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<image>火箭沿垂直方向由静止向上发射，其加速度随时间的变化规律如图所示。试求火箭在 $t=50 \mathrm{~s}$ 时燃料用完那一瞬时的速度。
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501
<image><image><image>Fig. 5.2 shows the variation with time $t$ of $V_{\mathbb{IN}}$ and Fig. 5.3 shows the variation with $t$ of $V_{\text{OUT}}$. Determine the frequency of $V_{\mathbb{IN}}$.
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502
<image>A Fresnel phase zone plate is made of a plane-parallel glass plate with refractive index $n$ by cutting grooves with depth $h$ at even Fresnel zones. A magnified fragment of the central part of such a plate is shown in the figure. Derive the formula for calculating groove depth $h$ if the Fresnel plane is to ope...
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503
<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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504
<image><image>A trolley on a smooth surface is attached by springs to fixed blocks. The trolley oscillates horizontally about its equilibrium position with an amplitude of 12 cm. Fig. 4.2 shows the variation of the acceleration $a$ of the trolley with displacement $x$ from its equilibrium position. Friction between the...
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505
<image>The circuit for a non-inverting amplifier incorporating an ideal op-amp is shown in Fig. 7.1. The light-emitting diode (LED) emits light when the potential difference across it is at least 2.0 V. The current in the LED must not be greater than 20 mA. State the maximum value of the output potential $V_{\text{OUT}...
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506
<image>What is the equivalent resistance of the circuit with resistances $R_{1}=4.00 \, \Omega$, $R_{2}=3.00 \, \Omega$, and $R_{3}=2.00 \, \Omega$?
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507
<image>An ideal op-amp is incorporated into the circuit of Fig. 8.1. Determine the resistance $R_{\mathrm{T}}$ of the thermistor T at which the output potential difference $V_{\text{OUT}}$ is zero.
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508
<image>火箭沿垂直方向由静止向上发射，其加速度随时间的变化规律如图所示。试求火箭在 $t=50 \mathrm{~s}$ 时燃料用完那一瞬时所能到达的高度。
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509
<image>Two monochromatic plane waves with wavelengths $\\lambda=$ 600 nm linearly polarized in orthogonal directions are incident on the $(x, y)$ plane under different angles with the $x$ axis, $\\alpha_{01}=0$ deg and $\\alpha_{02}=30$ deg. Determine the spatial period $\\Lambda$ along the $x$ axis for the variation o...
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510
<image>一边长为 $l=0.15 \mathrm{~m}$ 的立方体如图放置，有一均匀磁场 $B=(6 \boldsymbol{i}+3 \boldsymbol{j}+1.5 \boldsymbol{k}) \mathrm{T}$ 通过立方体所在区域，计算：通过立方体上阴影面积的磁通量
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511
<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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512
<image>The circuit for a non-inverting amplifier incorporating an ideal op-amp is shown in Fig. 7.1. The light-emitting diode (LED) emits light when the potential difference across it is at least 2.0 V. The current in the LED must not be greater than 20 mA. When the op-amp is saturated, the potential difference across ...
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513
<image>The circuit for an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1. When the op-amp is saturated, the potential difference across the LED is 2.3 V. Calculate the minimum resistance of resistor $R$ so that the current in the LED is limited to 30 mA.
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514
<image>A spring with spring constant $k=20 \text{kN/m}$ is used to stop a 50 kg box sliding on a horizontal surface. The box has a speed of $3.0 \text{m/s}$ at position $A$. The compression of the spring when the box is at rest at position $B$ is 120 mm. What is the coefficient of kinetic friction between the box and t...
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515
<image>Determine the energy transmission coefficient $T$ of a glass plane-parallel plate with $n_{2}=1.5$ in air ( $n_{1}=n_{3}=1.0$ ) when linearly polarized light with polarization azimuth $\theta_{0}=$ 30 deg is incident at the Brewster angle $\alpha_{B}$.
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516
<image>The stars $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ rotate with the same angular velocity $\omega$ about a point P, as illustrated in Fig. 1.2. Point P is at a distance $x$ from the centre of star $S_{1}$. The period of rotation of the stars is 44.2 years. By considering the forces acting on the two stars, deduce an...
