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<image>如图所示，航天飞机 $P$ 开始时沿 $A = B$ 的椭圆轨道绕地球巡航。$P$ 在轨道任一位置均可通过短时间点火喷气来改变速度大小和方向，使其进入圆轨道航行。规定将速度增大简称为“加速”，将速度减小简称为“减速”。试问 $P$ 在图中哪些位置为点火喷气＂加速＂，＂减速＂区域转换点?
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701
<image>A diffraction-limited optical system of image formation includes an aperture diaphragm with diameter $D=30 \text{ mm}$, coinciding with the back principal plane $\text{H}^{\text{'}}$ of the system. Evaluate the resolution R (in lines $/ \text{mm}$) of this optical system in the paraxial domain for the surface of...
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702
<image>如图所示，两列波长为 $\lambda$ 的相干波在点 $P$ 相遇。波在点 $S_{1}$ 振动的初相是 $\varphi_{1}$ ，点 $S_{1}$ 到点 $P$ 的距离是 $r_{1}$ 。波在点 $S_{2}$ 的初相是 $\varphi_{2}$ ，点 $S_{2}$ 到点 $P$ 的距离是 $r_{2}$ 。以 $k$ 代表零或正，负整数，则点 $P$ 是干涉极大的条件为（）
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703
<image>两根等长度的均质梁铰接于 $C$ 点，同时在 $A$ 点和 $B$ 点铰接于支座．每根梁的重量为 $P$ ．重物 $Q$ 挂在 $C$ 点．距离 $A B=d$ ．$C$ 点到水平线 $A B$ 的距离为 $b$ ．求铰链 $A$ 和 $B$ 的反力．
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704
<image>A beaker contains a liquid of mass 120 g. The liquid is supplied with thermal energy at a rate of 810 W. The beaker has a mass of 42 g and a specific heat capacity of $0.84 \mathrm{Jg}^{-1} \mathrm{K}^{-1}$. The beaker and the liquid are in thermal equilibrium with each other at all times and are insulated from ...
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705
<image>相对论的光束角分布变换。惯性系 $S, S^{\text{prime}}$ 间的相对运动关系如图示，点光源 $P$ 静止于 $S^{\text{prime}}$ 系坐标原点 $O^{\text{prime}}$ ，在 $S^{\text{prime}}$ 系的 $O^{\text{prime}} x^{\text{prime}} y^{\text{prime}}$ 平面上各向同性地发射光子，即光子数角密度 $$ \mathrm{d} N^{\text{prime}} / \mathrm{d} \theta^{\text{prime}}=n^{\text{prime}}\left(\theta^{\text{prime}...
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706
<image>如图所示，质量 $m=60 \text{ kg}$ ，半径 $R=0.25 \text{ m}$ 的飞轮以 $n=10^{3} \text{ r} \times \text{min}^{-1}$ 的转速高速运转，如果用闸瓦将其在 5 s 内停止转动，则制动力需要多大？设闸瓦和飞轮间的摩擦系数 $\nmu=0.40$ ，飞轮的质量全部分布在轮缘上。
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707
<image>两根等长杆 $A C$ 和 $B D$ 铰接于 $D$ 点，并分别在 $A$ 点和 $B$ 点用铰链连接于铅垂墙．杆 $A C$ 是水平的，杆 $B D$ 与铅垂墙成 $60^{\circ}$ 角．杆 $A C$ 在 $E$ 点承受铅垂力 $P_{1}=40 \mathrm{~N}$ ，并在 $C$ 点承受与水平线成 $45^{\circ}$ 角的力 $Q=100 \mathrm{~N}$ ．杆 $B D$ 在 $F$ 点承受铅垂力 $P_{2}=40 \mathrm{~N}$ ．已知 $A E=E C, B F=F D$ ．求铰链 $A$ 和 $B$ 的反力．
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708
<image>试计算如图所示线形电四极子在很远处 $ (r\gg l) $ 的电势。
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709
<image>A monatomic ideal gas is the working substance for a refrigerator that undergoes the cyclic process (ABCDA) shown in the PV diagram. The processes are all isochoric or isobaric with pressures between $P_{0}$ and $2 P_{0}$ and volumes between $V_{0}$ and $2 \text{V}_{0}$. What is the coefficient of performance fo...
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710
<image>一振动质点的振动曲线如图所示，试求：从振动开始到达点 $P$ 相应位置所需的时间
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711
<image>An alternating voltage of peak value 150 V is applied across the 1200 turns of the primary coil. The variation with time $t$ of the e.m.f. $E$ induced across the secondary coil is shown in Fig.9.2.\n\nA resistor is connected between the output terminals of the secondary coil. The mean power dissipated in the res...
