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<image>Solar energy at the rate $800 \, \mathrm{W} / \mathrm{m}^{2}$ strikes a flat solar panel for water heating. If the panel has absorptance $=0.96$ for all wavelengths and the sides are perfect insulators, calculate the maximum temperature of the water.
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401
<image>Solar energy at the rate $800 \, \mathrm{W} / \mathrm{m}^{2}$ strikes a flat solar panel for water heating. If the absorptance dropped by $1 / 2$, how would this affect the final temperature?
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402
<image>质量分别为 $m_{1}$ 和 $m_{2}$ 的两个滑块 A 和 B ，分别穿于两条平行且水平的光滑导杆上，两杆间的距离为 $L$ ，再以一劲度系数为 $k$ ，原长为 $L$ 的轻质弹簧连接两滑块，如图所示。设开始时滑块 A 位于 $x_{1}=0$ 处，滑块 B 位于 $x_{2}=l$ 处，且其速度均为零。试求释放后滑块 B 的最大速度是多少？
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403
<image>An insulating spherical shell of radius $R$ carries surface charge density $\sigma(\theta)=\sigma_{o} \cos \theta$, where $\sigma_{o}$ is a constant. The shell is sent spinning around the $x$-axis $(\vec{\omega}=\omega \hat{x})$. Calculate the power radiated.
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404
<image><image><image>An n.t.c. thermistor and a resistor are connected as shown in Fig. 7.2. The temperature of the thermistor is increased. State and explain the change, if any, to the reading on the voltmeter. The variation with the fractional change in length $\Delta x / x$ of the fractional change in resistance $\D...
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405
<image>For the RC circuit shown, the resistance is $R=10.0 \, \Omega$, the capacitance is $C=5.0 \, F$ and the battery has voltage $\xi=12$ volts. The capacitor is initially uncharged when the switch S is closed at time $t=0$. At some time later, the current in the circuit is 0.50 A. What is the magnitude of the voltag...
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406
<image>Planets have been observed orbiting a star in another solar system. Measurements are made of the orbital radius $r$ and the time period $T$ of each of these planets. The variation with $R^{3}$ of $T^{2}$ is shown in Fig. 1.1. The relationship between $T$ and $R$ is given by $$T^{2} = \frac{4\pi^{2} R^{3}}{GM}$$ ...
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407
<image>Derive the expression for the intensity of the frequency spectrum $I(v)=|E(v)|^{2}$ of the wave train of damped oscillations: $E(t)=E_{0} \\exp \\left(-t / \tau_{c}\right) \\cos \\left(2 \\pi v_{0} t\right)$, where $\\tau_{c}$ is the damping time. Determine the width of the spectral contour $\\Delta v$ at the ha...
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408
<image>系统如图示，小滑轮固定不动，轻绳与滑轮间无摩擦，小物块 $A, B$ 质量相同，$B$ 与水平桌面间无摩擦。开始时 $A, B$ 静止，右侧绳段与水平桌面间的夹角为 $30^{\circ}$ 。今将系统自由释放，通过计算，判断释放后一瞬间物块 $B$ 是否会向上离开水平桌面？
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<image><image><image>A spring is hung vertically from a fixed point. A mass M is hung from the other end of the spring, as illustrated in Fig. 3.1. The mass is displaced downwards and then released. The subsequent motion of the mass is simple harmonic. The variation with time $t$ of the length $L$ of the spring is show...
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410
<image>Consider an infinite sheet in the $x y$-plane carrying surface current $\\vec{K}(t)=\left\{\begin{array}{ll} 0, & t \leqslant 0 \\ K \\hat{x}, & t>0 \end{array}\right.$. Find the generated magnetic field.
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411
<image>The circuit of an amplifier incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1. Derive an expression, in terms of the resistances $R_{1}$ and $R_{2}$, for the gain of the amplifier circuit.
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412
<image>In which Regions is there a place on the x-axis (aside from infinity) at which the electric potential is equal to zero?
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413
<image><image>A bridge rectifier contains four diodes. The output of the rectifier is connected to a resistor $R$, as shown in Fig. 10.1. The variation with time $t$ of the input e.m.f. $E$ to the rectifier is given by the expression $E=15\cos(210t)$ where $t$ is measured in seconds and $E$ in volts. The variation with...
