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<image>Fig. 7.1 shows an op-amp circuit that uses negative feedback. Determine the value of $V_{\text{OUT}}$ when $V_{\text{IN}}$ is -5.4 V.
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601
<image>The light from an extended light source $S$ with wavelength $\\lambda_{0}=0.6 \\mu \\mathrm{~m}$ is incident on an optical wedge with small angle \\alpha=10^{-2} rad and refractive index \\n=1.5, and is reflected from the wedge faces. The incidence can be considered normal. Determine the period \\Lambda of the i...
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602
<image>如图所示，$AB=2l$, $OCD$ 是以 $B$ 为中心，$l$ 为半径的半圆，$A$ 点处有正电荷 $+q$, $B$ 点处有负电荷 $-q$，求：把单位正电荷从 $D$ 点沿 $AB$ 的延长线移到无穷远处，电场力对它做了多少功？
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603
<image><image><image>An object is suspended from a spring that is attached to a fixed point as shown in Fig. 3.1. The object oscillates vertically with simple harmonic motion about its equilibrium position. The variation with displacement $x$ from the equilibrium position of the velocity $v$ of the object is shown in F...
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604
<image>A sample of radioactive material contains atoms of an unstable nuclide $X$. The activity of the sample due to the atoms of $X$ is $A$. The variation with time $t$ of $\ln A$ is shown in Fig. 12.1. Use Fig. 12.1 to determine the half-life, in minutes, of nuclide $X$.
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605
<image>The exit face of the waveguide strip of a semiconductor laser has a rectangular shape with dimensions $a=3 \, \mu \mathrm{~m}$ and $b=8 \, \mu \mathrm{~m}$. Determine the maximal $\alpha_{x}$ and the minimal $\alpha_{y}$ divergence angles of the laser beam in the corresponding directions $x$ and $y$ if the wavel...
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606
<image>A student designs the circuit shown in Fig. 8.1 in order to indicate changes in temperature of the thermistor T. At a temperature of $13^{\circ} \mathrm{C}$, the resistance of the thermistor T is $230\,\mathrm{k}\Omega$. Calculate the potential difference measured with the voltmeter.
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607
<image>Consider the motion of an object given by the position vs. time graph shown. At what time is the speed of the object greatest?
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608
<image>质量均为 $m$ 的小球 $1, ~ 2$ 用长 $4 a$ 的柔软轻细线相连，同以速度 $v$沿着与线垂直的方向在光滑水平面上运动，线处于伸直状态。在运动过程中，线上距离小球 1 为 $a$ 处与固定在水平面上的竖直光滑细钉相遇，如图所示。设在以后的运动过程中两球不相碰，试求：小球 1 与钉的最大距离（给出 4 位有效数字）；
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609
<image>如图所示，均匀带电直线 $A B$ 长为 $l$，电荷线密度为 $\lambda$。求：在 $A B$ 的垂直平分线上与直线中点相距 $d$ 处的 $Q$ 点的电场强度。
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610
<image>如图所示，$S_{1}$ 和 $S_{2}$ 是两个相干光源，它们到 $P$ 点的距离分别为 $r_{1}$ 和 $r_{2}$。路径 $S_{1} P$ 垂直穿过一块厚度为 $t_{1}$，折射率为 $n_{1}$ 的介质板，路径 $S_{2} P$ 垂直穿过厚度为 $t_{2}$，折射率为 $n_{2}$ 的另一介质板，其余部分可看作真空。这两条路径的光程差是多少？
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611
<image><image>A model of a limb consists of soft tissue and bone, as illustrated in Fig. 11.1. The soft tissue has a thickness of 9.0 cm. The bone within the soft tissue has a thickness of 3.0 cm. Data for the linear attenuation (absorption) coefficient $\mu$ of X-rays in soft tissue and in bone are shown in Table 11.1...