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517
<image>四冲程汽油内燃机的工作循环称为奥托（OTTO）循环。设用理想气体作为工作物质，进行如图所求的循环过程。其中 $a \rightarrow b$ 为绝热压缩过程，$b \rightarrow c$ 为等体升压过程，$c \rightarrow d$为绝热膨胀过程，$d \rightarrow a$ 为等体降压过程，试求循环的效率，并用压缩比 $V_{2} / V_{1}$ 表示。
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518
<image>A long straight wire has a conventional current directed into the plane of the page as shown in the figure. Which one of the arrows shown best indicates the direction of the magnetic field associated with this wire at the location labeled $P$ ?
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519
<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. Determine the resistance of resistor $R$.
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520
<image>如图所示，质量为 $m$ 的物体用平行于斜面的细线连接置于光滑的斜面上，若斜面向左方作加速运动，当物体刚脱离斜面时，它的加速度的大小为（ ）
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521
<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 10 m 处的跨步电压。
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522
<image>1 mol 单原子分子理想气体所经准静态循环过程是如热图 2.21.1 所示的圆。有参量已在热图 2.21.1 中标明。 试求一次循环对外所做的功 $W$ 。
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523
<image>Two capacitors of capacitances $22 \mu \mathrm{~F}$ and $47 \mu \mathrm{~F}$, and a resistor of resistance $2.7 \mathrm{M}\Omega$, are connected into the circuit of Fig. 5.2. The battery has an e.m.f. of 12 V. Calculate the combined capacitance of the two capacitors.
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524
<image><image>A U-tube contains liquid, as shown in Fig. 4.1. The total length of the liquid column is $L$. The column of liquid is displaced so that the change in height of the liquid level from the equilibrium position in each arm of the U-tube is $x$, as shown in Fig. 4.2. The liquid in the U-tube then oscillates su...
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525
<image>如力图 4.3.1 所示，设质量为 $M$ 的恒星固定不动。质量为 $m$ 的行星在其引力作用下运动，已知距恒星 $\boldsymbol{r}_{0}$ 时的速度为 $v_{0}$ ，且 $\boldsymbol{v}_{0}$ 的方向与径矢垂直。试讨论：行星轨迹分别为抛物线，椭圆，圆和双曲线时，$v_{0}$ 应取何值？
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526
<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 amplitude of the mass's oscillation in meters?
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527
<image>Three charges are located at the vertices of a right triangle as shown at right. What is the magnitude of the resultant electric field at the midpoint, $M$, on a line between $A$ and $C$?
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528
<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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529
<image>An ideal op-amp is incorporated into the amplifier circuit shown in Fig. 8.1. Determine the output potential difference $V_{\text{OUT}}$ for input potential differences $V_{\text{IN}}$ of $-0.10\,\mathrm{V}$
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530
<image>一个通有电流 $I$ 的导体，厚度为 $D$ ，横截面积为 $S$ ，放在磁感应强度为 $\boldsymbol{B}$ 的匀强磁场中，磁场方向如图所示。现测得导体上下两面电势差为 $U$ ，则此导体的霍尔系数等于 $(\quad)$ 。
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531
<image><image>A metal sphere of radius $R$ is isolated in space. Point $P$ is a distance $x$ from the centre of the sphere, as illustrated in Fig. 7.1. The variation with distance $x$ of the electric field strength $E$ due to the charge on the sphere is shown in Fig. 7.2. An $\alpha$-particle is situated a distance 8.0...
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532
<image>The partially completed circuit of a non-inverting amplifier, incorporating an ideal op-amp, is shown in Fig. 7.1. For the completed circuit of Fig. 7.1, the gain of the amplifier is 25 . The resistance of resistor $R_1$ is $12 \mathrm{k}\Omega$. Calculate the resistance of resistor $R_2$.
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533
<image><image>A solenoid $S$ has a small coil $C$ placed near to one of its ends, as shown in Fig. 11.1. The coil $C$ has a circular cross-section of diameter $3.6 \times 10^{-2}\,\mathrm{m}$ and contains 63 turns of wire. The solenoid $S$ produces a uniform magnetic field of flux density $B$, in tesla, in the region o...