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712
<image><image>An object is suspended from a vertical spring as shown in Fig. 3.1.\n\nThe object is displaced vertically and then released so that it oscillates, undergoing simple harmonic motion.\n\nFig. 3.2 shows the variation with displacement $x$ of the energy $E$ of the oscillations.\nThe kinetic energy, the potent...
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713
<image>如电图 2.8.1 所示，在水平面上有一根光滑的刚性细长杆，它可以无摩擦地绕固定的坚直轴旋转，转动惯量为 $I$ 。在杆周围有与转轴平行的匀强磁场 $B$ ，其方向如电图 2.8.1 所示。把质量为 $m$ ，电量为 $q(q>0)$ 的光滑带电小圆环套在杆上，设环与杆之间无电荷转移。 若杆的初始角速度改取第 2 问中所给初始角速度的 $\alpha$ 倍 $(\alpha>0)$ 。试问：为使圆环的运动轨道保持不变，应如何改变磁场的大小？
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714
<image>The temperature of the gas at point A is $227^{\circ} \mathrm{C}$. Calculate the number of molecules in the fixed mass of the gas.
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715
<image>如图所示，在内壁光滑，固定直立的圆筒形气缸内，有一个质量可略的活塞 $A$ 紧密地与气缸壁接触，此活塞某处有一小孔，装有只朝下打开的阀门 $\text{K}_{1}$ 。气缸的下部有一个固定的隔板 $C$ 和一个固定在气缸壁上的卡环 $B$ ，隔板 $C$ 的中央有一小孔，装有只能朝下打开的阀门 $\text{K}_{2}$ 。隔板 $C$ 与气缸底部的距离为 $L$ ，卡环 $B$ 到隔板 $C$的距离 $L / 2$ ，活塞 $A$ 能够到达的最高位置在隔板 $C$ 的上方 $4 L$ 处。开始时 $A$ 在最高位置，气缸内 $A$ 到 $C$ 之间以及 $C$ 下方的气体压强与外界大气压强相同，均为 $p_{0}...
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716
<image>The diagram below shows combinations X, Y, and Z of three identical resistors. What is the correct order of the total resistance of the combinations going from lowest resistance to highest resistance?
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717
<image>如电图 3.18.1 所示，在光滑的水平面上，有边长为 $l=0.8 \text{ m}$ 的正方形导线框，其质量 $m=100 \text{ g}$，自感 $L=10^{-3} \text{ V} \cdot \text{s} / \text{A}$，电阻可忽略不计。在 $t=0$ 时，线框右侧 $bc$ 边所在位置刚好是匀强磁场区域的左边界，磁场区域的宽度为 $s=0.2 \text{ m}$，$\boldsymbol{B}$ 的方向垂直纸面（即水平面）向里，$B=0.5 \text{ T}$。如电图 3.18.1 所示，取 $t=0$ 时 $bc$ 边所在位置为坐标原点 $O$，取 $x$ 轴与 $bc$ 边垂直...
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718
<image>在工程上常常用多个弹簧振子的串联来描述一个实际的力学系统（习题 10－30 图所示），例如一列火车是多节车厢挂接在一起，每节车厢可看做是一个弹簧振子。分析由多个振子串联系统的运动是很有意义的工作。为简单起见，试对两个弹簧振子串联的振动作一描述。设两个振子的劲度系数相同均为 $0.5\mathrm{~N}/\mathrm{m}$ ，质量分别为 0.5 kg 和 1 kg ，写出第二个弹簧振子的运动方程。
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719
<image>The figure to the right shows the position-time graph of an object traveling in a straight line, starting out moving to the right (the positive x-direction). At which points is the object moving to the left?
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720
<image>如图所示，利用铰链机构从四面挤压水泥立方块 $M$ ，其中杆 $A B, B C$ 和 $C D$ 分别与正方形 $A B C D$ 的三边重合，杆 $1,2,3,4$ 完全相同，分别沿着正方形的对角线．大小相等，方向相反的一对力 $\boldsymbol{P}$ 分别加在 $A, D$ 两点上．设 $P=50 \mathrm{kN}$ ，求加在立方块的压力 $N_{1}, N_{2}, N_{3}, N_{4}$ 以及杆 $A B, B C$ 和 $C D$ 的内力 $S_{1}, S_{2}, S_{3}$ ．
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721
<image>在半径为 $a$，电荷体密度为 $\rho$ 的均匀带电球内，挖去一个半径为 $b$ 的小球，$OO'=c$，如图所示。试求：$P$ 点的电场强度。$O, ~ O^{\prime}, ~ P, ~ P^{\prime}$ 在一条直线上。
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722
<image>The output voltage $V$ of an a.c. power supply varies sinusoidally with time $t$ as shown in Fig. 7.2. Determine the equation for $V$ in terms of $t$, where $V$ is in volts and $t$ is in seconds.
