香港中学物理竞赛Word文档下载推荐.docx

1、Density of water = 1.0 x 103 kg/m3Density of iron = 7.7 x 103 kg/m3Density of mercury = 13.6 x 103 kg/m3Speed of sound in air = 340 m/s除非特别说明，本卷将使用下列符号和常数：g 地球表面重力加速度, 9.8 （m/s2）G 重力常数, 6.67 x 10-11 （N m2/kg2）e 电子电荷, 1.6 x 10-19 （A s） 0 静电常数, 8.85 x 10-12 （A s）/（V m）me 电子质量, 9.11 x 10-31 kgc 真空光速, 3

2、.0 x 108 m/s地球半径 = 6378 km太阳-地球距离 = 1.5 x 1011 m水的密度 = 1.0 x 103 kg/m3铁的密度 = 7.7 x 103 kg/m3水银的密度= 13.6 x 103 kg/m3空气中声速= 340 m/sThe following conditions will be applied unless otherwise specified:1） All objects are near Earth surface and the gravity is pointing downwards.2） Neglect air resistance.3

3、） All speeds are much lower than the speed of light.除非特别说明，本卷将使用下列条件：1） 所有物体都处于地球表面，重力向下；2） 忽略空气阻力；3） 所有速度均远低于光速.Multiple choice questions （2 points each. Select one answer in each question.）选择题（每道题二分，每道题选择一个答案）1 A car of mass m is slipping down a slope of inclination angle at a constant acceleratio

4、n a. The static friction coefficient between the wheels and the slope is . What is the friction force between the wheels and the slope?一质量为m的小车从斜度为 的斜坡以匀加速度a滑落下来。其轮与坡面的静磨擦系数为 。求轮与坡面的磨擦力。（a） mmgcosq. （b） mmg. （c） mg（sinq - m）. （d） m（g - a）.（e） mgsinq - ma.2 Refer to the figure, rectangle PQRS represe

5、nts the cross-section of a uniform magnetic field region of 0.20 T. An electron is projected at a speed of v = 2.0 106 m/s into the region at an angle of 30 to the direction of the magnetic field. The length of the magnetic field region is 0.01 m. Find the number of revolutions made by the electron

6、before it leaves the magnetic field region.如图所示。长方型区域PQRS为一0.20 T的均匀磁场的横截面。区域长度为0.01 m。一电子以v = 2.0 106 m/s 的速度和与磁场成 30 的角度射入。求电子离开区域前转的圈数。（a） 28 （b） 16 （c） 9 （d） 6 （e） 323 Two weights, both of mass m, are joined by a weightless spring of natural length l and force constant k. They are placed on a sm

7、ooth surface and at rest. One weight is suddenly given an impulse and acquires an initial velocity v towards the other weight. What is the speed of the center of mass of the weights-spring system?在光滑平面上有两质量均为m的物体，中间由一自然长度为l 、力常数为k的轻弹簧相连。现突然给其中一物体一冲量，使它具有指向另一物体的初速度v。求两物体的共同质心的速度。（a） 0.5v. （b） . （c） .

8、 （d） v. （e） .4 Following the above MC. What is the minimum distance between the two weights?接上题。求两物体间最小距离。（a） . （b） . （d） （e） 5 As shown, a wheel of weight W and radius 0.8 m is placed against a 0.3 m height rectangular block fixed on the ground. The wheel has an axle of radius 0.1 m. A force F is a

9、pplied tangentially to the axle to lift the wheel. The minimum value of F is_.一重量为W 半径为0.8 m的轮子放在0.3 m高的固定方砖前。轮轴的半径为0.1 m。现沿轮轴切向施力F以拉起轮子。求所需最小力。（a） 1.05W （b） 0.86W （c） 0.69W （d） 0.32W（e） 2.45W6 A helicopter is trying to land on a ship deck which is drifting south （unit vector） at 17m/s. A 12m/s wind