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534
<image>Electrons, each of mass $m$ and charge $q$, are accelerated from rest in a vacuum through a potential difference $V$. Derive an expression, in terms of $m$, $q$ and $V$, for the final speed $v$ of the electrons. Explain your working.
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535
<image>如图所示，置于地面和塔顶的两架弹射器，以相同的速率 $v_{0}$ 沿它们的连线同时弹射出两球。如果塔顶高 $h=10\,\mathrm{m}$ ，两弹射器相隔的水平距离 $s=20\,\mathrm{m}$ ，这两个球会不会在空中相碰？
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536
<image>用方解石切割成一个 $60^{\circ}$ 的正三角棱镜，光轴垂直于棱镜的正三角形截面。设非偏振光的人射角为 $i$ ，而 e 光在棱镜内的折射线与镜底边平行如图所示。求人射角 $i$ 。已知 $n_{e}=1.49, n_{o}=1.66$ 。
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537
<image>The circuit for an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1. For the circuit of Fig. 7.1: calculate the gain of the amplifier.
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538
<image>The circuit for a non-inverting amplifier incorporating an ideal op-amp is shown in Fig. 7.1. The light-emitting diode (LED) emits light when the potential difference across it is at least 2.0 V. The current in the LED must not be greater than 20 mA. Determine the value of $V_{\text{IN}}$ for which the value of ...
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539
<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 $x=10$ m 处的速率。
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540
<image>如图所示乒乓桌的一边，乒乓球作斜抛运动。已知桌高 $h=1.0\ \mathrm{m}$ ，宽 $a=2.0\ \mathrm{m}$ 。欲使乒乓球能从桌面的另一边切过，并落在离该边水平距离 $b=0.50\ \mathrm{m}$ 处。求乒乓球的抛射角 $\theta_{0}$ 为多少？
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541
<image><image>An ideal gas, sealed in a container, undergoes the cycle of changes shown in Fig. 2.1. At point A, the gas has volume $2.4 \times 10^{-3} \mathrm{~m}^{3}$, pressure $1.6 \times 10^{5} \mathrm{~Pa}$ and temperature 300 K. The gas is compressed suddenly so that no thermal energy enters or leaves the gas dur...
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542
<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 $y=3 \times 10^{-2} \text{ cos } 4 \text{ π } t(\text{SI})$ 。以距 $A$ 点 5 m 处的 $B$ 点为坐标原点，写出波的表达式。
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543
<image>如图所示，载流长直导线的电流为 $I$ ，试求通过矩形面积的磁通量。
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544
<image>Two blocks $X$ and $Y$ are in contact on a frictionless horizontal surface. A constant $35 N$ force is applied to the right onto block $X$. What is the magnitude of the force that block $Y$ exerts onto block $X$?
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545
<image>A block of aluminium of mass 670 g is heated at a constant rate of 95 W for 6.0 minutes. The specific heat capacity of aluminium is $910 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$. The initial temperature of the block is $24^{\circ} \mathrm{C}$. In practice, there are energy losses to the surroundings. The actual varia...
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546
<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. Determine ...
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547
<image>如图所示为一装有喷嘴的水枪，在活塞上施加力 $F$ 时，水枪内部的水可以从喷嘴中喷出。设水枪的半径为 $R$ ，喷嘴半径为 $d$ 。求施加力 $F$时，水的喷出速度。
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548
<image>An amplifier circuit incorporating an ideal operational amplifier (op-amp) is used to amplify the output of a microphone. The circuit is shown in Fig. 7.1. When the potential at point $P$ is 48 mV , the output potential difference $V_{\text{OUT}}$ is 3.6 V . Determine the resistance of resistor R .
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549
<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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550
<image>Before testing the circuit shown at right, and taking the current and voltage readings, a student is asked to predict what the meters will read at each location indicated. What will be the ammeter reading at $A_{2}$?
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551
<image>有一半径为 $R$ 的圆线圈，通有电流 $I_{1}$ ，另有一通有电流 $I_{2}$ 的无限长直导线，垂直于圆线圈平面放置，如图所示。设圆线圈可绕 $y$ 轴转动。试求圆线圈在图示的位置时所受到的磁力矩；
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552
<image>For the circuit shown, all three light bulbs have the same resistance. The battery and wires have no resistance. How do the brightness levels of the bulbs compare?
