【AP物理C】【真题】解答题C2004

2004年普通高等学校招生全国统一考试(甘肃、青海、宁夏、贵州、新疆等地)14．在核反应方程式kX Xe Sr n U ++→+1365490381023592中（ ）A ．X 是中子，k=9B ．X 是中子，k=10C ．X 是质子，k=9D ．X 是质子，k=1015．如图所示，在x ≤0的区域内存在匀强磁场，磁场的方向垂直于x y 平面（纸面）向里。

具有一定电阻的矩形线框a bcd 位于x y 平面内，线框的a b 边与y 轴重合。

令线框从t=0的时刻起由静止开始沿x 轴正方向做匀加速运动，则线框中的感应电流I （取逆时针方向的电流为正）随时间t 的变化图线I —t 图可能是下图中的哪一个？16．一定质量的理想气体，从某一状态开始，经过系列变化后又回一开始的状态，用W 1表示外界对气体做的功，W 2表示气体对外界做的功，Q 1表示气体吸收的热量，Q 2表示气体放出的热量，则在整个过程中一定有（ ）A ．Q 1—Q 2=W 2—W 1B ．Q 1=Q 2C ．W 1=W 2D ．Q 1>Q 217．图中M 是竖直放置的平面镜，镜离地面的距离可调节。

甲、乙二人站在镜前，乙离镜的距离为甲离镜的距离的2倍，如图所示。

二人略错开，以便甲能看到乙的像。

以l 表示镜的长度，h 表示乙的身高，为使甲能看到镜中乙的全身像，l 的最小值为 （ ） A ．h 31B ．h 21C ．h 43D ．h18．已知：一简谐横波在某一时刻的波形图如图所示，图中位于a 、b 两处的质元经过四分之一周期后分别运动到a '、b '处。

某人据此做出如下判断： ①可知波的周期， ②可知波的传播速度， ③可知的波的传播方向， ④可知波的波长。

其中正确的是（ ）A ．①和④B ．②和④C ．③和④D ．②和③19．如图，在倾角为α的固定光滑斜面上，有一用绳子拴着的长木板，木板上站着一只猫。

已知木板的质量是猫的质量的2倍。

2004高考力学题【湘鄂、全国】18．如图所示，四个完全相同的弹簧都处于水平位置，它们的右端受到大小皆为F 的拉力作用，而左端的情况各不相同：①中弹簧的左端固定在墙上。

②中弹簧的左端受大小也为F 的拉力作用。

③中弹簧的左端拴一上物块，物块在光滑的桌面上滑动。

④中弹簧的左端拴一小物块，物块在有摩擦的桌面上滑动。

若认为弹簧的质量都为零，以l 1、l 2、l 3、l 4依次表示四个弹簧的伸长量，则有【D 】A ．l 2＞l 1 B.l 4＞l 3 C.l 1＞l 3 D.l 2=l 4【上海】5．物体B 放在物体A 上，A 、B 的上下表面均与斜面平行（如图），当两者以相同的初速度靠惯性沿光滑固定斜面C 向上做匀减速运动时【C 】（A ）A 受到B 的摩擦力沿斜面方向向上。

（B ）A 受到B 的摩擦力沿斜面方向向下。

（C ）A 、B 之间的摩擦力为零。

（D ）A 、B 之间是否存在摩擦力取决于A 、B 表面的性质。

【两广】7．用三根轻绳将质量为m 的物块悬挂在空中,如图所示.已知ac 和bc 与竖直方向的夹角分别为030和060，则 ac 绳和bc 绳中的拉力分别为【A 】 A1,2mg B．12mg C1,2mg D．12mg 【新课程】32．三个完全相同的物块1、2、3放在水平桌上，它们与桌面间的动摩擦因数都相同。

现用大小相同的外力F 沿图示方向分别作用在1和2上，用21F 的外力沿水平方向作用在3上，使三者都做加速运动，令a 1、a 2、a 3分别代表物块1、2、3的加速度，则【C 】A ．a 1=a 2=a 3B ．a 1= a 2，a 2＞a 3C ．a 1＞a 2，a 2＜a 3D ．a 1＞a 2，a 2＞a 3【山西】15．如图所示，ad 、bd 、cd 是竖直面内三根固定的光滑细杆，a 、b 、c 、d 位于同一圆周上， a 为圆周的最高点，d为最低点。

每根杆上都套着一个小滑环（图中未画出），三个滑环分别从 a 、b 、c 处释放（初速为0），用t 1、、、t 2、、t 3依次表示m各滑环到达d 所用的时间，则【D 】A ．t 1=、t 2、=t 3B ．t 1、>、t 2、>t 3C ．t 3 > t 1、>t 2、、D ．t 1、、<t 2、<t 3【两广】9．一杂技演员,用一只手抛球.他每隔0.40s 抛出一球,接到球便立即把球抛出,已知除抛、接球的时刻外，空中总有四个球，将球的运动看作是竖直方向的运动，球到达的最大高度是（高度从抛球点算起，取210/g m s =）【C 】A ． 1.6mB ． 2.4mC ．3.2mD ．4.0m【湘鄂、全国】21．放在水平地面上的一物块，受到方向不变的水平推力F 的作用，F 的大小与时t 的关系和物块速度υ与时间t 的关系如图所示。