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612
<image>如热图1.16.1所示，竖直石英管内有： 下方空气柱长度$2l_0$，上方可分解双原子分子气体长度$l_0$。气体分解规律满足$\frac{\Delta n}{n_0}=\frac{\Delta T}{T_0}$（$\Delta T\ll T_0$）。初始水银柱压强为$\alpha$倍空气压强（$0<\alpha<1$）。当温度$T$从$T_0$稍增加时，试判断水银柱运动方向（上升/下降）。
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613
<image>如图所示，质量为 0.01 kg 的子弹，以 $500 \mathrm{~m} / \mathrm{s}$ 的速度射入并嵌在木块中，同时使弹簧压缩并作简谐振动，设木块的质量为 4.99 kg ，弹簧的劲度系数为 $8.0 \times 10^{3} \mathrm{~N} / \mathrm{m}$ ，若以弹簧原长时物体所在处为坐标原点，向右为正方向，子弹和木块一起开始运动时刻为计时起点，求简谐振动方程。
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614
<image>A light source $S$ moves with velocity $|\vec{v}|=30 \mathrm{~km} / \mathrm{s}$ in a direction, forming an angle $\theta=45 \mathrm{deg}$ with the direction pointing at the photodetector PD. Determine the shift of the wavelength $\Delta \lambda$ of light received by the light detector with respect to the wavelen...
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615
<image>如图所示，两根无限长载流直导线相互平行，通过的电流分别为 $I_{1}$ 和 $I_{2}$ ，则 $\\oint_{L_{1}} \boldsymbol{B} \\cdot \\mathrm{d} \\boldsymbol{l}=\\oint_{L_{2}} \boldsymbol{B} \\cdot \\mathrm{d} \\boldsymbol{l}$
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616
<image>惯性系 $S, S^{\text{prime}}$ 间相对关系如图所示，其间相对速度 $v=0.6 c$ ，当 $O, O^{\text{prime}}$ 重合时 $t=t^{\text{prime}}=0$。质点 $P_{1}, P_{2}$ 开始时分别静止于 $S^{\text{prime}}$ 系 $x_{10}^{\text{prime}}=0, x_{20}^{\text{prime}}=L_{0}=0.6 c \times \text{~s}$ 处。设 $P_{1}, P_{2}$ 于 $t^{\text{prime}}=0$ 开始，同时以 $a_{0}=0.8 c / \text{s}$沿 $x^{\te...
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617
<image>如图所示，一长为 $l$ 的细长直杆，水平放置，杆上均匀带电，电荷量为 $q$ 。试求在杆的延长线上任意一点的电势。
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618
<image>单斜屋顶梁由梁木 $A B$ 构成，上端 $B$ 自由地揢在光滑的支座上，下端 $A$ 固定在墙上．屋顶斜度 $\tan \alpha=0.5 . A B$ 梁中部承受铅垂负荷 9 kN ，求 $A$ 点和 $B$ 点的支座反力．
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619
<image>A small object is placed in front of a concave mirror and to the left of the center of curvature at point $P$ in the picture. As the object is moved from point $P$ to point Q, how does the size of the image produced change?
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620
<image><image>In a strain gauge, the increase in resistance $\Delta R$ depends on the increase in length $\Delta L$. The variation of $\Delta R$ with $\Delta L$ is shown in Fig.7.1. The strain gauge is connected into a circuit incorporating an ideal operational amplifier (op-amp), as shown in Fig.7.2. The strain gauge ...
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621
<image>A fixed mass of an ideal gas has volume $2.40 \times 10^{3} \;\mathrm{cm}^{3}$ at pressure $3.51 \times 10^{5} \;\mathrm{Pa}$ and temperature 290 K. The gas is heated at constant volume until the temperature is 310 K at pressure $3.75 \times 10^{5} \;\mathrm{Pa}$. The quantity of thermal energy required to raise...
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<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：在山顶 $M_{2}$ 处测出的温...
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623
<image>A beam of linearly polarized light with intensity $I_{i}$ is passed through a linear polarizer P and then through a Wollaston prism. The linear polarizer rotates in its own plane with angular velocity $\\Omega$. Derive the equations describing the time dependence of the intensity of the ordinary $I_{o}(t)$ and e...