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<image><image><image>A spring is hung vertically from a fixed point. A mass M is hung from the other end of the spring, as illustrated in Fig. 3.1. The mass is displaced downwards and then released. The subsequent motion of the mass is simple harmonic. The variation with time $t$ of the length $L$ of the spring is show...
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415
<image>如力图 7.24.1 所示，质量为 $M$ 的小球两侧分别用劲度系数均为 $k$ 的弹簧与两个质量均为 $m$ 的小球连成一条直线，水平放置，忽略一切阻力和摩擦力。试求特征频率和振动模式。
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416
<image>A radio wave is modulated by an audio signal. The variation with frequency $f$ of the amplitude of the modulated wave is shown in Fig. 5.1. Determine: the wavelength of the carrier wave.
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417
<image>An electron moves in the plane of the page through two regions of space along the dotted-line trajectory shown in the figure. There is a uniform electric field in Region I directed into the plane of the page (as shown). There is no electric field in Region II. What is a necessary direction of the magnetic field ...
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418
<image>For the diagram shown, what is the magnitude of the torque from the applied force as measured from the center of the disk?
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419
<image>The circuit for the microphone and amplifier is shown in Fig. 7.1. The output potential difference $V_{\text{OUT}}$ is 2.6 V when the potential at point P is 84 mV. For the circuit of Fig. 7.1, state and explain the effect on the output potential difference $V_{\text{OUT}}$ of increasing the resistance of resist...
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<image>图示的电路中，$t<0$ 时，电容器充电过程已完成。$t=0$ 时，接通电键 K 。将接通前瞬间时刻记为 $t=0^{-}$，接通后瞬间时刻记为 $t=0^{+} . t \geqslant 0^{+}$时，按图中虚线所示方向设定各路电流 $I_{1}, I_{2}, I_{C}$ 和 $I_{3}$ 的流向。导出电容器上方极板电量 $Q(0^{+})$；
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421
<image>一波源 S （振动的频率为 2040 Hz ）以速度 $v_{\mathrm{S}}$ 向一反射面接近（见习题 11－37 图），观察者在 $A$ 点听得拍音频率为 $\Delta \nu=3 \mathrm{~Hz}$ 。若波源没有运动，而反射面以速度 $v=0.20\,\mathrm{m}/\mathrm{s}$ 向观察者 $A$ 接近，所听得的拍音频率为 $\Delta \nu=4\,\mathrm{Hz}$ ，求波源的频率。
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<image><image>Polonium-211 $({ }_{84}^{211} \mathrm{Po})$ decays by alpha emission to form a stable isotope of lead $(\mathrm{Pb})$. The variation with time $t$ of the number of unstable nuclei $N$ in a sample of polonium-211 is shown in Fig. 9.1. At time $t=0$, the sample contains only polonium-211. Use Fig. 9.1 to de...
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<image>What is the equivalent resistance in the circuit that is shown at right?
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<image>一平面波在介质中以速度 $u=20 \mathrm{~m}/\mathrm{s}$ 沿 $x$ 轴负方向传播．已知 $M$ 点的振动表达式为 $y_{M}=3 \cos 4 \pi t$, $t$ 的单位为 $\mathrm{s}$, $y$ 的单位为 m．以 $M$ 为 $Ox$ 坐标原点写出波云表达式．
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425
<image>What is the current in $\text{R}_{3}$?
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<image>如图所示，一根长直导线载有电流 $I_{1}$ ，矩形回路上的电流为 $I_{2}$ ，计算作用在回路上的合力。
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427
<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：B 部分气体的温度是多少？
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<image>三个弹簧秤的吊环 $A, B, C$ 固定在水平木板上．弹簧秤的钩子上各系着一条绳子．将三条绳子拉紧，并将自由端在 $D$ 点联结．已知弹簧秤上的读数分别为 $8 \mathrm{~N}, 7 \mathrm{~N}$ 和 $13 \mathrm{~N}$ ，试求绳子之间的夹角 $\alpha$ 和 $\beta$ ．
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<image>An audio signal is transmitted by means of a modulated radio wave. The variation with frequency of the amplitude of the radio wave is shown in Fig. 4.1. For this transmission, determine: the wavelength, in km, of the carrier wave
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430
<image>一长 $l=0.40~\mathrm{m}$ 的均匀木棒，质量 $m'=1.00~\mathrm{kg}$，可绕水平轴 $O$ 在坚直平面内转动，开始时棒自然坚直地悬垂。现有质量 $m=8~\mathrm{g}$ 的子弹以 $v=200~\mathrm{m/s}$ 的速率从 $A$ 点射入棒中，假定 $A$ 点与 $O$ 点的距离为 $\frac{3l}{4}$。求棒开始运动时的角速度。
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431
<image>The variation with time $t$ of the number $N$ of undecayed nuclei in a sample of a radioactive isotope is shown in Fig. 12.1. Use the gradient of the line in Fig. 12.1 to determine the activity, in Bq, of the sample at time $t=4.0$ hours. Show your working.