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2004年全国高等学校统一招生考试（江苏省）物理试题第一卷(选择题共40分)一、本题共10小慰；每小题4分，共40分．在每小题给出的四个选项中，有的小题只有一个选项正确，有的小题有多个选项正确．全部选对的得4分，选不全的得2分，有选错或不答的得0分．1. 下列说法正确的是(A)光波是—种概率波(B)光波是一种电磁波(c)单色光从光密介质进入光疏介质时．光子的能量改变(D)单色光从光密介质进入光疏介质时，光的波长不变2．下列说法正确的是(A)物体放出热量，温度一定降低(B)物体内能增加，温度一定升高(C)热量能自发地从低温物体传给高温物体(D)热量能自发地从高温物体传给低温物体3．下列说法正确的是(A)α射线与γ射线都是电磁波(D)β射线为原子的核外电子电离后形成的电子流(C)用加温、加压或改变其化学状态的方法都不能改变原子核衰变的半衰期(D)原子核经过衰变生成新核，则新核的质量总等于原核的质量4，若人造卫星绕地球作匀速圆周运动，则下列说法正确的是(A)卫星的轨道半径越大，它的运行速度越大(D)卫星的轨道半径越大，它的运行速度越小(C)卫星的质量一定时，轨道半径越大，它需要的向心力越大(D)卫星的质量一定时，轨道半径越大，它需要的向心力越小5．甲、乙两个相同的密闭容器中分别装有等质量的同种气体，已知甲、乙容器中气体的压强分别为p甲、p乙，且p甲<p乙，则(A)甲容器中气体的温度高于乙容器中气体的温度(B)甲容器中气体的温度低于乙容器中气体的温度(C)甲容器中气体分子的平均动能小于乙容器中气体分子的平均动能(D)甲容器中气体分子的平均动能大于乙容器中气体分子的平均动能6，如图所示，一个有界匀强磁场区域，磁场方向垂直纸面向外．一个矩形闭合导线框abcd，沿纸面由位置1(左)匀速运动到位置2(右)．则(A)导线框进入磁场时，感应电流方向为a→b→c→d→a(B)导线框离开磁场时，感应电流方向为a→d→c→b→a(C)导线框离开磁场时，受到的安培力方向水平向右(D)导线框进入磁场时．受到的安培力方向水平向左7．雷蒙德·戴维斯因研究来自太阳的电子中徽子(ve)而获得了2002年度诺贝尔物理学奖．他探测中徽子所用的探测器的主体是一个贮满615t 四氯乙烯(C 2Cl 4)溶液的巨桶．电子中微子可以将一个氯核转变为一个氩核，其核反应方程式为e Ar Cl v e 0137183717-+→+已知核的质量为36.95658u ，核的质量为36.95691u ，的质量为0.00055u ，1u Cl 3717Ar 3718e 01-质量对应的能量为931.5MeV ．根据以上数据，可以判断参与上述反应的屯子中微子的最小能量为 (A )0.82 MeV (B )0.31 MeV (C )1.33 MeV (D )0.51 McV 8．图1中，波源S 从平衡位置y =0开始振动，运动方向竖直向上(y 轴的正方向)，振动周期T =0.01s ，产生的简谐波向左、右两个方向传播，波速均为v =80m /s ．经过一段时间后，P 、Q 两点开始振动,已知距离SP =1.2m 、SQ =2.6m ．若以Q 点开始振动的时刻作为计时的零9．如图所示，只含黄光和紫光的复色光束PO ，沿半径方向射入空气中的玻璃半圆柱后，被分成两光束OA 和OB 沿如图所示方向射出．则(A )OA 为黄光，OB 为紫光 (B )OA 为紫光，OB 为黄光 (C )OA 为黄光，OB 为复色光 (D )Oa 为紫光，OB 为复色光10．若原子的某内层电子被电离形成空位，其它层的电子跃迁到该空位上时，会将多余的能量以电磁辐射的形式释放出来，此电磁辐射就是原子的特征X 射线．内层空位的产生有多种机制，其中的一种称为内转换，即原子中处于激发态的核跃迁回基态时，将跃迁时释放的能量交给某一内层电子，使此内层电子电离而形成空位(被电离的电子称为内转换电子)．214Po 的原子核从某一激发态回到基态时，可将能量E 0=1.416MeV 交给内层电子(如K 、L 、M 层电子，K 、L 、M 标记原子中最靠近核的三个电子层)使其电离．实验测得从214Po 原子的K ,L 、M 层电离出的电子的动能分别为E k =1.323MeV 、E L =1.399MeV 、E M =1.412MeV ．则可能发射的特征X 射线的能量为 (A )0.013MeV (B )0.017MeV (C )0.076MeV (D )0.093MeV 第二卷(非选择题 共110分)二、本题共2小题，共20分．把答案填在题中的横线上或按题目要求作答．11．(8分) (1)某实验中需要测量一根钢丝的直径(约0.5mm )．为了得到尽可能精确的测量数据，应从实验室提供的米尺、螺旋测微器和游标卡尺(游标尺上有10个等分刻度)中，选择___________进行测量．(2)用游标卡尺(游标尺上有50个等分刻度)测定某工件的宽度时，示数如图所示，此工件的宽度为___________mm。

2004高考力学题【湘鄂、全国】18．如图所示，四个完全相同的弹簧都处于水平位置，它们的右端受到大小皆为F 的拉力作用，而左端的情况各不相同：①中弹簧的左端固定在墙上。

②中弹簧的左端受大小也为F 的拉力作用。

③中弹簧的左端拴一上物块，物块在光滑的桌面上滑动。

④中弹簧的左端拴一小物块，物块在有摩擦的桌面上滑动。

若认为弹簧的质量都为零，以l 1、l 2、l 3、l 4依次表示四个弹簧的伸长量，则有【D 】A ．l 2＞l 1 B.l 4＞l 3 C.l 1＞l 3 D.l 2=l 4【上海】5．物体B 放在物体A 上，A 、B 的上下表面均与斜面平行（如图），当两者以相同的初速度靠惯性沿光滑固定斜面C 向上做匀减速运动时【C 】（A ）A 受到B 的摩擦力沿斜面方向向上。

（B ）A 受到B 的摩擦力沿斜面方向向下。

（C ）A 、B 之间的摩擦力为零。

（D ）A 、B 之间是否存在摩擦力取决于A 、B 表面的性质。

【两广】7．用三根轻绳将质量为m 的物块悬挂在空中,如图所示.已知ac 和bc 与竖直方向的夹角分别为030和060，则 ac 绳和bc 绳中的拉力分别为【A 】 A1,2mg B．12mg C1,2mg D．12mg 【新课程】32．三个完全相同的物块1、2、3放在水平桌上，它们与桌面间的动摩擦因数都相同。

现用大小相同的外力F 沿图示方向分别作用在1和2上，用21F 的外力沿水平方向作用在3上，使三者都做加速运动，令a 1、a 2、a 3分别代表物块1、2、3的加速度，则【C 】A ．a 1=a 2=a 3B ．a 1= a 2，a 2＞a 3C ．a 1＞a 2，a 2＜a 3D ．a 1＞a 2，a 2＞a 3【山西】15．如图所示，ad 、bd 、cd 是竖直面内三根固定的光滑细杆，a 、b 、c 、d 位于同一圆周上， a 为圆周的最高点，d为最低点。

每根杆上都套着一个小滑环（图中未画出），三个滑环分别从 a 、b 、c 处释放（初速为0），用t 1、、、t 2、、t 3依次表示m各滑环到达d 所用的时间，则【D 】A ．t 1=、t 2、=t 3B ．t 1、>、t 2、>t 3C ．t 3 > t 1、>t 2、、D ．t 1、、<t 2、<t 3【两广】9．一杂技演员,用一只手抛球.他每隔0.40s 抛出一球,接到球便立即把球抛出,已知除抛、接球的时刻外，空中总有四个球，将球的运动看作是竖直方向的运动，球到达的最大高度是（高度从抛球点算起，取210/g m s =）【C 】A ． 1.6mB ． 2.4mC ．3.2mD ．4.0m【湘鄂、全国】21．放在水平地面上的一物块，受到方向不变的水平推力F 的作用，F 的大小与时t 的关系和物块速度υ与时间t 的关系如图所示。