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624
<image>Particles having mass $m$ and charge $+1.6 \times 10^{-19} \mathrm{C}$ pass through a velocity selector. They then enter a region of uniform magnetic field of magnetic flux density 94 mT with speed $3.4 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}$, as shown in Fig. 8.1. The direction of the uniform magnetic field...
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625
<image>路灯距地面的高度为 $h$，一个身高为 $l$ 的人在路上匀速运动，速度为 $v_{0}$，如图所示，求影子长度增长的速率
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626
<image>Estimate the coherence time $\tau_{c}$ of an optical field whose spectral contour $G(\omega)$ in the circular frequency scale $\omega$ has the width $\Delta \omega \approx 2 \pi \cdot 0.05 \cdot 10^{14} \mathrm{~Hz}$ at the half-maximum value of the spectral density.
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627
<image>定体摩尔热容量 $C_{V}$ 为常量的某理想气体，经历如热图 2.17.1 所示的 $p$-$V$ 平面上的两个循环过程 $A_{1} B_{1} C_{1} A_{1}$ 和 $A_{2} B_{2} C_{2} A_{2}$，相应的效率分别为 $\nu_{1}$ 和 $\nu_{2}$。试比较 $\nu_{1}$ 与 $\nu_{2}$ 的大小（用不等式或等式表示）。
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628
<image><image>A square coil of wire of side length 12 cm consists of 8 insulated turns. The coil is stationary in a uniform magnetic field. The plane of the coil is perpendicular to the magnetic field, as shown in Fig. 6.1. The flux density $B$ of the magnetic field varies with time $t$ as shown in Fig. 6.2. Calculate ...
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629
<image><image>A sphere of mass $1.6\times10^{-10}\,\mathrm{kg}$ has a charge of +0.27 nC. The sphere is in a uniform electric field that acts vertically upwards, and the force exerted on the sphere by the electric field causes the sphere to remain at a fixed vertical height in a horizontal plane. There is a uniform mag...
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630
<image>A laser beam with wavelength $\lambda_{0}=0.63 \mu \mathrm{~m}$ is diffracted by a traveling acoustic wave propagating in quartz with velocity $v_{a}=5960 \mathrm{~m} / \mathrm{s}$. The alternating voltage $\tilde{U}$ applied to the piezoelectric transducer exciting the acoustic wave has frequency $f=40 \mathrm{...
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631
<image>A photosensitive layer with refractive index $n=1.5$ is coating a metallic mirror M, on which a collimated laser beam with the wavelength $\\lambda_{0}=633 \\mathrm{~nm}$ is incident at the angle \\alpha_{0}=45 \\mathrm{deg}$. Determine the separation \\Lambda between the antinodes of the standing wave produced ...
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632
<image>单原子分子理想气体的两个循环过程 $A D C A$ 和 $A C B A$ 如图所示，其中 $A C$ 是绝热线， $D$ 态温度是 $B$ 态温度的 16 倍。试求 $\eta_{A D C A}$ ：$\eta_{A C B A}$ 值，答案用纯数表示。
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633
<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 1 所示，其中 $Q^{\prime}=-Q$ 为镜像电荷。
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634
<image>What is the instantaneous acceleration of an object moving along a straight line at the time of $t=5.0 \text{ s}$, given the velocity vs. time graph?
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635
<image><image><image>A capacitor of capacitance $C$ and a resistor of resistance $R$ are connected as shown in Fig. 6.1. Initially, the capacitor is charged and the switch is open. The switch is closed at time $t=0$. Fig. 6.2 and Fig. 6.3 show, respectively, the variations with $t$ of the charge $Q$ on the capacitor an...