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553
<image>Five identical light bulbs are connected into a circuit as shown. All wires are ideal with no resistance, and the ideal battery has emf $\xi$. When the switch S in the circuit is closed, aside from bulb #5, which bulbs brighten?
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554
<image>For the change in the gas described above, state the quantity of external work done on the gas.
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555
<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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556
<image>滑轮的转动惯量为 $J=0.5 \mathrm{~kg}\cdot\mathrm{~m}^{2}$ ，半径 $r=30 \mathrm{~cm}$ ，弹簧的劲度系数 $k=20 \mathrm{~N}/\mathrm{m}$ ，重物的质量 $m=2.0 \mathrm{~kg}$ 。当此滑轮一重物系统从静止开始启动，开始时弹簧没有伸长。如摩擦可忽略，问物体能沿斜面滑下多远？
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<image>A student designs the circuit shown in Fig. 8.1 in order to indicate changes in temperature of the thermistor T. Calculate the potential at point Q.
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558
<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 bandwidth
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559
<image>滑轮的转动惯量为 $J=0.5 \mathrm{~kg}\cdot\mathrm{~m}^{2}$ ，半径 $r=30 \mathrm{~cm}$ ，弹簧的劲度系数 $k=20 \mathrm{~N}/\mathrm{m}$ ，重物的质量 $m=2.0 \mathrm{~kg}$ 。当此滑轮一重物系统从静止开始启动，开始时弹簧没有伸长。如摩擦可忽略，问当物体沿斜面滑下 1.00 m 时，它的速率有多大？
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<image>如图所示，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 $\boldsymbol{B}$ ，其方向如图所示。把质量为 $m$ ，电量为 $q>0$ 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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<image>如图所示，滑轮的转动惯量 $\boldsymbol{J}=0.5 \mathrm{~kg} \cdot \mathrm{~m}^{2}$ ，半径 $r=30 \mathrm{~cm}$ ，弹簧的劲度系数 $k=2.0 \mathrm{~N} / \mathrm{m}$ ，重物的质量 $m=2.0 \mathrm{~kg}$ 。当此滑轮－重物系统从静止开始启动，开始时弹簧没有伸长。滑轮与绳子间无相对滑动，其它部分摩擦忽略不计。问物体能沿斜面下滑多远？当物体沿斜面下滑 1.00 m 时，它的速度有多大？
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562
<image>Three blocks, labeled A, B, and C, remain at rest on a table. The magnitude of the gravitational force on each block is indicated on the figure. What is the magnitude of the contact force on block C from block B?
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563
<image>如图所示，平行放置在同一平面内的三条载流长直导线，要使导线 $A B$ 所受的安培力等于零，则 $x$ 等于 $\\qquad$。
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564
<image>如力图5.7.1 所示，$A B, B C, C D$ 和 $D E$ 为质量可略的等长细线，长度均为 5 m ，$A$ 端和 $E$ 端悬挂在水平天花板上，$A E=14 \text{ m} . B$ 和 $D$ 是质量均为 $m_{0}=7 \text{ kg}$ 的相同小球。质量为 $m$ 的重物挂于 $C$ 点，平衡时 $C$ 点离天花板的垂直距离为 7 m 。试求质量 $m$ 。
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565
<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 $A B$ 延长线上与 $B$ 端相距 $d$ 的点 $P$ 处的电场强度。
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566
<image>如图所示，钟摆由一根均匀细杆和匀质圆盘构成，圆盘的半径为 $r$ ，质量为 $4 m$ ，细杆长为 $6 r$ ，质量为 $m$ ，试求这钟摆对端点 $O$ 轴的转动惯量。
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567
<image><image>直角三角板 $A B C$ 的边长 $B C=a, A C=b$ ，开始时 $A B$ 边靠在 $y$ 轴上，$B$ 与坐标原点 $O$重合。今使 $A$ 点单调地沿 $y$ 轴负方向朝 $O$ 点移动，$B$ 点单调地沿 $x$ 轴正方向移动，如图 1所示。最终 $A$ 点到达 $O$ 点，$A B$ 边倒在 $x$ 轴上，如图 2 所示。试求三角板从图 1 到图 2 的移动过程中，$C$ 点经过的路程 $s_{C}$ 。
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568
<image>已知一沿 $x$ 轴负方向传播的平面余弦波，在 $t=1/3\,\mathrm{s}$ 时的波形如图所示，且周期 $T=2\,\mathrm{s}$；写出 $Q$ 点的振动表达式。
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569
<image>A uniform thin rod of length $l$ and resistance $R$ has its end $A$ constrained to move along a vertical smooth rail, and its end $B$ constrained to move along a horizontal smooth rail. The resistance of the rails can be neglected. Assume there is a uniform magnetic field in the direction shown in the figure. In...
