大学物理双语练习题
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Fundamentals of Physics-Test 5EXAMINEE NAME:Solve 8 of the following 10 problems.1. A particle moves so that its position as function of time in SI units isk t j t i r ++=24. Write expressions for (1) its velocity and (2) its acceleration asfunctions of time.2. The potential energy of a diatomic molecule (a two-atomic system like 2H ) is given by 612rB r A U -=, where r being the separation of the two atoms of the molecule and A and B being positive constants, This potential energy is associated with the force that binds the two atoms together. Find the equilibrium separation, that is, the distance between the atoms at which the force on each atom is zero.3. The figure shows a uniform disk, whose mass is M andwhose radius is R, mounted on a fixed horizontal axle (therotational inertia about the axis can be regarded as2/2MR ). A block, whose mass is m, hangs from amassless cord that is wrapped around the rim of the disk.Find (1) the acceleration of the falling block (assuming thatit does fall); (2) the angular acceleration of the disk; and (3)the tension in the cord. The cord does not slip, and there is no friction at the axle.4. A transverse sinusoidal wave of wavelength 20 cm is moving along a string, towardincreasing x. The transverse displacement of thestring particle at x=0 as a function of time isshown in the Figure. Find (1) the amplitude, (2)period of wave, (3) the velocity of propagation ofthe wave? (4) Write the equation for the wave with all the constants evaluated.5. Pressure p , volume V , and T for a certain material are related byV BT AT p /)(2-=, where A and B are constants. Find an expression for the work done by the material if the temperature changes from 1T to 2T while thepressure remains constant.6. For the hypothetical speed distribution for N gasparticles shown in the Figure. [2)(v C v P = for 0)(;00=≤<v P v v for 0v v >]. Find (1) anexpression for C in terms of N and 0v , (2) theaverage speed of the particles.7. 4 electrons are equally spaced and fixed around a circle of radius R. Relative to V=0 at infinity, what are the electric potential and electric field at the center of the circle due to these electrons?8. Charge is distributed uniformly through the volume of an infinitely long cylinder of radius R. Show that at a distance r from the cylinder axis (for r<R), )2/(0ερr E =, where ρ is the volume charge density.9. Two long wires a distance d apart carry equalanti-parallel current i, as in the Figure. (1) Show that themagnitude of the magnetic field at point P, which isequidistant from the wires, is given by)4(2220d R id B +=πμ. (2) In what direction does B point? 10. A rectangular loop of wire with length a, width band resistance R is placed near an infinitely longwire carrying current i, as shown in Figure. Thedistance from the long wire to the center of theloop is r. Find (1) the magnitude of the magneticflux through the loop and (2) the current in the loop as it moves away from the long wire with speed v .。
1. S: 2kv dtdva -==2kv dxdvv dt dx dx dv -==k d x v dvxx vv -=⎰⎰)(ln00x x k v v--= )(00x x k e v v --= (answer)2. S: j t i t dt rd v )3cos 15()3sin 15(+-== jt i t dtv d a )3sin 45()3cos 45(-+-==()()j t i t j t i t v r)3cos 15()3sin 15()3sin 5()3cos 5(+-⋅+=⋅j j t t i i t t⋅⋅+⋅⋅-=)3c o s 3s i n 75()3sin 3cos 75( 0= (proved c)3. S: dtdv v m k m f a =-==dt mkv dv t t v v -=⎰⎰0)(0t mkv t v -=0)(ln t m ke v t v -=0)( (answer) D: t m k e v dtdxv -==0dt e v dx t m k tt x -⎰⎰=00)(0kmv x e kmv ekmv t x t m k t t mk 0max 00),1()(=-=-=--4. S: )()32(j y d i dx j i x r d f dw+⋅+=⋅=dy xdx dw w fi32+==⎰⎰dy xdx 323342⎰⎰--+== -6 J (answer)5. S: 23230.60.4)0.30.4(t t t t t dtddt d +-=+-==θω, t t t dtddt d 60.6)30.60.4(2+-=+-==ωα 0.40300.60.4)0(2=⨯+⨯-=ω (answer of a)0.28)0.4(30.40.60.4)0.4(2=⨯+⨯-=ω rad/s (answer of a ) 60.266)0.2(=⨯+-=α rad/s 2 (answer of b )t t 60.6)(+-=α is time varying not a constant (answer of c) 6. S: ω20031222ML L v m L mv +⋅= MLmv ML L mv 4343020==ω (answer a))c o s 1(2)31(21m a x 22θω-=LMg ML ]1631[cos 2221maxgLM v m -=-θ (answer b) 7. G: m =1.0g, M =0.50kg, L =0.60m, I rod =0.0602m kg ⋅,s rod /5.4=ωR:I sys , v 0S: I sys =I rod +(M+m)L2=0.060+(0.50+0.0010)×0.602= 0.24 2m kg ⋅(answer)the system ’s angular momentum about rotating axis is conservative in the collision.sysI L mv ω=0s m mL I v sys/108.160.00010.024.05.430⨯=⨯⨯==ω (answer )D: The bullet momentum 0v m p=(before impact), its angular momentumabout rotating axis can be expressed as L mv 0(a scalar) 8. S:γ==00.800x xt v c -∆==0811800.600 3.0010t t γ∆=∆=⨯⨯ 9. S: 202202)(mc E cp E E γγ==+=222c p m