AP physics C 2004 真题多项选择试题题目Questions 40-4136. Three 1/2 μF capacitors are connected in series as shown in the diagram above. Thecapacitance of the combination is (A) 0.1 μF (B) 1 μF (C) 2/3 μF(D) ? μF (E) 1/6 μF37. A hair dryer is rated as 1200 W, 120 V. Its effective internal resistance is(A) 0.1 Ω (B) A particle of charge +e and mass m moves with 10 Ω (C) 12Ω speed v perpendicular to a uniform magnetic field (D) 120 Ω (E) B directed into the page. The path of the particle is 1440 Ω a circl eof radius r, as shown above. 40. Which of the following correctly gives thedirection of motion and the equationrelating v and r ?Direction Equation(A) Clockwise eBr = mv 2 (B) Clockwise eBr = mv 38. A point charge+Q is inside an uncharged (C) Counterclockwise eBr = mv conducting spherical shell that in turn is near 2(D) Counterclockwise eBr = mv several isolated point charges, as shown above. 22(E) Counterclockwise eBr = mv The electric field at point P inside the shell depends on the magnitude of 41. The period of revolution of the particle (A) Q only is (B) the charge distribution on the sphere only (A) mr/eB (B) meB/(C) Q and the charge distribution on the sphere (D) all of the point charges (C) 2πm/eB (D) 2/,meB(E) all of the point charges a nd the charge (E)2/,mreBdistribution on the sphere 42. A 20 μF parallel-plate capacitor is fully charged to 30 39. In a certain region, the electric field along V. The energy stored in the capacitor is most nearly the x-axis is given by 3-3-4(A) 9 x 10 J (B) 9 x 10 J (C) 6 x 10 J 2E = ax + b, where a = 40 V/m -4-7(D) 2 x 10 J (E) 2 x 10 J and b = 4 V/m. The potentialdifference between the origin 43. A potential difference V is maintained between and x = 0.5 m is two large, parallel conducting plates. An (A) -36 V (B) -7 V (C) -3 V (D) 10 V electron starts from rest on the surface of one (E) 16 V plate and accelerates toward the other. Its speed as it reaches the second plate isproportional to(A) 1/V(B)1VV(C)(D) V 2(E) V44. A wire of radius R has a current I uniformly 48. Two conducting cylindrical wires are made outdistributed across its cross-sectional area. of the same material. Wire X has twice theAmpere's law is used with a concentric length and twice the diameter of wire Y. Whatcircular path of radius r, with r < R, to /R of their resistances?is the ratio Rxycalculate the magnitude of the magnetic (A) 1/4 (B) ? (C) 1 (D) 2 (E) 4field B at a distance r from the center of the wire. Which of the following equationsresults from a correct application ofAmpere's law to this situation? 22(A) B(2πr) = μI (B) B(2πr) =μI(r/R) 00(C) B(2πr) = 0 (D) B(2πR) = μI (E) B(2πR) 022= μI(r/R) 0Questions 45-4649. A solid metallic sphere of radius R has chargeQ uniformly distributed on its outer surface. Agraph of electric potential V as a function ofposition r is shown above. Which of thefollowing graphs best represents the magnitudeof the electric field E as a function of position r Particles of charge Q and -4Q are located on the for this sphere? x-axis as shown in the figure above. Assumethe particles are isolated from all other charges.45. Which of the following describes the directionof the electric field at point P ?(A) +x (B) +y (C)-y(D) Components in both the -x- and+y-directions(E) Components in both the+x- and -y-directions46. At which of the labeled points on the x-axis is the electric field zero?(A) A (B) B (C) C (D) D (E) E47. When the switch S is open in the circuitshown above, the reading on the ammeter Ais 2.0 A. When the switch is closed, thereading on the ammeter is(A) doubled(B) increased slightly but not doubled(C) the same(D) decreased slightly but not halved (E) halved50. Two parallel wires, each carrying a current I, repel each other with a force F. If bothcurrents are doubled, the force of repulsion is (A) 2F (B) F (C) 4F22(D) F (E) 8F 4251. A circular current-carrying loop lies so that the plane of the loop is perpendicular to a constant 54. A conducting loop of wire that is initially magnetic field of strength B. Suppose that the around a magnet is pulled away from the radius R of the loop could be made to increase magnet to the right, as indicated in the figure with time t so that R = at, where a is a constant. above, inducing a current in the loop. What is What is the magnitude of the emf that would be the direction of the force on the magnet and generated around the loop as a function of t ? 2the direction of the magnetic field at the (A) 2πBat(B) 2πBat (C) 2πBt 223center of the loop due to the (D) πBat (E) (π/3)Bat induced current? Direction ofMagnetic Field atDirection of Center of Loop dueForce on the Magnet to Induced Current(A) To the right To the right(B) To the right To the left(C) To the left To the right 52. The figures above show parts of two circuits, (D) To the left To the left(E) No direction; To the left each containing a battery of emf ε and internal the force is zero. resistance r. The current in each battery is 1 A, but the direction of the current in one battery is opposite to that in the other. If the potential differences across the batteries' terminals are 10 V and 20 V as shown, what are the valuesof ε and r ? 55. A square loop of wire carrying a current I is (A) ε = 5 V, r = 15 Ω initially in the plane of the page and is located in a uniform magnetic field B that points (B) ε =IOV, r=100 Ω toward the bottom of the page, as shown above. (C) ε = 15 V, r = 5 Ω Which of the following shows the correct initialrotati on of the loop due to the force exerted on (D) ε = 20 V, r = 10 Ωit by the magnetic field? (E) The values cannot be computed unless the complete circuits are shown.53. A charged particle can move withconstant velocity through a regioncontaining both an electric field and amagnetic field only if the(A) electric field is parallel to the magnetic field(B) electric field is perpendicular to the magnetic field(C) electric field is parallel to the velocity vector(D) magnetic field is parallel to the velocity vector(E) magnetic field is perpendicular to the velocity vectorQuestions 59-6156. In the circuit shown above, the equivalent The diagram above shows equipotential lines resistance of the three resistors is produced by an unknown charge distribution. A, (A) 10.5 Ω (B) 15Ω (C) 20 ΩB, C, D, and E are points in the plane. (D) 50 Ω (E) 115 Ω59. Which vector below best describes the direction Questions 57-58of the electric field at point A ?(A) (B) (C) (D)(E) None of these; the field is zero.60. At which point does the electric field havethe greatest magnitude? (A) A As shown in the figure above, six particles, each (B) B with charge +Q, are held fixed and ate equally(C) C spaced around the circumference of a circle of(D) D radius R.(E) E57. What is the magnitude of the resultantelectric field at the center of the circle? 61. How much net work must be done by anexternal force to move a -1 μC point charge 6Q(A) 0 (B) (C) from rest at point C to rest at point E ? 24,,R0(A) -20 μJ(B) -10 μJ 23Q32Q (D) 22(C) 10 μJ ,,,,4R4R00(D) 20 μJ 3Q(E) 30μJ (E) 2,,2R 058. With the six particles held fixed, how muchwork would be required to bring a seventhparticle of charge + Q from very far awayand place it at the center of the circle?23Q6Q(A) 0 (B) (C) 2,,,,24RR00229Q3Q(D) (E) ,,,,2R00R62. One of Maxwell's equations can be written 65. A physics problem starts: "A solid sphere hascharge distributed uniformly throughout. . . " d,as. This equation expresses ,,,Eds,It may be correctly concluded that the dt(A) electric field is zero everywhere inside the the fact that sphere (A) a changingmagnetic field produces (B) electric field inside the sphere is the same an electric field as the electric field outside (B) a changing electric field produces a (C) electric potential on the surface of the magnetic field sphere is not constant (C) the net magnetic flux through a (D) electric potential in the center of the sphere closed surface depends on the is zero current inside (E) sphere is not made of metal (D) the net electric flux through a closed surface depends on the charge inside Questions 66-67 relate to the circuit represented (E) electric charge is conserved below. The switch S, after being open for a long time, is then closed., ,12 V4 HS63. The plates of a parallel-plate capacitor of cross 66. What isthe current in the circuit after the sectional area A are separated by a distance d, switch has been closed a long time? as shown above. Between the plates is a (A) 0 A dielectric material of constant K. The plates are (B) 1.2 A connected in series with a variable resistance R (C) 2 A and a power supply of potential difference V. (D) 3 A The capacitance C of this capacitor will (E) 12 A increase if which of the following isdecreased? (A) A (B) R (C) K 67. What is the potential difference across the (D) d (E) V resistor immediately after the switch is closed? (A) 0 V(B) 2 V(C) 7.2 V(D) 8 V(E) 12 V68. A uniform spherical charge distribution hasradius R.. Which of the following is true of the electric field strength due to this charge 64. The currents in three parallel wires, X, Y, and Z, distribution at a distance r from the center of each have magnitude l and are in the directions the charge? shown above. Wire Y is closer to wire X than to (A) It is greatest when r = 0. wire Z. The magnetic force on wire Y is (B) It is greatest when r = R/2. (A) zero (B) into the page (C) out of the page (C) It is directly proportional to r when r > (D) toward the bottom of the page R. (E) toward the left (D) It is directly proportional to r when r < R. 2(E) It is directlyproportional to r.69. When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown above, the leaves spring apart (I). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger and finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is(A) positive in both I and III(B) negative in both I and III(C) positive in I, negative in III(D) negative in I, positive in III(E) impossible to determine in either I or III70. A sheet of copper in the plane of the page is connected to a battery as shown above, causing electrons to drift through the copper toward the bottom of the page. The copper sheet is in a magnetic field B directed intothe page. P and P are points at the edges of 12the strip. Which of the following statements is true?(A) P is at a higher potential than P. 12(B) P is at a higher potential than P. 21(C) P and P are at equal positive potential. 12(D) P and P are at equal negative potential. 12(E) Current will cease to flow in the copper sheet.。