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723
<image>In a Michelson interferometer with point light source S, having central wavelength \lambda_{0} and width of the spectral contour \Delta \lambda, one of the mirrors ( \mathrm{M}_{2} in the figure) harmonically oscillates with amplitude l_{0} \gg l_{c}, where l_{c} is the length of temporal coherence. The photodet...
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724
<image>A slice of a conducting material has its face $QRLK$ normal to a uniform magnetic field of flux density $B$, as illustrated in Fig. 8.1. Electrons enter the slice travelling perpendicular to face $PQKJ$. For the free electrons moving in the slice: state the direction of the force on an electron due to movement o...
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725
<image>For the change in the gas described above, state the change in internal energy, with the direction of this change.
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726
<image>A mass is connected to the end of a spring and undergoes simple harmonic oscillation. The graph provided shows the position of the mass as measured from the floor as a function of time. What is the period of the mass's oscillation in seconds?
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727
<image>重 9.6 kN 的船被挂在两根吊杆上，船的重量在两杆上平均分配．吊杆 $A B C$ 的末端置于止推轴承 $A$ ，并在 1.8 m 高度处穿过轴承 $B$ ．吊杆的悬伸跨度为 2.4 m ．不计吊杆重量．求它对支点 $A$ 和 $B$ 的压力．
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728
<image>均质杆 $A B$ 长 2 m ，重 $50 \mathrm{~N}, A$ 端揢置在光滑的铅垂墙上，$B$ 端用绳 $B C$ 吊起，绳子另一端 $C$ 固定在墙上．当杆处于平衡时，$\angle B A D=45^{\circ}$ ，求距离 $A C$ ，并求绳子的张力 $T$ 和墙的反力 $R$ ．
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729
<image><image>（1）质量 $M$ 的质点（例如太阳）固定不动，质量 $m$ 的质点（例如小行星）以速度 $v_{0}$ ，瞄准距离 $b$ ，从无穷远处，在 $M$ 的万有引力作用下沿双曲线轨道靠近 $M$ 运动，最后又远离 $M$ 而去，试求图1所示的散射角 $\theta$（即运动方向偏转角 $\theta$ ）。
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730
<image>如图所示，体积为 $V$ 的水银被两块水平玻璃板夹在中间，水银与上，下玻璃间的接触角同为 $\theta=135^{\circ}$ 。已知上方玻璃板质量为 $m$ ，水银表面张力系数为 $\sigma$ ，水银自身重力压强影响可略，试求：平衡时，上下玻璃板之间的距离 $d_{0}$ ；
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731
<image>一根长为 $L$ 的水平粗管与一根竖直细管连接成如热图 3.12.1 所示的形状，把细管下端插入密度为 $\rho_{\mathrm{f}}$ 的液体之中，然后将粗管的管口封住，并使粗管绕细管以恒定的微小角速度 $\omega$ 旋转，已知空气的密度为 $\rho_{\mathrm{a}}$ ，细管的体积与粗管相比可以忽略，毛细现象也可忽略，在温度恒定的条件下，试求细管中液面上升的高度 $h$ 。
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732
<image>A，B 两个物体，质量分别为 $m_{A}=100\,\mathrm{kg}$, $m_{B}=60\,\mathrm{kg}$，装置如图所示，两斜面的倾角分别为 $\alpha=30^{\circ}$ 和 $\beta=60^{\circ}$。如果物体与斜面间无摩擦，滑轮和绳的质量忽略不计，问：系统将向哪边运动？
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733
<image>\n形状如图所示的导线，通有电流 $I$ ，放在与均匀强磁场垂直的平面内，导线所受的磁场力 $F=$ $\n
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734
<image>A thin metal strip is clamped at one end so that it is horizontal. A load of mass $M$ is attached to its free end. The load causes a displacement $s$ of the end of the strip, as shown in Fig. 2.1. The load is displaced vertically and then released. The load oscillates. The variation with the acceleration $a$ of ...
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735
<image>如习题 7－47图所示，$C_{1}=10\,\mu\mathrm{F},\; C_{2}=5.0\,\mu\mathrm{F},\; C_{3}=5.0\,\mu\mathrm{F}$。在 $A,\; B$ 间加上 100 V 的电压，求 $C_{2}$ 上的电荷量。
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736
<image>均质吊梯长 6 m ，重 2.4 kN ，可绕水平轴 $A$ 转动，并在端点 $B$ 用绳索 $B C$ 拉住．吊梯与水平线成 $60^{\circ}$ 角，绳索与水平线成 $75^{\circ}$ 角．有一个重 0.8 kN 的人站在吊梯上距 $B$ 端 2 m的 $D$ 点，求绳索的张力 $T$ 与轴 $A$ 的反力．
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737
<image><image><image>A student uses the apparatus illustrated in Fig. 3.1 to determine a value for the specific latent heat of fusion of ice. The balance reading measures the mass of the beaker and the melted ice (water) in the beaker. The heater is switched on and pieces of ice at $0^{\circ}\mathrm{C}$ are added conti...