c m c m c =10. S: 0i n t =-=∆n e t n e t W Q E n e t n e t W Q = 1(3010)(4.0 1.0)2=-- J 30= (answer)11. S: from nRT PV =and K T A 300= we can get:KT K T C B 100300== (answer of a)Change of internal energy between A and B:0)(23int =-=∆A B T T k n E (answer of b)The net work of the cycle:))(100300()13(2121m N AC BC W ⋅-⋅-=⋅=J 200= (answer of c) From the first law : W E Q +∆=int we can derive:the net heat of the whole cycle is J W Q 200== (answer)12. S: 131)(320===⎰⎰∞F v Av dv Av dv v p F33FvA =(answer of a ) F F v a v g v Av dv vAv v F4341420===⎰13. G: T 1=T 2=T , m 1, p 1, v rms,1, m 2, p 2=2p 1, v avg,2 = 2v rms,1 R: m 1 / m 2 S: v avg,2 =1.602m kTv rms,1 = 1.731m kTv avg,2 = 2v rms,167.4)60.173.12(221=⨯=m m (answer) 14. S: dE int =dQ – dWd Q = dE int + dW = n C v dT+pdV VdVnR T dT nC dV T p T dT nC T dQ dS v v +=+==if i f v VV v T T V V nR T T nC V dVnR T dT nC ds S f i filnln +=+==∆⎰⎰⎰ 15. S: dA E q θεcos 0⎰=212100)0.60100(1085.8⨯-⨯⨯=- C 61054.3-⨯= 16. S: 2041)(r Qr E πε=(R < r <∞) dr rQ dr r E udV dU 2022208421πεπε=⋅== RQ r dr Q udV U R0220288πεπε===⎰⎰∞(answer) RQ r dr Q U r r Rεπεεπε02202*88==⎰∞(answer ) 18. S: in the shell of r – r + drdr r R r dV r dq 204)/1()(πρρ-==)34(31)/(4)(4303200r Rr dr R r r dq r q r-=-==⎰⎰πρπρfrom the shell theorems , within the spherical symmetry distribution )34(12)(41)(20020r Rr Rr r q r E -==ερπε (answer of b)R r r R Rdr dE 320)64(12*00=⇒=-=ερ 00200*max 9])32(3324[12)(ερερRR R R R r E E =-⨯== 19. S: j yV i x V V gradV y x E∂∂-∂∂-=-∇=-=),( )0.20.2(y x x VE x +-=∂∂-= x yV E y 0.2-=∂∂-= )/(480.2)0.20.2()0.2,0.2(m V j i j x i y x E--=-+-=20. S: Q in = - q , Q out = q (answer ) 1010241241)0(R qq V q πεπε==104)0(R qV in πε-=204)0(R q V o u t πε=)0()0()0()0(out in q V V V V ++= )11(4210R R q +=πε21. S: from the planar symmetry and superposition principle, Emust in normal direction of the plates and 1σ,2σ,3σ,4σ must be const. Fromcharge conservationA Q S =+)(21σσ ⇒ SQ A=+21σσ (1) B Q S =+)(43σσ ⇒ SQ B=+43σσ (2) Apply Gauss ’ law in the closed surface shown in Fig. 032=+σσ (3)within the metal, 0=p Ewhich leads to002222432104030201=-++⇒=-++σσσσεσεσεσεσFrom(1), (2), (3), (4) yield:⎪⎪⎩⎪⎪⎨⎧-=-=+==S Q Q SQ Q B AB A 223241σσσσ (answer of a) (6 points) 004030201122222εεσεσεσεσS Q Q E BA p -=--+= (1 point) 004030201222222εεσεσεσεσS Q Q E BA p +=+++=(1 point) (answer of b) d S Q Q d E d E V BA p AB 012ε-==⋅= (2 points) (answer of c)27.33()(32)18w F x dx x dx J ==+=⎰⎰;at x=3m212W mV =, 6/V m s =。
Fundamentals of Physics-Test 4EXAMINEE NAME:Solve 8 of the following 10 problems.1.The position of an electron is given by k j t i t r 0.20.40.32+-= (where t is inseconds and the coefficients have the proper units for r to be in meters). Find theexpressions for (1) its velocity )(t v , and (2) its acceleration )(t a .2.Several planets possess nearly circular surrounding rings.Consider a homogeneous ring of mass M and radius R. (1)What gravitational attraction does it exert on a particle ofmass m located a distance x from the center of the ringalong its axis? (2) Suppose the particle falls from rest asa result of the attraction of the ring of matter. Find an expression for the speed with which it passes through the center of the ring.3.Two blocks of mass 1m and 2m (21m m <) are connected by a massless cord thatis wrapped around a uniform disk of mass M and radius R,whose rotational inertia about the axis is 2/2MR I =. Thedisk can rotate without friction about a fixed horizontal axisthrough its center; the cord cannot slip on the disk. Thesystem is released from rest. Find (1) the magnitude of theacceleration of the blocks, (2) the tension 1T in the cord at the left, and (3) thetension 2T in the cord at the right.4.A sinusoid transverse wave is travelingalong a string toward decreasing x. Thefigure shows a plot of the displacement asa function of position at time t=0. Thestring tension is N 6.3, and its lineardensity is m g /25. Find (1) theamplitude, (2) the wavelength, (3) thewave speed, and the period of the wave. (4) Write an equation describing the traveling wave.5.Show that the ideal gas equation nRT pV =can be written in the following alternative form M RT p /ρ=, whereρ is the mass density of the gas and M the molar mass.6.One mole of an ideal mono-atomic gas is takenthrough the cycle in the Fig. (1) How much workis done by the gas in going from state a to state calong path abc? What are the changes in internalenergy and entropy in going from b to c? Expressall answers in terms of the pressure 0p , volume 0V , and temperature 0T of statea.7.4 electrons are equally spaced and fixed around a circle of radius R. Relative to V=0 at