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432
<image>一质点沿 $x$ 轴运动，其受力如图所示，设 $t=0$ 时，$v_{0}=$ $5 \text{ m/s}, x_{0}=2 \text{ m}$ ，质点质量 $m=1 \text{ kg}$ ，该质点 7 s 末的速度为 $\blank$ ，位置坐标为 $\blank$。
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433
<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 ，从所得的结果是否可以判断两弹簧振子作什么性质的振动（周期振动或混沌）？
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434
<image>在载有电流 $I_{1}$ 的长直导线的磁场中，放置一等腰直角三角形线圈，直角边长为 $a$，通有电流 $I_{2}$。开始时线圈和长直导线在同一平面内，如习题8－49图所示。保持电流 $I_{1}$ 和 $I_{2}$ 不变而将线圈绕 $A C$ 边转动 $180^{\circ}$，试求转动过程中磁力所做的功。
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435
<image>一个半径为 $r$ 的半球面如图放在均匀磁场中，通过半球面的磁通量为（）
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436
<image>An alternating electric voltage $U_{s}$ with frequency $f_{s}=500$ MHz is applied to the piezoelectric transducer of an acoustooptical cell and excites a standing acoustic wave as a result of interference (superposition) of the direct traveling acoustic wave and the backward-traveling wave, reflected from the op...
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437
<image>A convergent spherical wave is incident on the $(x, y)$ plane and focused at point $S^{\text{prime}}$ of the $z$ axis with coordinates $\text{left}(0,0, z_{0}\text{right})$. Using the paraxial (parabolic) approximation, write the equation describing the spatial distribution of wave phase $\text{phi}(x, y)$ in th...
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438
<image>Three vector forces $F_{1}, F_{2}$, and $F_{3}$ act on a particle that has a mass of $3.00 \text{ kg}$. What is the particle's acceleration?
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439
<image>In the figure to the right, a box moves with speed $5.00 \text{ m/s}$ at the bottom of a rough, fixed inclined plane. The box slides with constant acceleration to the top of the incline as it is being pushed directly to the left with a constant force of $F=240 \text{ N}$. The box, of mass $m=20.0 \text{ kg}$, ha...
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440
<image><image>Fig. 7.1 shows the circuit diagram containing an operational amplifier (op-amp). Calculate the gain of the amplifier.
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441
<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。当斜面的加速度至少为多大时，小球开始脱离斜面？（分别取地面为参考系和取斜面为参考系计算。）
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442
<image>传动轴 $A B$ 上装有三个轮，重分别为 $P_{1}=3 \mathrm{kN}, P_{2}=5 \mathrm{kN}, P_{3}=2 \mathrm{kN}$ ，尺寸如图所示．欲使轴承 $A$ 的反力与轴承 $B$ 的反力相等，求重为 $P_{2}$ 的轮到轴承 $B$的距离 $x$ ．轴的重量不计．
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443
<image>设某系统中 $N$ 个粒子的速率分布曲线如图所示。试求：速率在 $1.5v_{0}\sim 2v_{0}$ 之间的粒子数
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<image>质量为 2 kg 的物体，在沿 $x$ 方向的变力作用下，在 $x=0$ 处由静止开始运动。设变力与 $x$ 的关系如图所示。试由动能定理求物体在 $x=15$ m 处的速率。
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445
<image>如图所示的打桩装置，半径为 $R$ 的带齿轮转盘绕中心轴的转动惯量为 $J$ ，转动角速度为 $\omega_{0}$ ，夯锤的质量为 $m$ ，开始处于静止状态，当转盘与夯锤碰撞后，问夯锤的速度能有多大？
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446
<image><image>A student sets up the apparatus shown in Fig. 3.1 in order to investigate the melting of ice. The heater is switched on. When the pure ice is melting at a constant rate, the data shown in Fig. 3.2 are collected. The specific latent heat of fusion of ice is $332 \mathrm{Jg}^{-1}$. Use the data in Fig. 3.2 ...