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636
<image>摩尔质量为 $\mu$，等体比热为 $c_{V}$（$c_{V}$ 为常量）的理想气体所经历的 $x$ 过程如热图 2.2.1 所示。若在此 $p-V$ 坐标面上，把上述 $x$ 过程向下平移 $p_{0}$（$p_{0}>0$），则所得之曲线刚好是该理想气体温度为 $T_{0}$ 的等温过程，试确定 $x$ 过程中的温度下限，并说明该温度在 $x$ 过程曲线的哪个部分。
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637
<image>移动式起重机（不带平衡锤时）重 $P_{1}=500 \mathrm{kN}$ ，重心位于 $C$ 点，与右轨所在铅垂面相距 1.5 m ．起重机跑车按吊起载荷 $P_{2}=$ 250 kN 设计，悬伸跨度为 10 m ．起重机跑车处于任何位置时，不论是满载或是空载，均不翻倒．求平衡锤的最小重量 $Q$ ，以及平衡锤重心到左轨所在铅垂面的最大距离 $x$ ．不计跑车重量．
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638
<image><image>In an experiment, electromagnetic radiation of frequency $f$ is incident on a metal surface. The results in Fig. 10.1 show the variation with frequency $f$ of the maximum kinetic energy $E_{\text {MAX }}$ of electrons emitted from the surface. Determine the work function energy in J of the metal used in t...
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639
<image>如力图 1.14.1 所示，轮子在水平面上以角速度 $\omega$ 做纯滚动，已知轮子的质心速度为 $v_{\mathrm{c}}$ ，试求轮边缘上任一一点 $A$ 的绝对速度，$A$ 点的位置用 $\theta$ 角表示。
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640
<image>求连续梁的支座 $A, B, C$ 和铰链 $D$ 的反力．梁与载荷如图所示．
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641
<image>Two concentric spheres of radii $a$ and $b$, with $b>a$, are separated by a material with conductivity $\sigma(r)=k r$, where $k$ is a constant with appropriate units. Find the resistance of the material if the potential between the spheres is $V$.
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642
<image>如图所示，一个质量为 $m$ 的小球从内壁为半球形的容器边缘点 $A$ 滑下。设容器质量为 $m^{\prime}$ ，半径为 $R$ ，内壁光滑，并放置在摩擦可以忽略的水平桌面上。开始时小球和容器都处于静止状态。当小球沿内壁滑到容器底部的点 $B$ 时，受到向上的支持力为多大？
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643
<image>In which Region is there a place on the x-axis (aside from infinity) at which the electric field is equal to zero?
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644
<image>A position vs. time graph of a particle moving along a horizontal axis is shown. What is the total distance traveled by the particle from $t=0 \text{ s}$ to $t=10 \text{ s}$?
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645
<image>如图所示为一理想气体循环过程，其中 $a b, c d$ 为绝热过程，$b c$ 为等压过程，$d a$ 为等体过程，已知 $T_{a}, ~ T_{b}, ~ T_{c}$ 和 $T_{d}$ 以及气体的热容比 $\\gamma$ ，求循环效率。
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646
<image>What is the voltage drop across $\text{R}_{5}$?
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647
<image>有一长方形木块，切成如图所示的两块，其质量分别为 $m_{1}$ 和 $m_{2}$，两木块靠在一起平放在桌面上，以水平力 $\boldsymbol{F}$ 推动木块 1，所有摩擦均不计。求：$\boldsymbol{F}$ 为多大时，木块 2 开始上滑？
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648
<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， 设 $N \rightarrow \infty$ ，试求其中一个负离子因受所有其余离子的电作用而具有的电势能 $W_{-}$
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649
<image>梁 $A B$ 长 4 m ，重 2 kN ，可绕水平轴 $A$ 转动，$B$ 端据在另一梁 $C D$ 上，梁 $C D$ 长 3 m ，重 1.6 kN ，在 $E$ 点支撑，用较链 $D$ 与墙连接．在 $M$ 点和 $N$ 点各有 0.8 kN 的重物．图中 $A M=3 \mathrm{~m}, E D=2 \mathrm{~m}, N D=1 \mathrm{~m}$ ．求支座反力．
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650
<image><image>Two point charges $A$ and $B$ are situated a distance 15 cm apart in a vacuum, as illustrated in Fig. 5.1. Point $P$ lies on the line joining the charges and is a distance $x$ from charge $A$. The variation with distance $x$ of the electric field strength $E$ at point $P$ is shown in Fig. 5.2. Use Fig. 5....