infinity, what are the electric potential and electric field at the center of the circle due to these electrons?8.A non-conducting rod of length Lhas charge -q uniformly distributedalong its length. (1) What is the linear charge density of the rod? (b) What is the electric field at point P, a distancea from the end of the rod?9.A particle of charge magnitude q and mass m moving perpendicular to a uniformmagnetic field B at speed v . The particle will move in a circle. Find (1) theradius of the circular path, (2) the period of the motion.10. A coil C of N turns is placed around a longsolenoid S of radius and n turns per unit length, asin the Fig. Show that the mutual inductance for thecoil-solenoid combination is given bynN R M 20πμ=.。
英文版物理题以下就是小编给大家盘点的英文版物理题,仅供大家参考。
以下是一些英文版物理题:1.A50kg block is resting on a frictionless horizontal surface.A force of100N is applied to the block in the horizontal direction.What is the acceleration of the block?2.An object is thrown vertically upwards with an initial velocity of20m/s.忽略空气阻力,计算该物体达到最高点所需的时间和高度。
3.A ball is thrown horizontally with a velocity of10m/s from a height of5m.Calculate the horizontal distance the ball travels before hitting the ground.4.A10kg mass is attached to a spring with a spring constant of50N/m.The mass is displaced 0.2m from its equilibrium position and released. Calculate the maximum speed of the mass as it oscillates back and forth.5.A current of5A flows through a resistor witha resistance of10Ω.Calculate the potential difference across the resistor.These are just a few examples of英文版物理题.The specific questions and topics will depend on the level of physics and the course curriculum.。
中南大学双语物理月日试卷09Question One. Fill in the blanks (24 marks total, 4 marks each)1. The surface charge density of a conductor of arbitrary shape in vacuum is (,,)x y z σ. Then the electric field near the conductor ’s surface has magnitude and its direction is .2. The electric potential at points in an xy plane is given by 22210V x y =--+. Find the magnitude and direction of the electric field at point (1, 2). E = ___, and the direction is __ .3. An alternating voltage of the form 0sin V V t ω=is applied across an air-filled parallel-plate capacitor of areaA and separation d . Find (a) the electric flux E Φthrough a surface between the two plates of the capacitor with area A and parallel to the plates, and (b) the displacement current d i in the capacitor. E Φ= ___, d i =____.4. A conducting rod MN of length L located on the horizontal plane rotates about point O , adistance L /3from end N, at a constant angular speed ω .A uniform magnetic field B pointsupward vertically (Fig.1-1). The magnitude of the motional emf in the rod is . Which endof the rod has higher potential? . 5. In vacuum, the energy density of an electromagnetic wave at a point is . The ratio of E to B is .6. The energy required for the quantum jump of the electron in ground state to the energy level with n =4 in hydrogen atom is . The number of spectra lines that this excited electron can emit is .Question Two. Multiple-choice questions (30 marks total, 3marks each)1. Figure 2-1 shows the electric field lines of concentric conducting solid sphere and conductingspherical shell. Then the spherical shell is (a) positively charged ;(b) electrically neutral;(c) negatively charged; (d) not enough information.2. An infinitely long straight charged plastic rod with uniform linear charge density λ is placed invaccum, and then electric field energy density at a point, a distance r from the rod, is given by (a) 22202r λεπ; (b) 22204r λεπ;(c) 22206r λεπ; (d) 22208rλεπ. 3. An electron with charge e moves in a circle of radius r at a constant speed v , and then its magnetic dipolemoment is given by (a) 232er vπ;(b) 12evr ; (c) 22er v π; (d) 2212ev r . 4. A particle of charge q and mass m moves at a radius r in a uniform magnetic field B , and then the particle ’skinetic energy is given by (a) 2222q B r m ;(b) 222mq B r ;(c) 222mB r q; (d) 222mq r B . 5. The diameter of a circular loop is equal to the side of a square. If the two loops carry the same current, the ratio of magnetic field magnitude B C at the center of the circular loop to the magnetic field magnitude B S at the center of the square /C S B B is (a)0.8;(b)1.00; (c) 1.22; (d) 1.11.6. Within which kind of material do magnetic domains exist?