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570
<image>马丁炉填送矿石的起重机由卷扬机 $A$ 和移动的桥 $B$ 构成，卷扬机装有轮子，可沿轨道移动，轨道装在移动的桥 $B$ 上．卷扬机下部有一个倾覆操纵杆 $D$ ，用来安装送料铲 $C$ ．铲中料重 $Q=15 \mathrm{kN}$ ，与卷扬机铅垂轴线 $O A$ 相距 5 m ．欲使卷扬机不倾翻，卷扬机连同操纵杆的重量 $P$ 应为多少？假定卷扬机的重心在轴线 $O A$上，每个轮子到 $O A$ 轴的距离均为 1 m ．
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571
<image>二氧化碳激光器谐振腔的布儒斯特窗一般用锗来制成，使能对 $10.6 \mu \mathrm{~m}$ 附近的红外激光有较大的透射率。如果锗的折射率为 4.5，如图所示，试计算用锗制成的布儒斯特窗与放电管轴线所成之角 $\alpha$ 。
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572
<image>如图所示，轻弹簧的一端与质量为 $m_{2}$ 的物体连接，另一端与一质量可忽略的挡板相连，它们静止在光滑的桌面上。弹簧的劲度系数为 $k$ 。今有一质量为 $m_{1}$ ，速度为 $v_{0}$ 的物体向弹簧运动并与挡板发生正面碰撞。求弹簧被压缩的最大距离。
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573
<image>A student uses a negative temperature coefficient thermistor in the circuit of Fig. 7.1 to indicate changes in temperature. The thermistor has a resistance of $360\,\mathrm{k}\Omega$ at a particular temperature. For this temperature of the thermistor, calculate the magnitude of the reading on the voltmeter.
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574
<image>Many moons are in circular orbit about a planet. The angular velocity of a moon is $\omega$ when the orbit of the moon has a radius $r$ about the planet. Fig. 1.2 shows the variation of $r^{3}$ with $1 / \omega^{2}$ for these moons. $r^{3}$ Determine the speed of a moon in orbit around the planet with an orbital...
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575
<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”。设航天飞机主体携带一个太空探测器在偏心率 $e=$ $\sqrt{3} / 2$（偏心率 $e=C / A, C$ 为椭圆半焦距，$A$ 为椭圆半长轴）的椭圆轨道上航行到图中 $D$ 位置时，因为朝后发射探测器而使航天飞机主体进人圆轨道航行，探测器相对地球恰好沿抛物线轨道远去，试求航天飞机主体质量 $m_{1}$ 与探测器质量 $m_{2}$ 的比值 $\gamma(\gamma=$ $\left.m_{...
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576
<image><image>A beaker of boiling water is placed on the pan of a balance, as illustrated in Fig. 2.1. The water is maintained at its boiling point by means of a heater. The change $M$ in the balance reading in 300 s is determined for two different input powers to the heater. The results are shown in Fig. 2.2. Use data...
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577
<image><image>A steel sphere of mass 0.29 kg is suspended in equilibrium from a vertical spring. The centre of the sphere is 8.5 cm from the top of the spring, as shown in Fig. 2.1. The sphere is now set in motion so that it is moving in a horizontal circle at constant speed, as shown in Fig. 2.2. The distance from the...