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447
<image><image>The variation with pressure $p$ of the volume $V$ of a fixed mass of an ideal gas is shown in Fig. 2.1. The gas undergoes a cycle of changes $A$ to $B$ to $C$ to $A$. During the change $A$ to $B$, the volume of the gas increases from $2.3 \times 10^{-3} \mathrm{~m}^{3}$ to $3.8 \times 10^{-3} \mathrm{~m}^...
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448
<image>A student uses a negative temperature coefficient thermistor in the circuit of Fig. 7.1 to indicate changes in temperature. Calculate the potential at point X.
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449
<image>An ideal op-amp is incorporated into the amplifier circuit shown in Fig. 8.1. Calculate the gain $G$ of the amplifier circuit.
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450
<image>An object of mass $12 M$ is at rest when it suddenly explodes into 3 pieces with masses $3 M, 4 M$, and $5 M$. The piece of mass $3 M$ moves with speed $V$ in the direction shown in the diagram. What is the speed of the piece with mass $5 M$ knowing that it is moving directly to the right?
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451
<image>1 mol氦气（理想气体）经历如热图2.19.1所示的循环过程，热图2.19.1中$AB$,$BC$,$CA$均为直线，有关参数已经标明，试求循环效率$\eta$。
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452
<image>An electron is travelling at speed $v$ in a straight line in a vacuum. It enters a uniform magnetic field of flux density $8.0 \times 10^{-4}\,\mathrm{T}$. Initially, the electron is travelling at right angles to the magnetic field, as illustrated in Fig. 9.1. The path of the electron in the magnetic field is an...
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453
<image>An audio signal is transmitted by means of a modulated radio wave. The variation with frequency of the amplitude of the radio wave is shown in Fig. 4.1. For this transmission, determine: the frequency of the audio signal
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454
<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. The work function energy in eV for some metals is given in Tab...
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455
<image>Fig. 7.1 shows an op-amp circuit that uses negative feedback. Calculate the gain of the circuit in Fig. 7.1.
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456
<image>For the inclined plane shown, what is the value of the incline's ideal mechanical advantage?
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457
<image>设电势沿 $O x$ 轴的变化曲线如图所示。试对所示 a-b 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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458
<image>一矩形线圈长 $l=20\,\mathrm{cm}$，宽 $b=10\,\mathrm{cm}$，由 100 匝表面绝缘的导线绕成，放置在一根长直导线的旁边，并和直导线在同一平面内，该长直导线是一个闭合回路的一部分，其余部分离线圈很远，其影响可略去不计。求习题 9－24 图（a）情况下，线圈与长直导线间的互感。
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459
<image>Fig. 7.1 shows an op-amp circuit that uses negative feedback. Determine the value of $V_{\mathrm{IN}}$ when $V_{\mathrm{OUT}}$ is +6.5 V.
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<image>The variation with frequency $f$ of the amplitude $A$ of a transmitted radio wave after amplitude modulation by an audio signal is shown in Fig. 5.1. For this transmission, determine: the wavelength of the carrier wave.
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461
<image>均质杆 $A B$ 用铰链 $A$ 固定在铅垂墙上，并用绳子 $B C$ 吊住，杆与铅垂线的夹角为 $60^{\circ}$ ，绳子与杆的夹角为 $30^{\circ}$ ．已知杆重为 20 N ，求较链的反力 $R$ 的大小和方向．
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462
<image>如图所示，一矩形线圈可绕 $O y$ 轴转动，线圈中载有电流 0.10 A ，放在磁感应强度 $B=0.50 \mathrm{~T}$ 的均匀磁场中，$B$ 的方向平行于 $O x$ 轴，求维持线圈在图示位置时的力矩。
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463
<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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464
<image><image><image>A coil of wire is situated in a uniform magnetic field of flux density $B$. The coil has diameter 3.6 cm and consists of 350 turns of wire, as illustrated in Fig. 9.1. The variation with time $t$ of $B$ is shown in Fig. 9.2. Calculate, for the time $t=0$ to time $t=0.20 \mathrm{~s}$, the electromot...