AP® Physics C1997 Free response QuestionsThese materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and theirprograms, 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 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, 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 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 TestingService.1997M1. A nonlinear spring is compressed horizontally. The spring exerts a force that obeys the equation F(x) = Ax½, where x is the distance from equilibrium that the spring is compressed and A is a constant. A physics student records data on the force exerted by the spring as it is compressed and plots the two graphs below, which include the data and the student's best-fit curves.a. From one or both of the given graphs, determine A. Be sure to show your work and specify theunits.b. i. Determine an expression for the work done in compressing the spring a distance x.ii. Explain in a few sentences how you could use one or both of the graphs to estimate a numerical answer to part (b)i for a given value of x.c. The spring is mounted horizontally on a countertop that is 1.3 m high so that its equilibrium positionis just at the edge of the countertop. The spring is compressed so that it stores 0.2 J of energy and is then used to launch a ball of mass 0.10 kg horizontally from the countertop. Neglecting friction,determine the horizontal distance d from the edge of the countertop to the point where the hall strikes the floor1997M2. An open-top railroad car (initially empty and of mass M o) rolls with negligible friction along a straight horizontal track and passes under the spout of a sand conveyor. When the car is under the conveyor, sand is dispensed from the conveyor in a narrow stream at a steady rate ∆M/∆t = C and falls vertically from an average height h above the floor of the railroad car. The car has initial speed v o and sand is filling it from time t = 0 to t = T. Express your answers to the following in terms of the given quantities and g.a. Determine the mass M of the car plus the sand that it catches as a function of time t for 0 < t < T.b. Determine the speed v of the car as a function of time t for 0 < t < T.c. i. Determine the initial kinetic energy K i of the empty car.ii. Determine the final kinetic energy K f of the car and its load.iii. Is kinetic energy conserved? Explain why or why not.d. Determine expressions for the normal force exerted on the car by the tracks at the following times.i. Before t = 0ii. For 0 < t < Tiii. After t = T1997M3. A solid cylinder with mass M, radius R, and rotational inertia ½MR2 rolls without slipping down the inclined plane shown above. The cylinder starts from rest at a height H. The inclined plane makes an angle θ with the horizontal. Express all solutions in terms of M, R, H, θ, and g.a. Determine the translational speed of the cylinder when it reaches the bottom of the inclined plane.b. On the figure below, draw and label the forces acting on the cylinder as it rolls down the inclinedplane Your arrow should begin at the point of application of each force.c. Show that the acceleration of the center of mass of the cylinder while it is rolling down the inclinedplane is (2/3)g sinθ.d. Determine the minimum coefficient of friction between the cylinder and the inclined plane that isrequired for the cylinder to roll without slipping.e. The coefficient of friction μ is now made less than the value determined in part (d), so that thecylinder both rotates and slips.i. Indicate whether the translational speed of the cylinder at the bottom of the inclined plane is greaterthan, less than, or equal to the translational speed calculated in part (a). Justify your answer.ii. Indicate whether the total kinetic energy of the cylinder at the bottom of the inclined plane is greater than, less than, or equal to the total kinetic energy for the previous case of rolling withoutslipping. Justify your answer.1997E1. A technician uses the circuit shown above to test prototypes of a new battery design. The switch is closed, and the technician records the current for a period of time. The curve that best fits the results is shown in the graph below.The equation for this curve is I = I o e -kt where t is the time elapsed from the instant the switch is closed and I oand k are constants.a. i.o across the resistorimmediately after the switch is closed.ii. Would the open circuit voltage of the fresh battery have been less than, greater than, or equal to the value in part i ? Justify your answer.b. Determine the value of k from this best-fit curve. Show your work and be sure to include units in your answer.c. Determine the following in terms of R, I o , k, and t.i. The power delivered to the resistor at time t = 0ii. The power delivered to the resistor as a function of time tiii. The total energy delivered to the resistor from t = 0 until the current is reduced to zero1997E2. A nonconducting sphere with center C and radius a has a spherically symmetric electric charge density. The total charge of the object is Q > 0.a. Determine the magnitude and direction of the electric field at point P, which is a distance R > a to theright of the sphere's center.b. Determine the flux of the electric field through the spherical surface centered at C and passingthrough P.A point particle of charge -Q is now placed a distance R below point P. as shown above.c. Determine the magnitude and direction of the electric field at point P.d. Now consider four point charges, q1, q2, q3, and q4, that lie in the plane of the page as shown in thediagram above. Imagine a three-dimensional closed surface whose cross section in the plane of the page is indicated.i. Which of these charges contribute to the net electric flux through the surface?ii. Which of these charges contribute to the electric field at point P1 ?iii. Are your answers to i and ii the same or are they different? Explain why this is so.e. If the net charge enclosed by a surface is zero, does this mean that the field is zero at all points on thesurface? Justify your answer.f. If the field is zero at all points on a surface, does this mean there is no net charge enclosed by thesurface? Justify your answer.1997E3. A long, straight wire lies on a table and carries a constant current I 0, as shown above.a. Using Ampere's law, derive an expression for the magnitude B of the magnetic field at a perpendicular distance r from the wire.A rectangular loop of wire of length l , width w, and resistance R is placed on the table a distance s from thewire, as shown below. b. What is the direction of the magnetic field passing through the rectangular loop relative to thecoordinate axes shown above on the right?c. Show that the total magnetic flux φm through the rectangular loop is Il s w s02μπln()+The rectangular loop is now moved along the tabletop directly away from the wire at a constant speed v = |ds/dt ∣as shown above.d. What is the direction of the current induced in the loop? Briefly explain your reasoning.e. What is the direction of the net magnetic force exerted by the wire on the moving loop relative to the coordinate axes shown above on the right? Briefly explain your reasoning.f. Determine the current induced in the loop. Express your answer in terms of the given quantities and fundamental constants.。