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651
<image>For the circuit shown, all wires have no resistance, the battery has a constant internal resistance of $r=8.0 \, \Omega$ and the two light bulbs (#1 and #2) are identical, each with resistance $R_{\text{bulb}}$. The variable resistor is initially set to $R=26.0 \, \Omega$. The switch $S$ in the circuit now is cl...
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652
<image>如电图 2.9.1 所示，半径为 $R$ ，质量为 $m$ 的匀质细圆环上均匀地分布着相对圆环固定不动的正电荷，总电量为 $Q \cdot t=0$ 时，圆环在水平地面上具有沿正东方向的平动速度 $\boldsymbol{v}_{0}$ ，且无滚动。假设圆环与地面之间的摩擦系数为 $\mu$ ，在圆环周围只有沿水平面指向北方（电图2.9.1 中垂直纸面向里为北方）的匀强地磁场 $B$ 。 若 $v_{0}$ 在第 1 问的取值范围内，假设圆环最后能达到纯滚状态，试导出在达到纯滚前，圆环的平动速度 $v$ 与时间 $t$的关系。
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653
<image>The diagram below shows the path taken by a monochromatic light ray traveling through three media. The symbols $v_{1}, \, \lambda_{1}$, and $f_{1}$ represent the speed, wavelength, and frequency of the light in Medium 1, respectively. What is the relationship between the wavelengths of the light in the three med...
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654
<image>Determine the optical path difference $\Delta_{12}$ in an airfilled Michelson interferometer with arms having geometric lengths $L_{1}$ and $L_{2}$.
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655
<image>惯性系 $S$ 中三艘已处于匀速直线运动状态的飞船 $1, ~ 2, ~ 3$ ，各自的速度大小同为 $v$ ，航向已在图中示出。某时刻三艘飞船 “相聚”（彼此靠近，但不相碰）于 $S$ 系的 $O$ 点，此时各自时钟都校准在零点。飞船 1 到达图中与 $O$ 点相距 $l$ 的 $P$ 处时，发出两细束无线电信号，而后分别被飞船 $2, ~ 3$ 接收到。在飞船 3 中确定接收信号的时刻 $t_{3}$ 。
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<image><image>The digital transmission of speech may be represented using the block diagram of Fig. 6.1. Part of the signal at point P on Fig. 6.1 is shown in Fig. 6.2. The analogue-to-digital converter (ADC) samples the signal at time intervals of 0.25 ms. Each sample is converted into a four‐bit number with the small...
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657
<image>(a)、(b)、(c)为三个不同的简谐振动系统，组成各系统的各弹簧的劲度系数及重物质量如图所示，(a)、(b)、(c)三个振动系统的 $\\omega^{2}$ 值之比为 $\\qquad$。
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658
<image>For the circuit shown, $ abla=6.0 \text{ V}, R_{1}=7.0 \text{ }\text{Ω}, R_{2}=3.0 \text{ }\text{Ω}, R_{3}=6.0 \text{ }\text{Ω},$ and $R_{4}=12.0 \text{ }\text{Ω}$. After operating for a long time, equilibrium is established. What is the voltage across the capacitor at equilibrium?
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659
<image>在匀强电场 $\boldsymbol{E}$ 中，有一半径为 $R$ 的闭合半球面，其底面与电场线垂直，如图所示。试求：通过闭合半球面底面的电场强度通量。
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660
<image><image>A hollow tube, sealed at one end, has a cross-sectional area $A$ of $24 \mathrm{~cm}^{2}$. The tube contains sand so that the total mass $M$ of the tube and sand is 0.23 kg . The tube floats upright in a liquid of density $\rho$, as illustrated in Fig. 3.1. The depth of the bottom of the tube below the li...