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465
<image>铁路通过山区，它在山谷中的一段如图所示．假设悬杆 $A B$ 的承载力为 $P=500 \mathrm{kN}$ ，求杆 $A C$ 和 $A D$ 的内力．
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466
<image>Consider the motion of an object given by the velocity vs. time graph shown. At which time is the acceleration of the object equal to $0 \text{ m/s}^2$?
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467
<image>\n在如电图 4．24．1 所示的电路中，各个电阻的阻值都是 $1 \Omega$ ，安培计与电源的内阻均可忽略不计，电源的电动势 $\mathscr{E}=10 \mathrm{~V}$ 。试求通过安培计的电流强度。
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468
<image>A beam of X-rays has an initial intensity $I_{0}$. The beam is directed into some body tissue. After passing through a thickness $x$ of tissue the intensity is $I$. The graph in Fig. 11.1 shows the variation with $x$ of $\ln\left(I/I_{0}\right)$. Determine the thickness of tissue that the X-ray beam must pass th...
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469
<image>如图所示，在水平地面上，有一横截面 $S=0.20 \text{ m}^{2}$ 的直角弯管，管中有流速为 $v=3.0 \text{ m/s}$ 的水通过，弯管所受力的大小为 $\boxed{\text{ }}$ ，方向为 $\boxed{\text{ }}$。
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470
<image>三个相同的管子，每个重 $M=120 \mathrm{~N}$ ，安放如图所示．求下面的管子对地面的压力和对两侧光滑墙面的压力．摩擦不计．
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471
<image>一平面波在介质中以速度 $u=20 \mathrm{~m}/\mathrm{s}$ 沿 $x$ 轴负方向传播．已知 $M$ 点的振动表达式为 $y_{M}=3 \cos 4 \pi t$, $t$ 的单位为 $\mathrm{s}$, $y$ 的单位为 m．以距 $M$ 点 5 m 处的 $N$ 点为 $O^{\prime}x^{\prime}$ 坐标原点，写出波动表达式．
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472
<image><image>A stiff metal wire is used to form a rectangular frame measuring $8.0\ \mathrm{cm}\times 6.0\ \mathrm{cm}$. The frame is open at the top, and is suspended from a sensitive newton meter, as shown in Fig. 8.1. The open ends of the frame are connected to a power supply so that there is a current of 5.0 A in ...
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473
<image><image>Fig. 4.1 shows the variation with time $t$ of the height $h$ above the ground of an object of mass 36 kg that is undergoing vertical simple harmonic motion. For the oscillations of the object: determine the amplitude $x_{0}$, in cm
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474
<image>设有 $N$ 个粒子的系统，其速度分布如图所示。求：速度在 $1.5 v_{0}$ 到 $2.0 v_{0}$ 之间的粒子数。
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475
<image>During the change in (b), the thermal energy supplied to the gas is 980 J. (i) Determine the work done on the gas during this change. Explain your working.
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476
<image>A radio wave is modulated by an audio signal. The variation with frequency $f$ of the amplitude of the modulated wave is shown in Fig. 5.1. Determine: the bandwidth of the modulated wave.
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477
<image>A radio wave is modulated by an audio signal. The variation with frequency $f$ of the amplitude of the modulated wave is shown in Fig. 5.1. Determine: the maximum frequency of the audio signal.
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478
<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 liq...
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479
<image><image><image>A light rod of length $l$ with a small ball of mass $m$ attached to its upper end can rotate freely without friction around its lower end fixed at point $O$ in space. A vertical $z$-axis is drawn upward from point $O$. Initially, the rod makes an angle $\theta_0$ ($\theta_0 > 0$) with the $z$-axis,...
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480
<image><image>A parallel beam of ultrasound passes normally through a layer of fat and of muscle, as illustrated in Fig. 5.1. The fat has thickness 0.45 cm and the muscle has thickness 2.1 cm. Data for fat and for muscle are given in Fig. 5.2. The intensity reflection coefficient $\alpha$ at a boundary between two medi...
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481
<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. Use data from Fig. 9.2 to state one time when the magnetic flux linking the secondary coil is a maximum.