2004年普通高等学校招生全国统一考试（北京卷）理科综合能力测试第I卷15. （2004年北京）下列说法正确的是（）A. 外界对气体做功,气体的内能一定增大B. 气体从外界吸收热量,气体的内能一定增大C. 气体的温度越低,气体分子无规则运动的平均动能越大D. 气体的温度越高,气体分子无规则运动的平均动能越大【答案】D【解析】根据热力学第一定律可得ΔU=W+Q,若外界对气体做功的同时,向外放热,即W>0的同时Q<0,则气体的内能不一定增大,选项A错误；同理选项B也错误；由于温度是分子平均动能的标志,温度越高,则分子的平均动能越大,故气体的温度越低,气体分子无规则运动的平均动能越小,选项C错误；气体的温度越高,气体分子无规则运动的平均动能越大,选项D正确.16. （2004年北京）声波属于机械波,下列有关声波的描述中正确的是（）A.同一列声波在各种介质中的波长是相同的B.声波的频率越高,它在空气中传播的速度越快C.声波可以绕过障碍物传播,即它可以发生衍射D.人能辨别不同乐器同时发出的声音,证明声音不会发生干涉【答案】C【解析】由于声波的传播速度取决于介质,故同一列声波在不同介质中的波速是不相同的,而同一列波,说明它的频率相同,故根据v=λf可知,波长也是不相同的,选项A错误；声波的传播速度与介质有关,与声波的频率无关,故它的频率越高,它在空气中传播的速度并不越快,选项B错误；声波也是一种波,任何波都有衍射现象,故它也可以绕过障碍物传播,即它可以发生衍射,选项C正确；人能辨别不同乐器同时发出的声音,是因为不同乐器发出的声音有自己的特色,即音色不同,而不是证明声音不会发生干涉,声音是波,它也是可以发生干涉的,选项D错误.17. （2004年北京）氦原子被电离一个核外电子,形成类氢结构的氦离子；已知基态的氦离子能量为E1= -54.4eV,氦离子能级的示意图如图所示.在具有下列能量的光子中,不能被基态氦离子吸收而发生跃迁的是（B）A.40.8eVB.43.2eVC.51.0eVD.54.4eV【答案】B【解析】如果基态的氦离子跃迁到第一激发态,需要吸收-13.6eV-(-54.4eV)=40.8eV的能量,故选项A是可能的；若跃迁到第二激发态,需要吸收-6.0eV-(-54.4eV)=48.4eV的能量,故选项B是不可能的；若跃迁到第三激发态,需要吸收-3.4eV-(-54.4eV)=51.0eV的能量,故选项C是可能的；若跃迁出去,需要吸收-0eV-(-54.4eV)=54.4eV的能量,故选项D也是可能的；所以选项B符合题意.18. （2004年北京）已知一束可见光a是由m、n、p三种单色光组成的,检测发现三种单色光中,n、p 两种色光的频率都大于m色光；n色光能使某金属发生光电效应,而p色光不能使该金属发生光电效应.那么,光束a通过三棱镜的情况是（A）【答案】A【解析】三种色光中,频率越大的色光,其折射率也会越大,故它在三棱镜中会偏折得更厉害,因为m色光的频率最小,故它的折射率也最小,故选项B D错误；又因为n色光能使某金属发生光电效应,而p色光不能使该金属发生光电效应,根据爱因期坦光电效应方程可知,n光能量大于p光,故它的折射率也会较大,所以选项A正确,C错误.19. （2004年北京）如图所示,正方形区域ab c d中充满匀强磁场,磁场方向垂直纸面向里.一个氢核从ad边的中点m沿着既垂直于ad边又垂直于磁场的方向,以一定速度射入磁场,正好从ab边中点n射出磁场.若将磁场的磁感应强度变为原来的2倍,其它条件不变,则这个氢核射出磁场的位置是（C）A.在b 、a 之间某点 B .在n 、a 之间某点C.a 点D.在a 、m 之间某点【答案】C【解析】粒子从m 点进入,从n 点射出,所以粒子的偏转半径为正方形边长的一半,根据粒子在磁场中做圆周运动的规律可知：Bqv =m 2v R ,得到偏转半径R =mv Bq ,所以当磁感应强度变为原来的2倍时,其偏转半径会变为原来的一半,即正方形边长的四分之一,所以粒子会从a 点射出磁场,选项C 正确.20. （2004年北京）1990年5月,紫金山天文台将他们发现的第2752号小行星命名为吴健雄星,该小行星的半径为16km .若将此小行星和地球均看成质量分布均匀的球体,小行星密度与地球相同.已知地球半径R ＝6400km ,地球表面重力加速度为g.这个小行星表面的重力加速度为（B ）A.400g B .1400g C.20g D. 120g 【答案】B【解析】由于行星与地球相比较而言,其半径的关系知道,密度的关系也知道,故我们可以判断出其质量的关系,进而求出其重力加速度的关系；根据F 万=F 向可知,m g=2GMm R ,所以重力加速度g=2GM R ,又因为M =ρV=343ρπR ,故g=43ρπG R ； 故小行星的重力加速度为：g 行=43行ρπG R ,地球的重力加速度为：g 地=43地ρπG R ,故166400行行地地==g R g R =1400,所以小行星表面的重力加速度为1400g,选项B 正确.21. （2004年北京）静电透镜是利用静电场使电子束会聚或发散的一种装置,其中某部分静电场的分布如右图所示.虚线表示这个静电场在x o y 平面内的一簇等势线,等势线形状相对于o x 轴、o y 轴对称.等势线的电势沿x 轴正向增加.且相邻两等势线的电势差相等.一个电子经过P 点（其横坐标为-x 0）时,速度与o x 轴平行.适当控制实验条件,使该电子通过电场区域时仅在o x 轴上方运动.在通过电场区域过程中,该电子沿y 方向的分速度v y 随位置坐标x 变化的示意图是（D ）【答案】D【解析】由于等势线的电势沿x 轴正向增加,而等势线与电场线是垂直的关系,故可做出经过P 点的电场线如图所示,电子所受的电场力与场强方向相反,故电子受到一个斜向右下方的电场力,故沿y 负方向加速运动；电子通过y 轴后受到的电场力斜向右上方,故沿y 轴负方向减速运动；又由于在x 轴方向始终加速,故在水平方向通过相同的位移时间变短,根据△v y =a y △t ,故通过相同的水平位移竖直向速度变化量减小．由于v y -x 的斜率代表竖直向速度v y 随x 轴变化的快慢,故D 正确.22. （2004年北京）（18分）为了测定电流表A 1的内阻,采用如图1所示的电路.其中：A 1是待测电流表,量程为300μA,内阻约为100Ω；A 2是标准电流表,量程是200μA ；R 1是电阻箱,阻值范围0～999.9Ω；R 2是滑动变阻器；R 3是保护电阻；E 是电池组,电动势为4V,内阻不计；S 1是单刀单掷开关,S 2是单刀双掷开关.（1）根据电路图1,请在图2中画出连线,将器材接成实验电路(2)连接好电路,将开关S2扳到接点a处,接通开关S1,调整滑动变阻器R2使电流表A2的读数是150μA；然后将开关S2扳到接点b处,保持R2不变,调节电阻箱R1,使A2的读数仍为150μA.若此时电阻箱各旋钮的位置如图3所示,电阻箱R1的阻值是Ω,则待测电流表A1的内阻R g＝Ω.（3）上述实验中,无论怎样调整滑动变阻器R2的滑动端位置,都要保证两块电流表的安全.