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738
<image><image>（2）电量 $Q>0$ 的带电质点（例如重原子核）近似不动，质量 $m$ ，电量 $q>0$ 的带电质点 （例如 $\alpha$ 粒子）以速度 $v_{0}$ ，瞄准距离 $b$ ，从无穷远处（或足够远处）靠近 $Q$ 运动，又在库仑斥力作用下远离 $Q$ 而去，试求图 2 所示的散射角 $\theta$ 。
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739
<image>如图所示，两个平行放置的均匀带电圆环，它们的半径均为 $R$ ，电荷量分别为 $+q$ 和 $-q$ ，其间距离为 $l$ ，且 $l \ll R$ ，以两环的对称中心为坐标原点。试求垂直于环面的 $O x$ 轴上的电势分布。
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740
<image>在天花板下用两根长度同为 $l$ 的轻杆，通过光滑的轻钩链悬挂一质量为 $M$ 的光滑匀质平板，板的中央有一质量为 $m$ 的光滑小球。开始时系统处于静止的水平状态，而后如图所示，使板有一水平方向的小初速度 $v_{0}$，此板便会作小角度摆动。假设摆动过程中细绳始终处于伸直状态，试求板的摆动周期。
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741
<image>飞轮的质量为 60 kg ，直径为 0.50 m ，转速为 $1000 \mathrm{r}/\mathrm{min}$ ，现要求在 5 s内使其制动，求制动力 $F$ 。假定闸瓦与飞轮之间的摩擦因数 $\mu=0.40$ ，飞轮的质量全部分布在轮的外周上。尺寸如图所示。
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742
<image>Two parallel metal plates $A$ and $B$ are situated a distance 1.2 cm apart in a vacuum, as shown in Fig. 6.1. Plate $A$ is earthed and plate $B$ is at a potential of -75 V. A helium nucleus is situated between the plates, a distance $x$ from plate $A$. Initially, the helium nucleus is at rest on plate A where $x...
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743
<image>What is the voltage across resistor $R_{4}$?
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744
<image>In the circuit diagram below, all of the bulbs are identical. Which bulb will be the brightest?
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745
<image>将质量为 $m$ 的小球挂在倾角为 $\theta$ 的光滑斜面上，如图所示。当斜面以加速度 $a$ ，沿如图所示的方向运动时，求绳中的张力。
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746
<image>如图所示，一个半径为 $R$ 的透明材料制成的球，$A B$ 为某一条直径，$A, B$ 两点附近的球表面透光，球表面的其他部分均涂黑而不透光。设在球内 $B$ 处有个小发光泡。 若球的折射率为 $n$ ，像在球的右侧,像的横向放大率为多少？
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747
<image>一带有电荷量为 $4.0 \times 10^{-9}\,\mathrm{C}$ 的粒子，在 $yz$ 平面内沿着和 $Oy$ 轴成 $45^{\circ}$ 角的方向以速度 $v_{1}=3\times10^{6}\,\mathrm{m/s}$ 运动，它受到均匀磁场的作用力 $F_{1}$ 逆 $Ox$ 轴方向；当这个粒子沿 $Ox$ 轴方向以速度 $v_{2}=2\times10^{6}\,\mathrm{m/s}$ 运动时，它受到沿 $Oy$ 轴方向的作用力 $F_{2}=4\times10^{2}\,\mathrm{N}$ 。求磁感应强度的大小（如图所示）。
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748
<image>在半径为 $R$ 的无限长金属圆柱体内部挖去一半径为 $r$ 的无限长圆柱体，两柱体的轴线平行，相距为 $d$ ，今有电流沿空心柱体的轴线方向流动，电流 $I$ 均匀分布在空心柱体的截面上。求圆柱轴线上的磁感应强度的大小。
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749
<image>一定量的乙醇封装在玻璃管内，一部分呈液态，另一部分呈气态，管内无其他杂质。若管内体积恰好为这些乙醇的临界体积，那么在缓慢加热到临界温度时，因气、液两相不再有差别而使液面消失，这就是临界现象的演示实验。假设 1 mol 乙醇的状态方程为 $(p+\frac{a}{V^{2}})(V-b)=RT$，即为范德瓦尔斯方程，如热图 4.3.1 所示。在 $V_{\text{g}} \gg V_{1}$ 的条件下，试用 $a$, $b$, $T$ 来表述 $V_{1}$。
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750
<image>For the figure shown, the variable resistance in the circuit on the left is increased at a constant rate. What direction is the conventional current through the resistor in the right-hand circuit?