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482
<image><image>Data for linear attenuation coefficients are given in Fig. 5.2. Determine the ratio intensity of ultrasound transmitted through the medium intensity of ultrasound entering the medium for the layer of fat of thickness 0.45 cm.
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483
<image>如图所示，$N \geqslant 2$ 块相同的导体平板相互间隔地平行放置，各自带电量分别为 $Q_{1}, Q_{2}, \cdots Q_{N}$ 。静电平衡后，试求：第 1 块平板左侧面电荷 $Q_{18}$ 和第 $N$ 块平板右侧面电荷 $Q_{\text {N右；}}$
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484
<image>长 $l=0.40 \text{ m}$ ，质量 $M=1.00 \text{ kg}$ 的匀质木棒，可绕水平轴 $O$ 在坚直平面内转动，开始时棒自然坚直悬垂，现有质量 $m=8 \text{ g}$ 的子弹以 $v=200 \text{ m/s}$ 的速度从 $A$ 点射入棒中，$A, ~ O$ 点的距离为 $3l/4$ ，如图所示。求：棒的最大偏转角。
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485
<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 $C_{2}$ 上的电压。
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486
<image>设某系统中 $N$ 个粒子的速率分布曲线如图所示。试求：所有粒子的平均速率
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487
<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 $7.0 \frac{\mathrm{~m}}{\mathrm{~s}}$. Body 2 initially is at rest. What is the mass of Body 2?
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488
<image>Determine the phase difference $\\delta$ between the $p$ - and $s$-components in a laser beam reflected by the hypotenuse face of a right-angle prism at incidence angle $\\alpha_{0}=45 \\mathrm{deg}$, where the refractive indices of the prism and surrounding medium are $n_{1}=1.5$ and $n_{2}=1$, respectively. Th...
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489
<image><image>A circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1. The variation with temperature $\theta$ of the resistance $R_{T}$ of the thermistor is shown in Fig. 7.2. The output potential $V_{\text{OUT}}$ of the op-amp circuit changes sign when the temperature of the thermistor is...
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490
<image>Find the self-inductance $L$ per unit length for an infinitely long coaxial cable of radii $a, b$ with $a<b$, carrying a current $I$, as in the figure. Use energy calculations.
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491
<image>如图所示，一平面波在介质中以波速 $u=20 \text{ m/s}$ 沿 $x$ 轴负方向传播，已知 $A$ 点的振动方程为 $y=3 \times 10^{-2} \text{ cos } 4 \text{ π } t(\text{SI})$ 。以 $A$ 点为坐标原点写出波的表达式；
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492
<image>如图所示，两振动方向相同的平面简谐波波源分别位于 $A, ~ B$ 两点。设它们相位相同，且频率均为 $\nu=30 \text{~Hz}$ ，波速 $u=0.50 \text{~m/s}$ 。求在 $P$ 点处两列波的相位差。
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493
<image>Derive the expression for the intensity of the frequency spectrum $I(v)=|E(v)|^{2}$ of the wave train of damped oscillations: $E(t)=E_{0} \\exp \\left(-t / \tau_{c}\right) \\cos \\left(2 \\pi v_{0} t\right)$, where $\\tau_{c}$ is the damping time.
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494
<image>长为 $l$ 的两根相同的细棒，均匀带电，电荷密度为 $\lambda$ ，沿同一直线放置，两棒的近端相距也是 $l$ ，求两棒间的电场力。
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495
<image><image>An ideal gas is contained in a cylinder by means of a movable frictionless piston, as illustrated in Fig. 2.1. Initially, the gas has a volume of $1.8 \times 10^{-3} \, \mathrm{m}^{3}$ at a pressure of $3.3 \times 10^{5} \ \mathrm{Pa}$ and a temperature of 310 K. The gas expands so that its volume increas...
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496
<image>设有 $N$ 个粒子的系统，其速度分布如图所示。求：分布函数 $f(v)$ 的表达式；
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497
<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. Calculate the mass of Artemis.
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498
<image>A solid spherical conductor has charge $+Q$ and radius $R$. It is surrounded by a solid spherical shell with charge $-Q$, inner radius $2 R$, and outer radius $3 R$, which point has both the electric potential and electric field achieving maximum magnitude?
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499
<image>During the change in (b), the thermal energy supplied to the gas is 980 J. (ii) Determine the change $\Delta U$ in internal energy of the gas.
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