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578
<image>如习题 7－47图所示，$C_{1}=10\,\mu\mathrm{F},\; C_{2}=5.0\,\mu\mathrm{F},\; C_{3}=5.0\,\mu\mathrm{F}$。求 $A$ ， $B$ 间的电容。
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579
<image>A light beam with wavelength $\lambda=532 \mu \mathrm{~m}$ is incident at the angle $\alpha_{0}$ on a profiled reflective grating with the groove period $d=1 \mu \mathrm{~m}$. Determine the value of angle $\alpha_{0}$ at which the first-order diffracted beam ( $m=1$ ) propagates perpendicularly to the grating pl...
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580
<image>如图所示，一对伞形齿轮 A 和 B，其圆半径分别为 $r_{1}$ 和 $r_{2}$ ，对通过各自的对称轴的转动惯量为 $J_{1}$ 和 $J_{2}$ 。开始时 A 轮以角速度 $\omega_{0}$ 转动，然后与 B 轮正交啮合，求啮合后两轮的角速度。
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581
<image>In a setup similar to that of Young's experiment, it was found that the interference pattern disappears when the separation between the pinholes $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ in the opaque screen becomes equal to $d=0.6 \mathrm{~mm}$. Determine diameter $D$ of the extended source of light if the distance...
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582
<image>由长为 $l$ 的轻杆与半径为 $r$ 的匀质圆盘组成两个摆，其中另一个摆的圆盘装在杆端的光滑转轴上，可相对地自由转动如图（b）所示；当摆作微小振动时，试求该摆的周期。
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583
<image>一轻绳绕过一定滑轮，滑轮轴光滑，滑轮的质量为 $m/4$ ，均匀分布在其边缘上。绳子的一端有一质量为 $m$ 的人 A 抓住了绳端，而在绳的另一端系了一质量为 $m/2$ 的重物 B。设人从静止开始相对绳以匀速向上爬时，绳与滑轮间无相对滑动，求重物 B 上升的加速度？（已知滑轮对过滑轮中心且垂直于轮面的轴的转动惯量 $J=mR^{2}/4$。）
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584
<image>一同轴电缆，由半径为 $a$ 的导体圆柱芯线及内，外半径分别为 $b$ 和 $c$ 的同轴导体圆筒组成，如图所示。筒与柱间有相对磁导率为 $\mu_{\mathrm{r}}$ 的磁介质，导体圆柱和圆筒的磁导率近似为 $\mu_{0}$ 。电缆工作时，电流由圆柱流入，沿圆筒济回，而且在导体横截面上电流是均匀分布的。试求一段长为 $l$ 的电缆所储存的磁场能量。
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585
<image> 系统及几何参数如图示，小物块 $P, Q$ 与两个斜面间无摩擦，质量同为 $m$ ，轻绳与小的轻滑轮之间无摩擦，长度几乎也是 60 cm （即与右边斜面长度相同）。将系统从静止开始自由释放，直到 $Q$ 几乎到达 $B_{2}$ 处为止。计算过程中 $P, Q$ 运动加速度大小 $a$ ；
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586
<image>At which time is the car the greatest distance from the origin?
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587
<image>Determine the angle of incidence of a light beam $\alpha_{0}$ onto the boundary between two dielectrics with refractive indices $n_{1}$ and $n_{2}$, and the state of its polarization if the reflected beam is practically absent and the intensity of refracted beam $I_{2}$ is equal to that of incident wave $I_{1}$....
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588
<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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589
<image>A particle moves with velocity $\\vec{v}$ in the domain of superposition of two mutually coherent plane waves. Owing to the Doppler effect, the waves-scattered by the particle-have frequencies $\\omega_{1}$ and $\\omega_{2}$, different from the frequency $\\omega_{0}$ of the plane waves incident on it. Consideri...