(a) Diamagnetic material ;(b) Paramagnetic material; (c) Ferromagnetic material; (d) None of above.7. A plane electromagnetic wave travels along positive x -axis , and then its wave function can be expressed as (a) sin(),sin()m m E E kx t B B kx t ωω=+=-;(b) sin(),sin()m m E E kx t B B kx t ωω=-=-; (c) sin(),sin()m m E E kx t B B kx t ωω=+=+;(d) sin(),sin()m m E E kx t B B kx t ωω=-=+.8. A beam of light with wavelength λ travels along the +x -axis. If the uncertainty in wavelength is represented by Fig. 1-1Fig.2-1λ, then using Heisenberg ’s uncertainty principle 2x x p ≥ (here /2h π=), the uncertainty inphoton ’s position ?x can be expressed as (a) 22x πλλ?≥?;(b) 24x πλλ≥?; (c) 24x λπλ?≥?; (d)22x λπλ?≥?. 9. For a given value of n =2, the possible values of the magnitude of orbital angular momentumfor an electron confined to an atom are (a) 0,; (b) 0,; (c) 0,; (d) .10. There are different types of artificial electron traps. Which one is not an electron trap below?(a) nano-crystallites ;(b) quantum dots; (c) quantum corrals;(d)quantum numbers.Question Three. Calculation problems (40 marks total, 10 marks each)1. A solid nonconducting sphere of radius R has anonuniform charge distribution of volume charge density 20/kr e r ρρ-=, where ρ0 and k ar e constant and r is the distance from the center ofthe sphere. (a) Calculate the total charge of the sphere. (b) Determine the distribution of electricfield inside and outside the charged sphere.2. A charge q is uniformly distributed along a nonconducting rod of length 2l (Fig. 3-1). Assumingthat V =0 at infinity, find (a) the electric potential at point P , a distance d from the midpoint of therod along the perpendicular bisector of the rod, and (b) the work done by the electric field inbringing a point charge q 0 from infinity to point P .(Hint:ln(x C =+)3. A straight wire ab of length L carrying current i 2 is placed near a long straight wire cd carryingcurrent i 1 in the same plane. The straight wire ab makes an angle α with the long straig ht wire and end a is at a distance D away from it, as shown in Fig.3-2. Calculate the force acting on wire ab due to wire cd .4. A toroid with N turns has a rectangular cross-section as shown in Fig.3-3. If the toroidcarries a current i , the magnetic flux through the cross-section can be expressed as02Nih μπΦ=. (a) Find the ratio of R 2 to R 1, where R 2 and R 1 are the outer radius andthe inner radius of the toroid respectively. (b) If h =0.01 m and N=100, determine theself-inductance of the toroid. (c) If the current in the toroid is 0cos i i t ω=, where i 0 is aconstant, calculate the induced emf in the toroid. Question Four. Proof (6 marks)A beam of light of wavelength λ is incident on the surface of a metal and knocks outphotoelectrons which pass through a slit and then enter a uniform magnetic field, where the photoelectrons would undergo a uniform circular motion, as shown in Fig.4-1. Suppose that the maximum radius of the uniform circular motion is R . Show that the wor k function Φ of the metal is given by 222 2e hce B R m λΦ=-. Fig. 3-1 Fig. 3-2Fig. 3-3Fig. 4-1。
2010─2011年 第 一 学期 《 大学物理》双语试卷( A 卷)注意:1、本试卷共 3 页; 2、考试时间: 120 分钟 3、姓名、学号必须写在指定地方 4、可以携带计算器常用常数:R =8.31J·mol -1·K -1k=1.38×10-23J·K -1c=3.00×108m/sg=9.8m/s 2 N A =6.02×1023mol -1 1atm=1.013×105PaⅠ. Filling the Blanks(每小题 2 分,共 20 分)1.一空气平行板容器,两板相距为d ,与一电池连接时两板之间相互作用力的大小为F ,在与电池保持连接的情况下,将两板距离拉开到3d ,则两板之间的相互作用力的大小是2. There is a point charge of electric quantity Q at the center of a cube, the electric flux through one surface of cube is3.如图1,一根无限长直导线通有电流I ,在P 点处被弯成了一个半径为2R 的圆,且P 点处无交叉和接触,则圆心O 处的磁感强度大小为_______________,方向为______________4. As shown in the figure 2, in the vacuum let the metal sphere with radius R be grounded, place a point charge q with a distance r (r>R) away from the center O of the sphere, the total induced charge on the surface of the metal sphere is5. 如图3所示,AOC 为一折成∠形的金属导线(AO =OC = L ),位于xoy 平面上. 磁感应强度为B 的匀强磁场垂直于xoy 平面. 当AOC 以速度v 沿x 轴正向运动时,导线上A 、C 两点间的电势差U AC = ,当以速度v 沿y 轴正向运动时A 、C两点中 点电势高.6.一空气平行板电容器,接电源充电后电容器中储存的能量为W 0,在保持电源接通的条件下,在两极间充满相对电容率为rε的各向同性均匀电介质,则该电容器中储存的能量W 为________________7. The period of a pendulum(单摆) is measured to be 3.0s in the reference frame of the pendulum. The period when measured by an observer moving at a speed of 0.95c relative to the pendulum is8.把一个静止质量为0m 的粒子,由静止加速到0.6v c =(c 为真空中的光速)需做功为 Ⅱ.Choose the Correct Answer(每小题 3 分,共 30 分)1. 关于刚体对轴的转动惯量,下列说法中正确的是 ( d ) (A) 只取决于刚体的质量,与质量的空间分布和轴的位置无关. (B) 取决于刚体的质量和质量的空间分布,与轴的位置无关. (C) 只取决于转轴的位置,与刚体的质量和质量的空间分布无关.(D) 取决于刚体的质量,质量的空间分布和轴的位置.2.When a mass point is in a circular motion then ( b ) (A) The tangential acceleration definitely change, the normal acceleration also change.(B) The tangential acceleration may not change, the normal acceleration definitely change.Figure 3(C) The tangential acceleration may not change, the normal acceleration does not change.