10、 is blowing from east （unit vector）. The ship crew sees the helicopter descending at 5 m/s. Take the downwards direction as unit vector. What is its velocity relative to water and air?一直升机要降落在以17m/s向南（单位向量）飘流的船上。此时刮的是风速为12m/s 的东风（单位向量）。船员见到直升机以5 m/s的速度垂直降落下来。取向下方向为单位向量。求直升机相对于水和空气的速度。m/s; m/s（b） （c）

11、 （d） 7 Suppose the force by air to a plane is always perpendicular to its wings surfaces. The plane is moving in a circle of radius R at speed v. The inclination angle of the wings should satisfy _.假设空气对机翼的力总是与机翼面垂直，当飞机以速度v作半径为 R 的圆周运动时，机翼面与水平线的角度应该满足_。 （b） （c） （e） 8 The mass of the sun is_.太阳的质量为_。

12、（a） 2 x 1027 kg （b） 2 x 1028 kg （c） 2 x 1029 kg （d） 2 x 1030 kg （e） 2 x 1031 kg 9 A loudspeaker L is placed in the hall with two doors D1 and D2 open to the playground, as shown below. The distance between D1 and D2 is 8.5 m. The loudspeaker L is at equidistance from D1 and D2. Monotonic sound waves

13、 are emitted from the loudspeaker, and it is found that at point P which is 6.0 m from D1 and at point Q the sound intensities are minimum. The line joining D1, P and Q is perpendicular to the line joining D1 and D2. No other minimum intensity locations can be found between PQ and beyond Q along the

14、 PQ line. Find the frequency of the sound wave generated by the loudspeaker.如图，礼堂里有一扩音器L，离两门D1 和 D2等距，并发出单频声波。两门间距离为8.5 m。门外是操场。在离D1 6.0 m处的P点和Q点发现声波的强度最低。D1PQ联机与D1D2联机垂直。PQ联机上PQ点之间和过了Q点后再无最弱声波点。求声波频率。（a） 17 Hz （b） 41 Hz （c） 52 Hz （d） 116 Hz（e） 123 Hz10 As shown in the figure, a smooth rod is mounte

15、d horizontally on a tabletop. A 10-kg collar, which is able to slide on the rod without friction, is fastened to a spring whose other end is fixed at point-O. The nearest point of the rod to point-O is point-A, and the distance is 20 cm. The spring has a natural length of 10 cm and of negligible mas

16、s, and a spring constant of 500 N/m. The collar is released at 15 cm from point-A. Find its speed when reaching point-A.如图，水平桌面上有一固定的光滑杆，上套一重10-kg的环。一弹簧一端连着环，另一端固定在距离杆20 cm 的O点。弹簧自然长度为10 cm，力常数500 N/m。A点是杆上离O点最近点。现将环拉到离A点15 cm处放开。求环到A点时的速度。（a） 0.59 m/s （b） 0.791 m/s （c） 1.04 m/s （d） 0.88 m/s（e） 1.24

17、 m/s11 As shown, a big box of mass M is resting on a horizontal smooth floor. On the bottom of the box there is a small block of mass m. The block is given an initial speed v0 relative to the floor, and starts to bounce back and forth between the two walls of the box. Find the final speed of the box

18、 when the block has finally come to rest in the box.一质量为M的大盒放在光滑地板上。盒底有一质量为m的物体。现给该物体一初速度v0，使它在盒的两壁来回碰撞。求最后物体在盒里停下后盒的速度。（a） 0 （b） v0 （c） （d） （e） 12 A jet of water from the 30cm-diameter nozzle of a fire hose can reach the maximum height of 25 meters. How large is the force from the water jet to the

19、hose?从直径为30 cm的消防水管射出的水柱最高可达25米。求水柱对水管的力。（a） 15 kN （b） 3.46 kN （c） 346 N （d） 3.46 N（e） 34.6 kN13 As shown in the figure, AB = 3.5 m, AC = 3.0 m, AD = 0.5 m. The two rods AC and BC weight 150 N each. The floor is frictionless. Find the tension in the rope. 如图，AB = 3.5 m, AC = 3.0 m, AD = 0.5 m。杆AC和BC