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751
<image>A quasi-monochromatic beam of light with mean wavelength $\lambda_{0} \approx 628 \mathrm{~nm}$ is produced by an extended spatially incoherent source $S$ having the shape of a round disc with diameter $D=4 \mathrm{~mm}$. Determine the maximal spacing $\Delta \rho_{c}$ between the points $\mathrm{P}_{1}$ and $\m...
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752
<image>A volume diffraction grating in a transparent layer with thickness $h$ is a periodic structure with refractive index $n(x)=n_{0}+\nabla n \text{cos}(2 \text{pi} x / \nabla)$, varying periodically along the coordinate $x$ and independent of $y$ and $z$. In the figure, the maxima of the refractive index are shown ...
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753
<image>Electrons flow to the left in a wire as shown. For the proton moving toward the top of the page at the instant shown, what is the direction of the magnetic force on the proton?
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754
<image>在 $20\,\mathrm{cm}\times20\,\mathrm{cm}$ 的荧光屏上的李萨如图形，如图所示。已知水平方向（$x$ 方向）的振动为 $50\,\mathrm{Hz}$, $t=0$ 时的光点位于左下角。试写出 $y$ 方向的谐振动方程。
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755
<image>$N$ 个一阶正离子与 $N$ 个一阶负离子静止地在一条直线上等间距交错排列，相邻间距为 $a$，图中字母 $e$ 代表电子电量绝对值， 当 $N$ 足够大时，每一个离子所具有的电势能均可近似处理为(1)、(2)所得的 $W_{+}$或 $W_{-}$，试求全系统所具有的电势能 $W$
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756
<image>For the bar magnet shown in the figure, what is the direction of the magnetic field at the point P located directly above the center of the magnet?
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757
<image>Determine frequency $f_{s}$ of an alternating electric signal applied to the piezoelectric transducer of an acousto-optical cell if the laser beam diffracted by the acoustic wave in the cell is observed propagating at an angle $\alpha=6 \mathrm{deg}$ with respect to the direction of the laser beam incident on th...
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758
<image>A heater supplies energy at a constant rate to 0.045 kg of a substance. The variation with time of the temperature of the substance is shown in Fig. 3.1. The substance is perfectly insulated from its surroundings. Determine the temperature at which the substance melts.
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759
<image>说明了在实验室中用亥姆霍兹线圈能产生均匀磁场的原理．写出线圈轴线上各点磁感应强度 $B$ 的变化率函数；（设线圈半径 $R=0.2\,\mathrm{m}$ ，线圈匝数 $N=1000$ 以及电流 $I=1\,\mathrm{A}$ ）
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760
<image>一质点的质量为 $1\,\mathrm{kg}$ ，沿 $Ox$ 轴运动，所受的力如图所示。$t=0$ 时，质点静止在坐标原点，试求此质点第 7 s 末的坐标。
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761
<image>如力图3．25．1 所示，台阶每级的宽和高均为 $l$ 。一小球向下逐级弹跳，每次反弹后，相对本级达到的最高高度均为 $H$ ，每次的下落点均在各级的同一地点，已知小球与台阶碰撞时的恢复系数为 $e$ ，忽略空气阻力，试求：小球的水平速度。
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762
<image>\n一质量为 $m$ 的小球在高度 $h$ 处以初速度 $v_{0}$ 水平抛出，求：落地前瞬时小球的 $\frac{\text{d} \boldsymbol{r}}{\text{d} t}, \frac{\text{d} v}{\text{d} t}, \frac{\text{d} v}{\text{d} t}$ 。
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763
<image>已知太阳质量为 $M$ ，小行星 $Q$ 与太阳相距 $r_{0}$ 时速度 $v_{0}$ 的方向如图所示，若 $Q$ 的轨道是抛物线，试求 $Q$ 在运动过程中的最大速度 $v_{\text {max }}$ 。
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764
<image>Two point charges $A$ and $B$ are separated by a distance of 12.0 cm in a vacuum, as illustrated in Fig. 5.1. The charge of $A$ is $+2.0 \times 10^{-9} \mathrm{C}$. A point $P$ lies on the line joining charges $A$ and $B$. Its distance from charge $A$ is $x$. The variation with distance $x$ of the electric poten...
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765
<image>Light of wavelength 600 nm is transmitted from air into a piece of glass. Which labeled arrow indicates the path of the light ray after it enters the glass?
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766
<image>In the circuit shown, the voltage source, switch, capacitor, and connecting wires have no resistance. The switch is closed until the circuit achieves steady state, at which point the switch is opened. What is the potential differences across the resistor and capacitor after the switch is opened?
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767
<image>机械手操纵器的机构是一个较接三杆机构，所有杆都在铅垂平面内转动．问：为使机构中所有杆都维持水平，在铰链 $A$ 和 $B$ 中必须施加多大的力矩？操纵对象的质量 $m_{C}=15 \mathrm{~kg}$ ，杆长 $l_{1}=0.7 \mathrm{~m}, l_{2}=0.5 \mathrm{~m}$ ．所有杆都是均质的，质量分别为 $m_{1}=35 \mathrm{~kg}, m_{2}=25 \mathrm{~kg}$.