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661
<image>一高压输电线被风吹断，一端触及地面，从而使 200 A 的电流流入地内。设地面为水平，土地的电导率 $\gamma=1.0\times10^{-2} \mathrm{~S}/\mathrm{m}$ 。当一人走近输电线的触地端，两脚间（约 0.6 m）的电压称为跨步电压（即习题 8－3 图中 $U_{ab}$）。求距离触地点 1 m 处的跨步电压。
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662
<image>A monatomic ideal gas undergoes the reversible cyclic process (ABCA) shown in the PV diagram. Process $A ightarrow B$ is adiabatic. What is the efficiency of this engine?
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663
<image>A toy car moves along the $x$-axis according to the velocity versus time curve shown to the right. When does the car have zero acceleration?
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664
<image>如图所示，在坚直平面内有一个半径为 $R$ 的固定光滑绝缘圆环，空间有垂直于该坚直平面水平朝外的匀强磁场 $\boldsymbol{B}$。质量 $m$ ，电量 $q>0$ 的质点 $P$ ，开始时静止在圆环外侧最高点 $A$ 处。假设 $\boldsymbol{B}$ 的大小 $B=\frac{\sqrt{3}}{2} \frac{m}{q} \sqrt{\frac{g}{R}}$ 而 $P$ 因受扰动获得水平朝左的微小速度（其值在计算时可略），试问 $P$ 下降多大高度 $h$ 即会离开圆环？
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665
<image>The graph shows the magnitude of the linear momentum of two solid objects colliding on the x-axis. Based on the information provided, can object 2 have more mass than object 1?
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666
<image>For the circuit shown, when a shorting wire (no resistance) connects the points labeled A and B, which of the numbered light bulbs become brighter?
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667
<image>图示梁 $A B$ 由铅垂杆 $C D$ 支持于水平位置．梁的一端作用的力 $F=$ 30 kN 与水平线成 $60^{\circ}$ 角．在 $A, C$ 与 $D$ 各点的连接均为铰链连接，按图示尺寸求杆 $C D$ 的内力 $S$ 和梁对墙的压力 $Q$ ．杆与梁的重量不计．
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668
<image>如果存在磁荷（磁单极子），那么在对磁荷量 $q_{\mathrm{m}}$ 的单位作适当定义后，真空中麦克斯韦方程组的微分形式应补充修改为下述形式： $$ \left\{ \begin{array}{l} \nabla \cdot \boldsymbol{E} = \frac{\rho}{\varepsilon_{0}} \\ \nabla \cdot \boldsymbol{B} = \frac{\rho_{\mathrm{m}}}{\mu_{0}} \\ \nabla \times \boldsymbol{E} = -\frac{\partial \boldsymbol{B}}{\partial t} - \fra...
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669
<image>Which resistor dissipates the most power?
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670
<image>What is the average velocity of the object for the twenty-eight second interval?
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671
<image>Fig. 1.1 shows the path of a comet of mass $2.20 \times 10^{14}\,\mathrm{kg}$ as it passes around a star of mass $1.99 \times 10^{30}\,\mathrm{kg}$. At point X, the comet is $8.44 \times 10^{11}\,\mathrm{m}$ from the centre of the star and is moving at a speed of $34.1\,\mathrm{km\,s}^{-1}$. At point Y, the come...
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672
<image>如图所示，一条轻绳跨过摩擦可被忽略的轻滑轮，在绳的一端挂一质量为 $m_{1}$ 的物体，在另一侧有一质量为 $m_{2}$ 的环，求当环相对于绳子以恒定的加速度 $a_{2}$ 沿绳向下滑动时，物体相对地面的加速度是多少？
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673
<image>A circularly polarized wave with wavelength $\lambda_{0}=630 \mathrm{~nm}$ is incident on the uniaxial crystal plate with thickness $d=$ 0.5 mm and principal values of the refractive index $n_{o}=1.71$ and $n_{e}=1.68$. A linear polarizer follows the plate with the transmission axis P forming the angle $\alpha=3...
