 points)A large pan is filled to the top with oil of density O r . A plastic cup of mass C m , containing a sample of knownmass S m , is placed in the oil so that the cup and sample float, as shown above. The oil that overflows from the pan is collected, and its volume is measured. The procedure is repeated with a variety of samples of different mass, and the pan is refilled each time.(a) On the dot below that represents the cup-sample system, draw and label the forces (not components) that acton the system when it is floating on the surface of the oil.∑(b) Derive an expression for the overflow volume O V (the volume of oil that overflows due to the floatingsystem) in terms of O r , S m , C m , and fundamental constants. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).Assume that the following data are obtained for the overflow volume O V for several sample masses S m .Sample mass S m (kg)0.020 0.030 0.040 0.050 0.060 0.070Overflow volume O V (3m ) 62910-¥63810-¥65410-¥66210-¥67610-¥ 68410-¥(c) Graph the data on the axes below, plotting the overflow volume as a function of sample mass. Place numbersand units on both axes. Draw a straight line that best represents the data.(d) Use the slope of the best-fit line to calculate the density of the oil.(e) What is the physical significance of the intercept of your line with the vertical axis?3. (10 points)Three particles are fixed in place in a horizontal plane, as shown in the figure above. Particle 3 at the top of thetriangle has charge 3q of 61.010 C -+¥, and the electrostatic force F on it due to the charge on the two otherparticles is measured to be entirely in the negative x -direction. The magnitude of the charge 1q on particle 1 is known to be 64.010 C -¥, and the magnitude of the charge 2q on particle 2 is known to be 61.710 C -¥, but their signs are not known.(a) Determine the signs of the charges 1q and 2q and indicate the correct signs below.1q ____ Negative 2q ____ Negative ____ Positive ____ Positive(b) On the diagram below, draw and label arrows to indicate the direction of the force 1F exerted by particle 1on particle 3 and the force 2F exerted by particle 2 on particle 3.(c) Calculate the magnitude of F , the electrostatic force on particle 3.(d) Calculate the magnitude of the electric field at the position of particle 3 due to the other two particles. (e) On the figure below, draw a small ¥ in the box that is at a position where another positively chargedparticle could be fixed in place so that the electrostatic force on particle 3 is zero.Justify your answer.4. (10 points)A locomotive runs on a steam engine with a power output of 64.510 W ¥and an efficiency of 12 percent. (a) Calculate the rate at which heat is being delivered to the steam engine.(b) Calculate the magnitude of the resistive forces acting on the locomotive when it is moving with a constantspeed of 7.0 m s . Suppose the gas in another heat engine follows the simplified path ABCDA in the PV diagram below at a rate of4 cycles per second.(c)i. What does the area bounded by path ABCDA represent?ii. Calculate the power output of the engine.(d) Indicate below all of the processes during which heat is added to the gas in the heat engine.____ AB ____BC ____CD ____DA5. (10 points) As shown above, a beam of red light of wavelength 76.6510 m -¥ in air is incident on a glass prism at an angle1q with the normal. The glass has index of refraction n = 1.65 for the red light. When 140,q =∞ the beam emerges on the other side of the prism at an angle 484.q =∞(a) Calculate the angle of refraction 2q at the left side of the prism.(b) Using the same prism, describe a change to the setup that would result in total internal reflection of the beam at the right side of the prism. Justify your answer.(c) The incident beam is now perpendicular to the surface. The glass is coated with a thin film that has an indexof refraction 1.38f n = to reduce the partial reflection of the beam at this angle.i. Calculate the wavelength of the red light in the film.ii. Calculate the minimum thickness of the film for which the intensity of the reflected red ray is nearzero.6. (10 points)The plastic cart shown in the figure above has mass 2.5 kg and moves with negligible friction on a horizontal surface. Attached to the cart is a rigid rectangular loop of wire that is 0.10 m by 0.20 m, has resistance 4.0 ,W and has a mass that is negligible compared to the mass of the cart. The plane of the rectangular loop is parallel to the plane of the page. A uniform magnetic field of 2.0 T, perpendicular to and directed into the plane of the page, starts at x = 0, as shown above.(a) On the figure below, indicate the direction of the induced current in the loop when its front edge is at0.12 m.x=x= its speed is 3.0 m s. Calculate the following(b) When the front edge of the rectangular loop is at 0.12 m,for that instant.i. The magnitude of the induced current in the rectangular loop of wireii. The magnitude of the net force on the loop(c) At a later time, the cart and loop are completely inside the magnetic field. Determine the magnitude of thenet force on the loop at that time. Justify your answer.7. (10 points) Light of wavelength 400 nm is incident on a metal surface, as shown above. Electrons are ejected from the metal surface with a maximum kinetic energy of 191.110-¥ J.(a) Calculate the frequency of the incoming light.(b) Calculate the work function of the metal surface.(c) Calculate the stopping potential for the emitted electrons.(d) Calculate the momentum of an electron with the maximum kinetic energy.END OF EXAM。