在下面提供的四个电阻中,保护电阻R3应选用：（填写阻值相应的字母）.A.200kΩB.20kΩC.15kΩD.20Ω（4）下面提供最大阻值不同的四个滑动变阻器供选用,既要满足上述实验要求,又要调整方便,滑动变阻器（填写阻值相应的字母）是最佳选择.A.1kΩB.5kΩC.10kΩD.25kΩ【答案】（1）电路连线如图所示：（2）86.3；86.3；（3）B；（4）C.【解析】（1）由电路图连接实物图时,一定要按照一定的顺序进行,一般是沿电流的方向进行,从正极出发,最后再回到负极；（2）电阻箱R1的阻值可以通过图3读出,得出86.3Ω,读数时注意的是最左下角的旋扭是×100的,而习惯上是左上角的是倍率较大的,这个容易出错,希望审题时加以注意；该实验是用替代的方法测电阻电流表A1电阻大小的,电流表与电阻R1在电路中所起的效果都是相同的,故电流表的内阻的大小也是86.3Ω；（3）保护电阻就是当变阻器的阻值为0时也不能让电路中的电流超过范围值而对电路起到保护的作用；因为电源的电动势为4V,电流表A2的量程小于电流表A1的量程,故要保证两电表的安全,只需要不让电路中的电流超过200μA即可,所以电路中的总电阻为R=4200μVA=20kΩ,故选项B正确；（4）该实验使用的是限流电路,即变阻器与被测电路串联,所以要使变阻器调节方便,应选用电阻值比较接近被测电阻的变阻器,由于测量时电路中的电流大约是150μA,故此时电路中的电阻为R′=4 150μVA=26.7kΩ,故变阻器的电阻大约为26.7kΩ-20kΩ=6.7kΩ,所以选项C是最佳的.23. （2004年北京）（18分）如图1所示,两根足够长的直金属导轨MN、PQ平行放置在倾角为θ的绝缘斜面上,两导轨间距为L.M、P两点间接有阻值为R的电阻.一根质量为m的均匀直金属杆ab放在两导轨上,并与导轨垂直,整套装置处于磁感应强度为B的匀强磁场中,磁场方向垂直斜面向下.导轨和金属杆的电阻可忽略.让ab杆沿导轨由静止开始下滑,导轨和金属杆接触良好,不计它们之间的摩擦.（1）由b向a方向看到的装置如图2所示,请在此图中画出ab杆下滑过程中某时刻的受力示意图；（2）在加速下滑过程中,当ab 杆的速度大小为v 时,求此时ab 杆中的电流及其加速度的大小；（3）求在下滑过程中,ab 杆可以达到的速度最大值.【答案】（1）示意图如图所示；（2）=BLv I R ；22sin θ=-B L v a g mR；（3）22sin m mgR v B L θ=.【解析】（1）受力示意图如图所示,杆受重力m g,竖直向下、支撑力N ,垂直斜面向上和安培力F ,沿斜面向上.（2）当ab 杆速度为v 时,感应电动势E =BLv ,此时电路中电流E BLv I R R== ab 杆受到安培力 22B L v F BIL R== 根据牛顿运动定律,有22sin sin θθ=-=-B L v ma mg F mg R, 解之得22sin θ=-B L v a g mR. （3）当加速度a =0时,即22sin B L v mg Rθ= 时,ab 杆达到最大速度v m , 故22sin m mgR v B L θ=.24. （2004年北京）（20分）对于两物体碰撞前后速度在同一直线上,且无机械能损失的碰撞过程,可以简化为如下模型：A 、B 两物体位于光滑水平面上,仅限于沿同一直线运动,当它们之间的距离大于等于某一定值d 时,相互作用力为零；当它们之间的距离小于d 时,存在大小恒为F 的斥力；设A 物体质量m 1=1.0k g,开始时静止在直线上某点；B 物体质量m 2=3.0k g,以速度v 0从远处沿该直线向A 运动,如图所示,若d =0.10m ,F =0.60N ,v 0=0.20m /s,求：（1）相互作用过程中A 、B 加速度的大小；（2）从开始相互作用到A 、B 间的距离最小时,系统（物体组）动能的减少量；（3）A 、B 间的最小距离.【答案】（1）210.60/=a m s 220.20/=a m s ；（2）||0.015∆=k E J ；（3）min 0.075s m ∆=.【解析】（1）根据牛顿第二定律可知,2110.60/==F a m s m 2220.20/==F a m s m （2）两者速度相同时,距离最近,由动量守恒：2012()=+m v m m v 解得20120.15/()==+m v v m s m m 故系统动能的减少量为22201211||()0.01522∆=-+=k E m v m m v J . （3）根据匀变速直线运动规律可知：11=v a t ；202=-v v a t当12v v =时,A 向右运动的位移21112=s a t ,B 向右运动的位移220212=-s v t a t 故最小距离12∆=+-s s d s解得A 、B 两者距离最近时所用时间t =0.25s将t =0.25s 代入,解得A 、B 间的最小距离min 0.075s m ∆=.25．（2004年北京）（22分）下图是某种静电分选器的原理示意图,两个竖直放置的平行金属板带有等量异号电荷,形成匀强电场.分选器漏斗的出口与两板上端处于同一高度,到两板距离相等.混合在一起的a 、b 两种颗粒从漏斗出口下落时,a 种颗粒带上正电,b 种颗粒带上负电.经分选电场后,a 、b 两种颗粒分别落到水平传送带A 、B 上.已知两板间距d =0.1m , 板的长度l =0.5m ,电场仅局限在平行板之间；各颗粒所带电量大小与其质量之比均为1×10-5C/k g.设颗粒进入电场时的初速度为零,分选过程中颗粒大小及颗粒间的相互作用不计.要求两种颗粒离开电场区域时,不接触到极板但有最大偏转量.重力加速度g 取10m /s 2.（1）左右两板各带何种电荷？两极板间的电压多大？（2）若两带电平行板的下端距传送带A 、B 的高度H ＝0.3m ,颗粒落至传送带时的速度大小是多少？（3）设颗粒每次与传送带碰撞反弹时,沿竖直方向的速度大小为碰撞前竖直方向速度大小的一半.写出颗粒第n 次碰撞反弹高度的表达式.并求出经过多少次碰撞,颗粒反弹的高度小于0.01m .【答案】（1）左板带负电荷,右板带正电荷；4110=⨯U V ；（2）4/=v m s ；（3）n =4.【解析】（1）通过颗粒a 落在左侧,且它带正电可知左板带负电荷,右板带正电荷； 依题意,颗粒在平行板的竖直方向上满足212l gt =① 在水平方向上满足2122d qU s t md== ② ①②两式联立得241102mgd U V ql==⨯ （2）根据动能定理,颗粒落到水平传送带上满足211()22++=qU mg l H mv即4/=≈v m s ； （3）在竖直方向颗粒作自由落体运动,它第一次落到水平传送带上沿竖直方向有4/y v m s == 反弹高度221(0.5)1()()242y y v v h g g== 根据题设条件,颗粒第n 次反弹后上升的高度211()()()0.8424y n n n v h m g ==⨯ 当n =4时,h n <0.01m。