(D) The tangential acceleration definitely change, the normal acceleration does not change.3.两容器内分别盛有氢气和氦气,若它们的温度和质量分别相等,则:( a )(A) 两种气体分子的平均平动动能相等. (B) 两种气体分子的平均动能相等. (C) 两种气体分子的平均速率相等. (D) 两种气体的内能相等.4. As shown in the Fig , an object with mass m tied by a thin thread, which isparallel to an inclined plane, is placed on a smooth inclined plane. If the inclined plane moves toward to left with acceleration, when the object departs the inclined plane, its acceleration is (d )(A) sin g θ (B) cos g θ (C) tan g θ (D)cot g θ5. 某时刻驻波波形曲线如图3所示,则a 、b 两点的相位差是(a )(A) π (B) 2π(C) 54π (D) 06. An uniform thin rod OA is pivoted on a frictionless hinge at one end O, as shown in Fig . The rod is held at rest horizontallyand then released. When it reaches the verticalposition which one is correct of following statements ( c )(A) Angular velocity varies from small to big, angular acceleration remains unchanged(B) Both angular velocity and angular acceleration vary from small to big(C) Angular velocity varies from small to big, while angular acceleration varies from big to small(D) Angular velocity remains unchanged, angular acceleration equals zero7. 如图所示系统置于以2g的加速度上升的升降机内,A 、B 两物体质量相同均为m ,A 所在的桌面是水平的,绳子和定滑轮质量不计,若忽略滑轮轴上和桌面上的摩擦并不计入空气阻力,则绳子张力为 ( c )(A) mg (B) 14mg (C) 34mg (D) 58mg8. Which of the following statements is NOT true: ( ) (A) No two electric field lines can cross each other(B) The electric field vector is tangent to the electric field line at each point. (C) Magnetic field lines are always closed curves(D) The magnetic fields can be produced by current, so magnetic fields have sources9. 在某地发生两件事,静止位于该地的甲测得时间间隔为3s ,若相对甲以4c/5(c 表示真空中光速)的速率作匀速直线运动的乙测得时间间隔为:(A) 2.4s (B) 4s (C) 3.6s (D) 5s ( )10. A Carnot heat engine works between the high temperature source of 327o C and low temperature heat source of 27 o C. It absorbs 2000J heat in each cycle, how many work does it do on exterior ( b ) (A) 2000J (B)1000J (C) 4000J (D) 500JⅢ.1.有一质量为m1、长为l 的均匀细棒,可绕过棒端且垂直于棒的光滑水平固定轴O 在竖直平面内转动.棒静止处于竖直位置,另有一水平运动的质量为m2的小物块,从侧面垂直于棒与棒的另一端A 相撞,设碰撞时间极短,已知小物块在和,方向如右图所示. 求碰撞后细棒(已知棒绕O 点的转动惯量J=m 1l 2/3).分)Ⅳ.A rectangular loop of width a and length b islocated near a long wire carrying a current I (Fig. 8). The distance between the wire and the closest side(10分)Figure 7Ⅴ如图9所示,一段长度为 l的直导线MN , 水平放置在载电流为I 的竖直长导线旁与竖直导线共面,并从静止由图示位置自由下落,求经过t 秒时导线两端的电势差。
物理练习题英语Physical Exercise Questions in English1. A car is traveling at a constant speed of 60 km/h. How much time will it take to cover a distance of 240 km?Solution:To find the time, we can use the formula: time = distance / speed.Substituting the given values, we have: time = 240 km / 60 km/h.Simplifying the equation, we get time = 4 hours.2. An object is dropped from a height of 100 meters. What will be its velocity after 2 seconds?Solution:The velocity of a freely falling object can be calculated using the formula: velocity = initial velocity + (acceleration × time).Since the object is dropped, the initial velocity is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s².Substituting the values, we have: velocity = 0 m/s + (9.8 m/s² × 2 s).Simplifying the equation, we get velocity = 19.6 m/s.3. A bullet is fired horizontally from a gun with an initial velocity of 400 m/s. How far will it travel in 10 seconds?Solution:Since the bullet is fired horizontally, there is no vertical acceleration. Therefore, the horizontal distance can be calculated using the formula: distance = initial velocity × time.Substituting the given values, we have: distance = 400 m/s × 10 s.Simplifying the equation, we get distance = 4000 meters.4. A block of mass 2 kg is placed on a horizontal surface. There is a force of 10 N acting on the block in the positive x-direction. What is the acceleration of the block?Solution:The force acting on an object can be related to its mass and acceleration using Newton's second law: force = mass × acceleration.Given that the force is 10 N and the mass is 2 kg, we can rearrange the equation to find the acceleration: acceleration = force / mass.Substituting the values, we have: acceleration = 10 N / 2 kg.Simplifying the equation, we get acceleration = 5 m/s².5. A spring has a spring constant of 100 N/m. How much work is done in stretching the spring by 0.05 meters?Solution:The work done in stretching a spring can be calculated using the formula: work = (1/2) × spring constant × (change in length)².Given that the spring constant is 100 N/m and the change in length is0.05 meters, we have: work = (1/2) × 100 N/m × (0.05 m)².Simplifying the equation, we get work = 0.125 Joules.6. A ball is thrown vertically upwards with an initial velocity of 20 m/s. How high will it rise?Solution:The maximum height reached by a vertically thrown object can be calculated using the formula: height = (initial velocity²) / (2 × acceleration due to gravity).In this case, the initial velocity is 20 m/s and the acceleration due to gravity is 9.8 m/s².Substituting the values, we have: height = (20 m/s)² / (2 × 9.8 m/s²).Simplifying the equation, we get height = 20.41 meters.These are some physical exercise questions in English along with their solutions. Practice these problems to enhance your understanding of physics concepts and problem-solving skills.。