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590
<image>如图所示，物体 1 和 2 的质量分别为 $m_{1}$ 与 $m_{2}$ ，滑轮的转动惯量为 $J$ ，半径为 $r$ 。 如物体 2 与桌面间为光滑接触，求系统的加速度 $a$ 及绳中的张力 $T_{1}$ 和 $T_{2}$（设绳子与滑轮间无相对滑动，滑轮与转轴无摩擦）。
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591
<image>如力图 7.21 .1 所示，质量为 $M$ ，长为 $L$ 的均匀刚性细杆的一端悬挂，可在铅垂面内绕悬点无摩擦地摆动。质量为 $m=M / 3$ 的小虫相对杆以速度 $v$ 缓慢地沿杆向下爬行，开始时，杆静止并与竖直线夹角为 $\theta_{0}$（设 $\theta_{0}$ 很小）；小虫位于杆上端的悬点，放开后，杆开始摆动，小虫开始爬行，试求：小虫沿杆爬行 $l$ 距离时，杆摆动的圆频率；
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592
<image>介质块缓慢进人空气平行板电容器过程中外力和电源作功问题。图示电路中空气平行板电容器可处理为真空平行板电容器，电键 K 合上后，充电过程已完成。图中外力 $\boldsymbol{F}$ 以朝右为正方向画出， $\boldsymbol{F}$ 的真实方向也可能朝左。若将电键 K 断开，利用图示外力 $\boldsymbol{F}$ 让介质块缓慢地全部进人电容器两极板之间，试求全过程 $\boldsymbol{F}$ 作功量 $A_{1}$ ；
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593
<image>如电图 2.5.1 所示，$C^+$和$C^-$是沿 $z$ 轴放置的两根互相绝缘的长直非磁性导体，其中的电流分别沿 $z$ 轴的正方向和负方向流动，电流强度均为 $I$。电图 2.5.1 中画斜线的部分是两导体的正截面，它们分别是 $xy$ 平面中的部分圆，两圆的直径均为 $D$，两圆心的间距为 $\frac{D}{2}$，不难算出，两导体正截面的面积均为 $\left(\frac{1}{12}\pi+\frac{1}{8}\sqrt{3}\right)D^{2}$。每一根导体中的电流均匀地分布在自身的正截面内。试求两根导体之间空白区域内的磁场分布 $B(x, y)$。
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594
<image>一简谐振动用余弦函数表示，振动曲线如图所示，则此简谐振动的三个特征量分别为 $A=$ $\bullet$ ，$\bullet=$ $\bullet$ ，$\bullet_{0}=$ $\bullet$。
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595
<image>在坚直平面上设置 $O x y$ 坐标面，形如图示的星形线其参数方程为 $$ x=A \cos ^{3} \phi, y=A \sin ^{3} \phi . $$ （注意，$\phi$ 并非 $O x y$ 坐标面上矢径的幅角） 沿参数 $\phi$ 从 $\pi$ 到 $\frac{3}{2} \pi$ 一段曲线设置一条无摩擦的轨道，令小球 $P$从 $A$ 无初速地沿轨道上侧下滑。 确定 $P$ 离开轨道的坐标值 $x_{0}$
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596
<image>在坚直平面上设置图示的水平 $x$ 轴和坚直向下的 $y$ 轴，$t=0$时刻位于 $x=0, y=0$ 处的小水桶从静止出发，以匀加速度 $a_{0}$ 沿 $x$轴运动。过程中桶底小孔向下漏水，单位时间漏水质量为常量 $m_{0}$ 。略去漏水相对水桶的初速度，在任意 $t_{0}>0$ 时刻，试求漏水迹线中的质量线密度 $\lambda$ 随 $y$ 坐标的分布函数，
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597
<image>A plane wave with free-space wavelength $\lambda_{0}$ is normally incident on a plane-parallel glass plate of stepped thickness $d_{1}$ and $d_{2}$ and refractive index $n$. The plate is submerged in a liquid with refractive index $n_{0}$. Determine the phase difference $\Delta \phi_{12}$ between the wave oscill...
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598
<image>如图所示，直杆 $AB$ 两端可以分别在两个固定而垂直的直线导槽内滑动。试求杆上任意点 $M$ 的轨迹方程。已知 $M$ 点距 $A$ 端的距离为 $a$，距 $B$ 端的距离为 $b$；又设杆的 $A$ 端的运动速率为 $v_{0}$ 。
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599
<image>For the circuit shown, the three light bulbs have identical resistance $R$, the battery is ideal, and all wires have no resistance. Which light bulbs become dimmer or go out completely when the switch, S, in the circuit is closed?
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