2004年普通高等学校招生全国统一考试物理（江苏卷）第一卷(选择题共40分)一、本题共10小慰；每小题4分，共40分．在每小题给出的四个选项中，有的小题只有一个选项正确，有的小题有多个选项正确．全部选对的得4分，选不全的得2分，有选错或不答的得0分．1. 下列说法正确的是 （ ）A. 光波是—种概率波B. 光波是一种电磁波C. 单色光从光密介质进入光疏介质时．光子的能量改变D. 单色光从光密介质进入光疏介质时，光的波长不变2．下列说法正确的是 （ ）A. 物体放出热量，温度一定降低B. 物体内能增加，温度一定升高C. 热量能自发地从低温物体传给高温物体D. 热量能自发地从高温物体传给低温物体3．下列说法正确的是 （ ）A. α射线与γ射线都是电磁波D. β射线为原子的核外电子电离后形成的电子流C. 用加温、加压或改变其化学状态的方法都不能改变原子核衰变的半衰期D. 原子核经过衰变生成新核，则新核的质量总等于原核的质量4．若人造卫星绕地球作匀速圆周运动，则下列说法正确的是 （ ）A. 卫星的轨道半径越大，它的运行速度越大D. 卫星的轨道半径越大，它的运行速度越小C. 卫星的质量一定时，轨道半径越大，它需要的向心力越大D. 卫星的质量一定时，轨道半径越大，它需要的向心力越小5．甲、乙两个相同的密闭容器中分别装有等质量的同种气体，已知甲、乙容器中气体的压强分别为p 甲、p 乙，且p 甲<p 乙，则 （ ）A. 甲容器中气体的温度高于乙容器中气体的温度B. 甲容器中气体的温度低于乙容器中气体的温度C. 甲容器中气体分子的平均动能小于乙容器中气体分子的平均动能D. 甲容器中气体分子的平均动能大于乙容器中气体分子的平均动能6．如图所示，一个有界匀强磁场区域，磁场方向垂直纸面向外．一个矩形闭合导线框abcd ，沿纸面由位置1(左)匀速运动到位置2(右)．则A. 导线框进入磁场时，感应电流方向为a →b →c →d →aB. 导线框离开磁场时，感应电流方向为a →d →c →b →aC. 导线框离开磁场时，受到的安培力方向水平向右D. 导线框进入磁场时．受到的安培力方向水平向左7．雷蒙德·戴维斯因研究来自太阳的电子中徽子(ve )而获得了2002年度诺贝尔物理学奖．他探测中徽子所用的探测器的主体是一个贮满615t 四氯乙烯(C 2Cl 4)溶液的巨桶．电子中微子可以将一个氯核转变为一个氩核，其核反应方程式为e Ar Cl v e 0137183717-+→+ 已知Cl 3717核的质量为36.95658u ，Ar 3718核的质量为36.95691u ，e0的质量为0.00055u，1u质量对应的能量为931.5MeV．根据以上数据，可以判断参1与上述反应的电子中微子的最小能量为（）A. 0.82 MeVB. 0.31 MeVC. 1.33 MeVD. 0.51 MeV8．图1中，波源S从平衡位置y=0开始振动，运动方向竖直向上(y轴的正方向)，振动周期T=0.01s，产生的简谐波向左、右两个方向传播，波速均为v=80m/s．经过一段时间后，P、Q两点开始振动,已知距离SP=1.2m、SQ=2.6m．若以Q点开始振动的时刻作为计时的零点，则在图2的振动图象中，能正确描述P、Q两点振动情况的是（）A. 甲为Q点振动图象B. 乙为Q点振动图象C. 丙为P点振动图象D. 丁为P点振动图象9．如图所示，只含黄光和紫光的复色光束PO，沿半径方向射入空气中的玻璃半圆柱后，被分成两光束OA和OB沿如图所示方向射出．则A. OA为黄光，OB为紫光B. OA为紫光，OB为黄光C. OA为黄光，OB为复色光D. Oa为紫光，OB为复色光10．若原子的某内层电子被电离形成空位，其它层的电子跃迁到该空位上时，会将多余的能量以电磁辐射的形式释放出来，此电磁辐射就是原子的特征X射线．内层空位的产生有多种机制，其中的一种称为内转换，即原子中处于激发态的核跃迁回基态时，将跃迁时释放的能量交给某一内层电子，使此内层电子电离而形成空位(被电离的电子称为内转换电子)．214Po的原子核从某一激发态回到基态时，可将能量E0=1.416MeV交给内层电子(如K、L、M层电子，K、L、M标记原子中最靠近核的三个电子层)使其电离．实验测得从214Po原子的K,L、M层电离出的电子的动能分别为E k=1.323MeV、E L=1.399MeV、E M=1.412MeV．则可能发射的特征X射线的能量为A. 0.013MeVB. 0.017MeVC. 0.076MeVD. 0.093MeV第二卷(非选择题共110分)二、本题共2小题，共20分．把答案填在题中的横线上或按题目要求作答．11．(8分) (1)某实验中需要测量一根钢丝的直径(约0.5mm)．为了得到尽可能精确的测量数据，应从实验室提供的米尺、螺旋测微器和游标卡尺(游标尺上有10个等分刻度)中，选择___________进行测量．（2）用游标卡尺(游标尺上有50个等分刻度)测定某工件的宽度时，示数如图所示，此工件的宽度为___________mm。