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674
<image>A 2.0 kg particle travels at a constant speed of $5.0 \text{ m/s}$ along the line shown in the figure. What is the magnitude of the particle's angular momentum calculated from the origin?
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675
<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 B 的加速度（滑轮的质量与摩擦不计）。
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676
<image>一根细杆AB竖直靠在墙壁上，B端沿水平方向以速度 v 滑离墙壁。当细杆运动到图示位置时，细杆中点C的速度大小和方向是多少？
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677
<image><image>A battery of electromotive force $\n\mathcal{E}$ and internal resistance $r$ is connected to either a system of $n$ identical resistors connected in series, or to $n$ resistors connected in parallel, all having the resistance $R$. Calculate which circuit (series or parallel) has greater power.
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678
<image>在半径为 $R$ 的圆柱体内，有磁感应强度为 $\boldsymbol{B}$ 的均匀磁场。一边长为 $l$ 的正方形线圈放在磁场中，其 ad 边的中点通过圆柱轴线 $O$ 点。设磁场以 $\frac{\mathrm{d} B}{\mathrm{~d} t}$ 的恒定速率增加，试求整个线框中的感应电动势。
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679
<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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680
<image>An ideal operational amplifier (op-amp) is incorporated into the circuit shown in Fig. 7.1. Determine the output potential difference $V_{\text{OUT}}$ for an input potential difference $V_{\text{IN}}$ of +0.60 V ,
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681
<image><image>The variation with potential difference $V$ of the charge $Q$ on one of the plates of a capacitor is shown in Fig. 5.1.\n\nThe capacitor is connected to an 8.0 V power supply and two resistors R and S as shown in Fig. 5.2.\nThe resistance of R is $25\,\mathrm{k}\Omega$ and the resistance of S is $220\,\ma...
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682
<image>如图所示，一个平面电磁波在真空中传播，设某点的电场强度为 $E_{x}=900 \cos \left(2 \pi \nu t+\frac{\pi}{6}\right)$ (SI 单位) 。试求这一点的磁场强度表示式。
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683
<image>如图所示，各边静长为 $L$ 的正方形面板 $A B C D$ ，在惯性系 $S$ 的 $x y$ 坐标面上以匀速度 $v$ 沿 $x$ 轴运动。运动过程中 $A B$ 边和 $B C$ 边各点均朝 $x$ 轴连续发光，在 $S$ 系中各点发光方向均与 $y$ 轴平行， 这些光在 $x$ 轴上照亮出一条随着面板运动的轨道线段，试求它的长度 $l$ 。
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684
<image>一个质量 $m=4 \mathrm{~kg}$ 表面光滑的凹槽，静止放在光滑的水平地面上，槽的凹面呈圆弧形，其半径 $R=0.2 \mathrm{~m}$ 如图所示。槽的 A 端与圆弧中心 $O$ 点在同一平面上，B 端与 $O$ 点的连线与坚直方向间的夹角 $\theta=60^{\circ}$ 。今有一质量 $m^{\prime}=1 \mathrm{~kg}$ 的小滑块自 A 端从静止开始沿槽面滑下。求小滑块在 B 端滑出时，凹槽相对地面的速度。
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685
<image>A collimated laser beam with wavelength $\lambda_{0}=0.65 \mu \mathrm{~m}$ is passed through a circular aperture with diameter $D=2 \mathrm{~mm}$ in an opaque screen. Determine the diameter $d_{z}$ of the laser beam passed through the aperture at distance $z=5 \mathrm{~m}$ from the screen.
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686
<image>A strong bar magnet is held very close to the opening of a solenoid. As the magnet is moved away from the solenoid at constant speed, what is the direction of conventional current through the resistor?
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687
<image>An amplifier circuit incorporating an op-amp is shown in Fig. 8.1. The resistance of resistor $R$ is to be fixed so that, for an input potential difference $V_{IN}$ of 0.40 V, the amplifier is on the point of saturation. Determine: the resistance of resistor R.