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768
<image>如图所示，两个平行放置的均匀带电圆环，它们的半径均为 $R$ ，电荷量分别为 $+q$ 和 $-q$ ，其间距离为 $l$ ，且 $l \ll R$ ，以两环的对称中心为坐标原点。求 $O x$ 轴上远处（即 $x \gg R$）的电场强度分布。
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769
<image><image>在海洋中，声波的速度随深度、温度和含盐量变化。已知声速随深度变化的规律如力图7.35.1所示，最小声速$v_{0}$出现在海洋表面和海底之间，以最小声速作为坐标原点，$z_{s}$和$z_{b}$分别表示海洋表面和海底的坐标，则声速$v$与$z$的关系为 $$ v=\left\{ \begin{array}{ll} v_{0}+b z, & z>0 \\ v_{0}, & z=0 \\ v_{0}-b z, & z<0 \end{array} \right. $$ 式中：$b$为正的常量。 如力图所示，现在在$x=0, z=0$处放置一声源$S$，在$zx$平面内，从$S$发出的声波的传播方向用初始发射...
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770
<image>如热图 2.14.1 所示，潮湿空气绝热地持续流过山脉。气象站 $M_{0}$ 和 $M_{3}$ 测出的大气压都是 100 kPa，气象站 $M_{2}$ 测出的大气压强为 70 kPa。在 $M_{0}$ 处，空气的温度是 $20{ }^{\text{°} }\text{C}$，随着空气的上升，在压强为 84.5 kPa 的高度处（图中 $M_{1}$ ）开始有云形成。空气由此继续上升，经过 1500 s 之后到达山顶的 $M_{2}$ 站。在上升过程中，空气里的水蒸气凝结成雨落下，设每平方米上空潮湿空气的质量为 2000 kg，每千克潮湿空气中凝结出 2.45 g 的雨水，试问：在山脉背面的气象站 $M_{3}$...
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771
<image>均质杆 $A B$ ，长 1 m ，重 20 N ，水平悬挂在平行绳子 $A C$ 和 $B D$ 上．在杆上距离 $A E=\frac{1}{4} \mathrm{~m}$ 处的 $E$ 点挂着重物 $P=120 \mathrm{~N}$ ．求绳子的张力 $T_{C}$ 和 $T_{D}$ ．
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772
<image>如电图2.12.1所示，在半径为$R$的圆筒形真空管中有两个隔板，将管内分为三个区域。两隔板中心各有小孔A和$A'$，两孔间距为$L$。区域I中有加速电场，区域II中有沿管轴方向的匀强磁场$B$，区域III中无电磁场。阴极$K$发射的电子经加速后，穿过小孔A的电子速度在管轴方向的分量为$v$（电子间相互作用可忽略）。当区域II的磁感应强度调至特定值$B_0$时，电子可穿过小孔$A'$射出。取$A\to A'$为正方向，磁场$B$随时间$t$的变化如电图2.12.2所示：从$t=0$起$B$沿正方向，每经$T/2$时间反向一次，$T$为变化周期。电子束从$t=0$开始连续进入区域II，遇管壁的电子被吸收。试求能使电子到达...
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773
<image>An isolated spherical conductor has charge $q$, as shown in Fig. 6.1. Point $P$ is a movable point that, at any one time, is a distance $x$ from the centre of the sphere. The variation with distance $x$ of the electric potential $V$ at point $P$ due to the charge on the sphere is shown in Fig. 6.2. Use Fig. 6.2 ...
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774
<image><image><image> 对下述三个与静电镜像相关的系统，试用两种方法计算沿无穷远路径线外力 $F$ 无限缓慢地作用时的作功能量 $A$。方法 1：$A$ 等于系统电势能增量；方法 2：$A$ 等于元功 $\boldsymbol{F} \cdot \mathrm{dr}$ 积分量。系统如图 3 所示，其中 $Q$ 为均匀带电球面电量，$Q^{\prime}=-Q$ 为球面均匀分布的镜像电荷。
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775
<image>在半径为 $a$，电荷体密度为 $\rho$ 的均匀带电球内，挖去一个半径为 $b$ 的小球，$OO'=c$，如图所示。试求：$O$ 点的电场强度。$O, ~ O^{\prime}, ~ P, ~ P^{\prime}$ 在一条直线上。
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776
<image>Interference fringes of equal inclination are observed in focal plane P of focusing lens L due to the reflection from a planeparallel glass plate (GP) illuminated by monochromatic light source $S$ with the help of an oblique glass plate functioning as a beam splitter (BS). The wavelength of light is $\lambda_{0}...