AP® Physics C2004 Free Response QuestionsThe materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought from theAdvanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distributethe materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of themmay not be resold, and the copyright notices must be retained as they appear here.The College Board is a nonprofit membership association whose mission is to connect students to college success and opportunity.Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges, through major programs and services incollege 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 equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.For further information, visit College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.2004M1. A rope of length L is attached to a support at point C. A person of mass m1 sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown above. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Derive expressions for each of the following in terms of m1, m2, L, and g.a. The speed of the person just before the collision with the objectb. The tension in the rope just before the collision with the objectc. The speed of the person and object just after the collisiond. The ratio of the kinetic energy of the person-object system before the collision to the kinetic energy after thecollisione. The total horizontal displacement x of the person from position A until the person and object land in the water atpoint D.2004M2. A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass m is released from rest and takes a time t to fall the distance D to the floor.a. Calculate the linear acceleration a of the falling block in terms of the given quantities.b. The time t is measured for various heights D and the data are recorded in the following table.i. What quantities should be graphed in order to best determine the acceleration of the block? Explain yourreasoning.ii. On the grid below, plot the quantities determined in (b) i., label the axes, and draw the best-fit line to the data.iii. Use your graph to calculate the magnitude of the acceleration.c. Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants.d. The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c),can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy.2004M3. A uniform rod of mass M and length L is attached to a pivot of negligible friction as shown above. The pivot is located at a distance L/3 from the left end of the rod. Express all answers in terms of the given quantities and fundamental constants.a. Calculate the rotational inertia of the rod about the pivot.b. The rod is then released from rest from the horizontal position shown above. Calculate the linear speed ofthe bottom end of the rod when the rod passes through the vertical.c. The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly from thisposition. Calculate the period of oscillation as it swings.2004E1. The figure above left shows a hollow, infinite, cylindrical, uncharged conducting shell of inner radius r1 and outer radius r2. An infinite line charge of linear charge density +λ is parallel to its axis but off center. An enlarged cross section of the cylindrical shell is shown above right.a. On the cross section above right,i. sketch the electric field lines, if any, in each of regions I, II, and III andii. use + and - signs to indicate any charge induced on the conductor.b. In the spaces below, rank the electric potentials at points a, b, c, d, and e from highest to lowest (1 = highestpotential). If two points are at the same potential, give them the same number.____V a ____V b ____V c- ____V d ____V ec. The shell is replaced by another cylindrical shell that has the same dimensions but is nonconducting and carries auniform volume charge density +ρ. The infinite line charge, still of charge density +λ, is located at the center of the shell as shown above. Using Gauss's law, calculate the magnitude of the electric field as a function of the distance r from the center of the shell for each of the following regions. Express your answers in terms of the given quantities and fundamental constants.i. r < r lii. r l≤ r≤ r2iii. r > r22004E2. In the circuit shown above left, the switch S is initially in the open position and the capacitor C is initially uncharged. A voltage probe and a computer (not shown) are used to measure the potential difference across the capacitor as a function of time after the switch is closed. The graph produced by the computer is shown above right. The battery has an emf of 20 V and negligible internal resistance. Resistor R1has a resistance of 15 kΩ and the capacitor C has a capacitance of 20 μF.a. Determine the voltage across resistor R2 immediately after the switch is closed.b. Determine the voltage across resistor R2 a long time after the switch is closed.c. Calculate the value of the resistor R2.d. Calculate the energy stored in the capacitor a long time after the switch is closed.e. On the axes below, graph the current in R2as a function of time from 0 to 15 s. Label the vertical axis withappropriate values.Resistor R2is removed and replaced with another resistor of lesser resistance. Switch S remains closed for a long time.(f) Indicate below whether the energy stored in the capacitor is greater than, less than, or the same as it was withresistor R2in the circuit._____Greater than _____Less than _____The same asExplain your reasoning.2004E3. A rectangular loop of dimensions 3 ℓ and 4 ℓ lies in the plane of the page as shown above. A long straight wire also in the plane of the page carries a current I.a. Calculate the magnetic flux through the rectangular loop in terms of I, ℓ , and fundamental constants. Starting at time t = 0, the current in the long straight wire is given as a function of time t byI (t) = I0e-kt , where I0 and k are constants.b. The current induced in the loop is in which direction?____Clockwise ____CounterclockwiseJustify your answer.The loop has a resistance R. Calculate each of the following in terms of R, I0 , k, ℓ , and fundamental constants.c. The current in the loop as a function of time td. The total energy dissipated in the loop from t = 0 to t=∞Copyright © 2004 by College Entrance Examination Board. All rights reserved.Visit (for AP professionals) and /apstudents (for AP students and parents)。