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688
<image>On a frictionless horizontal surface, two bodies make a head-on collision and stick together. Body 1 has a mass of 3.50 kg and initially moves to the right with speed $7.0 rac{\text{m}}{\text{s}}$. Body 2 initially is at rest. How much kinetic energy was transformed to other kinds of energy from the collision?
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689
<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。 试问：杆连同环的旋转角速度 $\\omega$ 取何值时，环在杆上任何位置均可相对杆静止？
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690
<image>For the diagram shown below, what is the ratio of the charges $q_{2} / q_{1}$, where the diagram shown has a representation of the field lines in the space near the charges?
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691
<image>如电图 3.2.1 所示，$ABCDA$ 是闭合导体回路，总电阻为 $R$，$AB$ 段的一部分绕成初始半径为 $r_{0}$ 的圆圈。圆圈所在区域有与圆圈平面垂直的均匀磁场 $\boldsymbol{B}$。回路的 $B$ 端固定，$C$ 和 $D$ 为自由端，$A$ 端在沿 $BA$ 方向的恒力 $F$ 的作用下向右移动，从而使圆圈缓慢缩小。设在圆圈缩小的过程中，始终保持圆的形状，设导体回路是柔软的，设阻力可以忽略。试求此圆圈从初始的半径 $r_{0}$ 到完全闭合所需的时间 $T$。
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692
<image>In the circuit shown, the switch $S$ has been left open for a very long time. All circuit elements are considered to be ideal. What is the steady-state current through the switch $S$ once it is closed?
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693
<image>Artemis is a spherical planet that may be assumed to be isolated in space. The variation with distance $x$ from the centre of Artemis of the gravitational potential $\phi$ is shown in Fig. 1.1. The radius of Artemis is 4800 km. A satellite is in an orbit at a fixed position above a point on the surface of Artemi...
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694
<image>如图所示，$AB=2l$, $OCD$ 是以 $B$ 为中心，$l$ 为半径的半圆，$A$ 点处有正电荷 $+q$, $B$ 点处有负电荷 $-q$，求：把单位正电荷从 $O$ 点沿 $OCD$ 移到 $D$ 点，电场力对它做了多少功？
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695
<image>质点沿轨道 $A B$ 作曲线运动，速率逐渐减小，图中哪一种情况正确地表示了质点在 $C$ 处的加速度？（ ）
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696
<image>地面上波源 $S$ 与高频率波探测器 $D$ 之间的距离为 $d$ ，从 $S$ 直接发出的波与从 $S$ 发出经高度为 $H$ 的水平层反射后的波，在 $D$ 处加强，反射线及入射线与水平层所成的角度相同。当水平层逐渐升高 $h$ 距离时，在 $D$ 处测不到信号。不考虑大气的吸收。试求此波源 $S$ 发出波的波长。
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697
<image>如电图3．6．1 所示，在匀强磁场区域与 $\boldsymbol{B}$ 垂直的平面（水平面）中有两根足够长的固定的平行金属导轨，在它们上面横放着两根平行导体棒，构成矩形回路。导体棒的长度均为 $l$ ，质量均为 $m$ ，电阻均为 $R$ ，回路中导轨部分的电阻可以忽略。设导体棒在导轨上可以无摩擦地滑行，设重力及电磁辐射均可不计，设开始时左导体棒静止，右导体棒具有向右的初速度 $v_{0}$ 。试求：右导体棒向右的速度 $v_{1}$ 随时间 $t$ 的变化。
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698
<image>Two cars, $P$ and $Q$, each start from rest at the origin and will move along the $x$-axis. Based on the acceleration vs. time graph for each car, what is the relationship between their speeds $v$ and positions $x$ at time $T$?
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699
<image>Determine the separation $\\Lambda$ between the adjacent antinodes and nodes of a standing wave, formed in a medium with refractive index $n=1.33$ under the superposition of counterpropagating waves $E_{1}(z, t)$ and $E_{2}(z, t)$ with the free-space wavelength $\\lambda_{0}=0.6 \\mu \\mathrm{~m}$.
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