20、各重150 N。地板与杆间无磨擦。求绳的张力。（a） 280 N （b） 500 N （c） 150 N（d） 300 N （e） 180 N14 9 kg of mercury is poured into a glass U-tube with inner diameter of 1.2 cm. The mercury can flow without friction within the tube. Find the oscillation period. 一内径为1.2 cm 的U型玻璃管里装有9 kg的水银。设水银可无磨擦地在管里流动。求振荡周期。（a） 1.2 s （b） 3.4

21、 s （c） 5.6 s （d） 7.8 s（e） 8.9 s15 A tank contains water on top of mercury. A cube of iron is sitting upright in equilibrium in the liquids. Find the fraction of its total volume in mercury. 一水缸的下部是水银，上部是水。一立方体的铁块正放在液体里。求铁块在水银里的体积与总体积之比。（a） 0.35 （b） 0.53 （c） 0.1 （d） 0.62 （e） 0.7316 The average densit

22、y of Earth is _ x 103 kg/m3.地球的平均密度为_ x 103 kg/m3。（a） 3.1 （b） 2.2 （c） 5.5 （d） 1.1 （e） 4.117 Each of the four cells shown has an emf of 3.0 V and a 0.0075-W internal resistance. Find the current through the 3-W resistor.如图，每个电池的电动势为3.0 V ，内阻为0.0075-W 。求通过3-W 电阻的电流。（a） 0.97 A （b） 0 （c） 1.95 A （d） 0.48

23、 A（e） 3.23 A18 The mass in the figure below slides on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2. The spring constants are k1 and k2 respectively. Find the force pulling back on the ma

24、ss.如图，物块可在光滑平面滑行。现将物块拉出，使弹簧-1拉长了x1 ，弹簧-2拉长了x2。弹簧-1和弹簧-2的力常数分别为k1 和 k2。求弹簧对物块的拉力。. （b） . （c） （e） 19 An empty open bottle has an inner volume of 1.31 x 10-4 m3. It has a mass of 112g when filled with air at 1 atm, and it displaces 1.63 x 10-4 m3 of water when fully submerged. What fraction of the tota

25、l volume of the bottle will be beneath the surface when it floats on water but without water inside the bottle?一开口小瓶的内体积为1.31 x 10-4 m3。装满1个大气压时的总质量为112g。当完全浸在水里时小瓶排开的水体积为1.63 x 10-4 m3。现将小瓶口向上浮在水面上，瓶里无水，求在水面下的体积部分与总体积之比。（a） 69% （b） 18% （c） 38% （d） 100% （e） 46%20 A parallel plate capacitor of capaci

26、tance C is charged to potential V by a battery. The battery is then disconnected. Which statement is correct?一平行板电容器被加上电压V后与电池断开。以下哪个说法是正确的？（a） There is no charge on either plate of the capacitor. 电容器板上无电荷。（b） The capacitor can be discharged by grounding any one of its two plates. 如要电容器放电可将其中任意一板接地。

27、（c） Charge is distributed evenly over both the inner and outer surfaces of the plates. 电荷均匀分布在两板的内外表面上。（d） The magnitude of the electric field outside the space between the plates is approximately zero. 电场在两板间以外的空间几乎为零。（e） The capacitance increases when the distance between the plates increases. 电容器

28、的电容会因板间距离增加而增加。Open Problems开放题Total 6 problems共6题Q1 （8 points）On a smooth and insulating ring of radius R there is a small ring of mass m and carrying charge q. The large ring is placed horizontally and in a uniform magnetic field of strength B0 and perpendicular to the ring plane. Starting from t

29、= 0, the magnetic field is changed to. Find the force of the small ring on the big ring afterwards.题1 （8分）一半径为R的光滑绝缘大圆环上有一质量为 m带电为q的小环。大圆环水平放置，与一强度为B0的均匀恒定磁场垂直。从时间t = 0开始该磁场变为求之后小环对大圆环的力。Q2 （8 points）As shown in the figure, separating two sealed gas chambers is a piston of mass m and area A that can move horizontally without friction. The volume and t