华东理工大学2014–2015学年第二学期《大学物理》双语课程期中考试试卷2015.4开课学院:理学院专业:中德环境/电子考试形式:闭卷,所需时间120分钟考生姓名:学号:班级任课教师谢海芬Part A.(45points)Each question is worth 3points.Write the letter corresponding to the best answer to the question to the answer sheet below.1.An object moves in a circle of radius R at constant speed with a period t .If you want to change only the period in order to cut the object's acceleration in half,the new period should be:A.4tB.t/2C.2tD.2/t E t22.Two identical stones are dropped from rest and feel no air resistance as they fall.Stone A is dropped from height h ,and stone B is dropped from height 2h .If stone A takes time t to reach the ground,stone B will take time:A.t/2B.4tC.t 2D.2tE.2/t upper stringlower string3.A heavy ball is suspended as shown.A quick jerk on the lower string will break that string but a slow pull on the lower string will break the upper string.The first result occurs because:A.the force is too small to move the ball;B.the ball has inertia;C.action and reaction is operatingD.air friction holds the ball backE.the ball has too much energy 题序Part A Part BPart C 总分123得分评卷人4..Two particles of equal mass undergo a two dimensional elastic collision(not headon),the target particle being initially at rest.The angle between the velocityvectors of the two particles after the collision is:A.less than90°B.greater than90°C.equal to90°D.depends on the speed of the incident particleE.cannot be predicted5.A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t.The speed of the particle is proportional to:(A)1/t(B)t(C)2t(D)t(E))1/t6.Three objects are connected by massless wires over a massless frictionless pulley as shown in Fig..The tension in the wire connecting the10.0-kg and15.0-kg objects is measured to be133N.the tension in wire A is closest to:A.245N;B.280N;C.87.5N;D.517N;E.333N7.The sketch below shows a block of mass m on an inclined plane that makes an angle θwith the horizontal direction.The block is being held stationary by the force of static friction between the block and the plane.The coefficient of static friction between the block and the plane is u s.The magnitude of the net force exerted on the block is:A.u s mg cosθ D.mg cosθB.u s mg sinθ E.mg sinθC.zero8.The pilot of a light airplane with an airspeed of200km/h wants to fly due west. There is a strong wind of120km/h blowing from the north.If the pilot points the nose of the airplane north of west so that her ground track is due west,what will be her groundspeed?A.160km/h.B.120km/hC.80km/hD.180km/hE.It would impossible to fly due west in this situation9.A projectile is fired straight upward from Earth’s surface with a speed that is half the escape speed.If R is the radius of Earth,and air resistance is ignored,the greatestdistance from the center of Earth that the projectile will reach is:A.5R /4;B.4R /3;C.3R /2;D.2R;E.4R10.A particle begins with kinetic energy K 1at point A.It moves along path 1to point B,then along path 2back to point A.It ends with kinetic energy K 2where K 2>K 1.Which statement below can one correctly conclude?A.The net force on the particle was always centripetal.B.The potential energy of the system decreased.C.At least one non-conservative force acted on the particle.D.The kinetic energy of the particle at point B is >K1and <K2.11.The graph below shows the potential energy U for a particle moving on the xaxis.Which of the following five graphs correctly gives the force F exerted on theparticle?12.A small object of mass m ,on the end of a light cord,is held horizontally at a distance r from a fixed support as shown.The object is then released.What is the tension in the cord when theobject is at the lowest point ofits swing?A.m g/2;B.mg ;C.3m g/2;D.2mg ;E.3mg13.The displacement of an object oscillating on a spring is given by x(t)=Acos(ωt +φ).If the object is initially displaced in the negative x direction and given a negative initial velocity,then the phase constant φis between:A.0and π/2rad;B.π/2and πrad;C.