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777
<image><image>A pendulum consists of a bob (small metal sphere) attached to the end of a piece of string. The other end of the string is attached to a fixed point. The bob oscillates with small oscillations about its equilibrium position, as shown in Fig. 4.1. The length $L$ of the pendulum, measured from the fixed poi...
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778
<image><image><image>Two coils of insulated wire are wound on an iron bar, as shown in Fig. 8.1. There is a current $I_{1}$ in coil 1 that varies with time $t$ as shown in Fig. 8.2. The variation with $t$ of $I_{1}$ can be represented by the equation $I_{1}=X\sin Yt$ where $X$ and $Y$ are constants. Use Fig. 8.2 to det...
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779
<image>在如电图 5.4.1 所示的电路中，适当选择电阻 $R_{1}, R_{2}, R_{3}, R_{4}$ 和电感 $L_{1}, L_{2}$ ，使得无论电源的电动势 $\mathscr{E}$ 是否随时间 $t$ 变化，都没有电流通过电流计 M ，设上述条件得到满足，并已知 $R_{2}=90 \Omega, R_{3}=300 \Omega, R_{4}=60 \Omega, L_{2}=900 \mathrm{mH}$ 。试求$L_{1}$ 。
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780
<image>一滑轮两边分别挂着 A 和 B 两物体，它们的质量分别为 $m_{\mathrm{A}}=20\,\mathrm{kg}$，$m_{\mathrm{B}}=10\,\mathrm{kg}$，今用力 $F$ 将滑轮提起，如图所示。当 $F=98\,\mathrm{N}$ 时，求物体 A 的加速度（滑轮的质量与摩擦不计）。
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781
<image>设电势沿 $O x$ 轴的变化曲线如图所示。试对所示 c-e 区间的电势分布（忽略区间端点的情况）确定电场强度的 $x$ 分量。
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782
<image>In the inertial frame $ S $, on the $ Oxy $ plane, there is a thin rod $ AB $ forming an angle $ \phi $ with the $ x $-axis and moving uniformly along the $ x $-axis at a high speed $ v $. It is known that when $ \phi = 30^\circ $, the length of the rod $ AB $ measured in the $ S $ frame is $ l_1 $. Still using ...
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783
<image>如力图 1.11 .1 所示，质点 $A$ 和质点 $B$ 同时从 $A, B$ 两点出发，分别以速度 $\boldsymbol{v}_{1}$沿 $A B$ 和以速度 $\boldsymbol{v}_{2}$ 沿 $B C$ 做匀速直线运动，$B C$ 和 $A B$ 的夹角为 $\alpha$ ，开始时质点 $A$ 和质点 $B$相距 $l$ ，试求两质点之间的最短距离，
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784
<image>压强为 $p_{0}$ ，温度为 $T_{0}(k)$ 的空气（设空气分子质量为 $m$ ，每个分子热运动的平均动能为 $\frac{5}{2} k T_{0}$ ）以 $v_{0}$ 速度流过一横截面积为 $S$ 的粗细相同的光滑导管，导管中有一个对气流的阻力可忽略的金属丝网，它被输出功率为 $P$ 的电源加热，因而气流变热。达稳定状态后空气在导管末端流出时的速度为 $v_{1}$ ，如图所示，试求空气受到的推力 $F$ 。
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785
<image>A heater supplies energy at a constant rate to 0.045 kg of a substance. The variation with time of the temperature of the substance is shown in Fig. 3.1. The substance is perfectly insulated from its surroundings. The power of the heater is 150 W. Use data from Fig. 3.1 to calculate, in $\mathrm{kJ} \mathrm{kg}^...
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786
<image>Two capacitors $P$ and $Q$, each of capacitance $C$, are connected in series with a battery of e.m.f. 9.0 V, as shown in Fig. 6.1. A switch S is used to connect either a third capacitor T, also of capacitance $C$, or a resistor R, in parallel with capacitor $P$. Switch S is in position X. Calculate the potential...
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787
<image>如图所示，质量为 $M$ ，宽度为 $d$ 的木块静放在光滑水平地面上，与一端固定在墙上，劲度系数为 $k$ 且处于自由长度状态的轻弹簧相连。一质量可略，质量为 $m$ 的子弹以 $v_{0}$ 速度水平射向木块，在穿透木块的过程中，受到木块的摩擦阻力恒为常量 $F$ 。木块第一次朝右运动过程中其速度会有一个极大值，不同的初速度 $v_{0}$ 对应的此极大值不尽相同，试找出这些极大值中的最大者 $v_{\text{max}}$ ，已知在子弹穿透木块过程中，木块的质量不因子弹的打击而变化且有 $k d \geqslant 2 F$ ， $m / M \geqslant 5 / 4$.