πand 3π/2rad;D.3π/2and 2πradE.none of the above (φis exactly 0,π/2,π,or 3π/2rad)14.Block A on the left has mass 1.00kg.Block B on the right has mass 3.00kg.The BPath 2A Path 1blocks are forced together,compressing the spring.Then the system is released from rest on a level,frictionless surface.After the blocks are released,the kinetic energy (KE)of block A isA.1/9the KE of blockB. B.1/3the KE of block B.C.3times the KE of block B.D.9times the KE of block B.E.the same as the KE of block B.15.a mass of 2kg is attached to three springs of spring constants 1N/m,andWhen the mass is at rest the springs are unstretched.For this system:A.2502s rad /.=ω;B.222s rad /=ω;C.2512s rad /.=ω;D.232s rad /=ω;E.212s rad /=ωAnswer sheet of the choices 123456789101112131415Part B Short Answer (20Points),each question is worth 2points1.The position of a particle moving along the x axis depends on the time according to the equation 2x t 4t 6=-+.where x in meters and t in seconds.From t=0s to t=4s.(a)What is the displacement?Answer:_____________________(b)What is the distance?Answer:_____________________2.A block of mass 4kg on a horizontal surface experiences a constant force of 8N in the +X direction and 6N in the –Y direction.It moves from X =2m,Y =2m to X =6m,Y =-1m.How much work does the force do on the block during the move?If the block is moving at the rest ,what is the final speedAnswer:_____________________Answer:_____________________3.3333 r cos(t )i sin(t )j =+where r in meters and t in seconds.When t=1sv =a =ets travel around the sun in elliptical orbits with large eccentricities.when the Comets travel from r 1to r 2,and r are the distance from the center of the sun.,(The sun’s mass is s M ,The gravity constant is S G ,The Comets’s mass is m )a)The change potential energy of the CometsU =b)What is the work done by the sun n moving the comets from r 1to r 2W =5.Imagine that you discover a new type of conservative force.This force F is a function of the position x of an object.Suppose that F(x)=2x -2N where x is measured in meters.(a)Find the change in the potential energy associated with this conservative force for an object that moves from x=1meters to x=2meters.U (b)If the position of zero potential is at x=1meter,How about the potential of the x=4meters?4U Part C.(35points)You must show all your work or state your reasoning in order to receive credit.1.(10points)Two companies,Company A and Company B,sell plastic ball launchers for physics demos.Both launchers cost the same and both are the same size.Both launch a plastic ball of 10grams.The two companies send us specifications of the net force on the ball during launch in graphical form.The respective graphs are shown below and on the next page.Both launchers reach a maximum force of 1.2N and the graphs are composed of straight line segments.We want to pick the launcher that gives the highest final speed to the ball,starting from e principles of physics to show which one we should select.t (s)00.100.080.060.040F (N)0.021.20.80.60.40.21.00F (N)x (cm)03624121.20.80.60.40.21.0Company A Graph of Force versus Time,Company B Graph of Force versus Distance2.(12points)A series of successive vibrations form a positive progressing wave whose snapshot at t=0is shown in the figure.The speed of the wave is u 5m /s(1)write the vibration equation of the particle O(2)Write the wave equation y(x,t )(3)write the vibration equation of the particle at x =λ/2(4)Find the speed of particle B when t =0y(cm)5 u m /soB C 20105-x(cm)10-3.(13points)A car with mass M is setting on the frictionless ground,A particle ball with mass m is released from horizontal position with rest.When the ball arrives at the vertical position.(suppose the length of the string is R)(a)What’s displacement of the car?(b)What is the velocity of ball and the car relative to the ground respectively?(c)What is the tension acted on the ball when the ball is at the vertical position?(d)(additional8points)What is the car’s speed when the ball is rotating through30 degrees relative to the car?m30°M。