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788
<image><image>Two point charges $A$ and $B$ are situated a distance 10.0 cm apart in a vacuum, as illustrated in Fig. 6.1. A point $P$ lies on the line joining the charges $A$ and $B$. Point $P$ is a distance $x$ from $A$. The variation with distance $x$ of the electric field strength $E$ at point $P$ is shown in Fig. ...
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789
<image>梁 $A B$ 长 $l$ ，承受分布载荷，如图所示．载荷集度在梁的 $A$ 端和 $B$ 端为 $q$ ，在梁的中点为 $2 q$ ．不计梁的重量，求支座 $D$ 和 $B$ 的反力．
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790
<image>厚玻璃块上方镀有双层增透膜，参量如图示，且有 $n_{0}<n_{1}<n_{2}>n_{3}$ 。以波长为 $\lambda$ 的单色光垂直入射到增透膜上，设三束反射光（只考虑一次反射）$a, b, c$ 在空气中的振幅相等，欲使这三束光相干叠加后的总强度为零，则第一层膜的最小厚度 $d_{1}$ 和第二层膜的最小厚度 $d_{2}$ 各为何值？
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791
<image>一绝热容器，中间由一无摩擦的绝热的可活动的活塞隔开，如图所示。$A, ~B$ 两部分各储有 $0.05\,m^{3}$ 的双原子分子理想气体，最初的压强都是 $1.0\times10^{5}\,Pa$ ，温度都是 $0^{\circ}C$ 。现在 A 中缓慢加热，直至 B 中的气体压缩到 $2.5\times10^{5}\,Pa$ 。试问：A 种气体在整个过程中吸收的热量是多少？
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792
<image>在两条平行长直载流输电导线的平面内，有一矩形线圈，如图所示。如两导线中电流同为 $I=I_{0} \sin \omega t$ ，但方向相反。试计算线圈中的感生电动势。
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793
<image>一射电望远镜的天线设在湖岸上，距湖面高度为 $h$，对岸地平线上方有一恒星刚在升起，恒星发出波长为 $\lambda$ 的电磁波，如图所示。试求当天线测得第一级干涉极大时恒星所在的角位置 $\theta$（提示：作为劳埃德镜干涉分析）。
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794
<image>有 25 mol 的某种单原子气体，作图所示的循环过程，其中 $ac$ 为等温过程。$p_{1}=4.15\times10^{5}\mathrm{~Pa}, V_{1}=2.0\times10^{-2}\mathrm{~m}^{3}$，$V_{2}=3.0\times10^{-2}\mathrm{~m}^{3}$。求循环的效率。
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795
<image>Electrons enter a rectangular slice PQRSEFGH of a semiconductor material at right-angles to face PQFE. A uniform magnetic field of flux density $B$ is directed into the slice at right-angles to face PQRS. The electrons each have charge $-q$ and drift speed $v$ in the slice. State the magnitude and the direction ...
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796
<image>如热图2.18.1所示，在$p-V$平面上用实线画出了$C_{V}$为常量的某理想气体的几条准静态过程线，其中两条实曲线是绝热过程，三条实直线是直线过程，其延长线交于原点$O$。试比较$\eta_{12431}$（循环过程12431的效率，余同）与$\eta_{12651}$的大小。
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797
<image><image>A metal plate is made to vibrate vertically by means of an oscillator, as shown in Fig. 2.1. Some sand is sprinkled on to the plate. The variation with displacement $y$ of the acceleration $a$ of the sand on the plate is shown in Fig. 2.2. Calculate the frequency of oscillation of the sand.
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798
<image>利用凸透镜，凹透镜组合方法测量凹透镜焦距的实验装置如图所示。图中 $L_{A}$ 为凸透镜，$L_{B}$ 为凹透镜，两者主光轴重合。高 1 cm 的物 $P$ 与 $L_{A}$ 相距 $20 \text{ cm}, L_{B}$ 右侧垂直于主光轴的屏幕移至与 $L_{B}$ 相距 30 cm 的 $M_{1}$ 处时，屏幕上出现高为 3 cm 的实像。取走 $L_{B}$ ，将屏幕从 $M_{1}$ 位置左移 10 cm 到达图中 $M_{2}$ 位置时，屏幕上又出现实像。由上述实验数据先算出 $f_{B}$ ，再算出 $f_{A}$ 。
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799
<image>一实验装置如图所示，一块平板玻璃片上放一油滴．当油滴展开成油膜时，在单色平行光（波光 $\lambda=600 \mathrm{~nm}$）垂直照射下，从反射光中观察油膜所形成的干涉条纹（用读数显微镜观察），已知玻璃的折射率 $n_{1}=1.50$ ，油膜的折射率 $n_{2}=1.20$ 。当油膜中心最高点与玻璃片的上表面相距 $h=1.2\mu\mathrm{~m}$ 时，明条纹所在处的油膜的厚度是多少？
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