一、Choice (4pts*5)1. Free expansion . A adiabaticcontainer has two parts connected bya valve (阀门). The volume of thetwo parts is the same ( Fig.1 ). Theleft part is filled with ideal gas (diatomic molecule 双原子分子)with temperature T . When the valve is opened, the gas will expand freely to fill both parts. After the system reach thermal equilibrium, the temperature of the gas is () (a) T (b) 2/T (c) 3/22/T (d) T 22 A red star and a blue star, which has higher surface temperature?(a) The red star (b) The blue star(c) They have the same surface temperature (d) Unable to determine3. A particle’s location is measured and specified as being exactly at x = 0, with zero uncertainty in the x direction. How does that location affect the uncertainty of its momentun component in the y direction?(a) It does not affect it. (b) It makes it infinite. (c) It makes it zero.4. Unpolarized light passes through two polarizers whose optical axes are in the same direction. The intensity of the emerging light is I 0. If a third polarizer is placed between the polarizers so that its axis is at an angle θ with the other two, the intensity of the emerging light is(a) zero (b) I 0 (c) I 0 cos 2θ (d) I 0 cos 4θ5. The following functions may represent the wave motion f (x ,t ) in a one-dimensional elastic medium in terms of position x , time t , and positiveconstants A , a , and b . Which function represents a traveling wave moving in the negative x-direction?(a) ()()bt ax At x f +=sin , (b) ()()bt ax A t x f -=sin ,(c) ()bt ax A t x f cos cos ,= (d) ()bt ax A t x f sin sin ,=Fig.1二、Blanks (20pts)6. (8 pts) A 500 g mass is undergoing simple harmonic oscillation that is described by the following equation for its position x (t ) from equilibrium:()⎥⎦⎤⎢⎣⎡+=rad 0.6rad/s 0.6cos )m 50.0()(ππt t x The amplitude A of the oscillation is m. The frequency of the oscillation is Hz. The period T of the oscillation is s. The phase of oscillator at t = 0 s is rad. The maximum speed of the oscillator is m/s .7. (3pts) When Newton ring apparatus is immersed in a liquid, the diameter of the eighth dark ring decreases form 2.92cm to 2.60cm, the refractive index of the liquid is .8. (3pts) In single slit diffraction experiment, 680nm light falls on a slit 0.0345mm wide. The angular width of the center diffraction peak is .9. (3pts) The angular separation of the two components of a double star is 8×10-3 rad and the light from the double stat har a wavelength of 550 nm. According to the Rayleigh criterion, the smallest diameter of a telescope mirror that will resolve the double star is ______ m.10. (3pts) The De Broglie wavelength of a electron moving at 5.9×106m/s is .三、Questions (10pts)11. (5pts) The oceans contains a tremendous amount of thermal energy. Why, in general, it is not possible to put it into useful work.12. (5pts) what are the two postulates of Einstein ’s Special Theory of Relativity?四、Problems (50pts)13. (10pts) For 1 mole O 2 at room temperature (20℃),(1) what is the average transitional kinetic energy of the molecules?(2) what is the rms speed of the molecules?(3) what is the internal energy of the gas?14. (10pts) The PV diagram of the cycle in Carnot ’s engine is shown in Fig 2. The Carnot cycle has 4 processes:1 2: Isothermal expansion with addition of heat |Q H |;2→3: Adiabatic expansion;3→4: Isothermal compression with heat |Q L | flowing out;4→1: Adiabatic compression.(1) Calculate |Q H | and |Q L |. (Suppose the gas is n mole) (2) Show that the efficiency of Carnot engine is H LT T -=1ηFig.215 (17pts) In the double - slit interference experiment (Fig. 3a), 550 nm light falls on the double-slit with two very narrow slit 0.10 mm apart. A viewing screen is 1.0 m far from the double-slit.(1) What is the separation between the 2nd-order bright fringe and the 3rd-order bright fringe?(2) A thin flake of mica (云母, n =1.58) is used to cover one slit of a double – slit (Fig. 3b). The central point on the viewing screen is now occupied by what had been the seventh bright slid fringe (m =7) before the mica was used. What is the thickness L of the mica?(3) Is the separation between adjacent bright fringes changed?16 (13 pts) A 1 kg mass oscillates on the end of a spring whose spring constant is k =2500N/m. If this system is in a spaceship moving pass the Earth with a speed of 0.8c, what ’s the period of the system seen by (1) the observers on the spaceship; (2) the observers on the Earth L 0.11mm 1.0m Fig. 3b 0.11mm1.0mFig. 3az。
大学物理试题(国外英文资料)College physics examination questionsFirst, the multiple-choice questions: (39 points)1. (3 points)The acceleration of a particle moving at a radius of R is the magnitude of the acceleration (V means the velocity of a particle at any time)(A) (B)(C) (D) [[]]2. (3 points)An object of mass m falls from the air and is affected by gravity as well as a resistance proportional to the square of velocity. The coefficient of proportionality is k, and K is the normal number. The closing velocity of the falling object (i.e., the speed at which the final object moves at uniform speed) will be(A) (B)(C) GK (D) [[]]3. (3 points)A spring oscillator of M quality is placed horizontally at rest in equilibrium. As shown, a bullet with a mass of M is injected into the oscillator at a horizontal velocity and then moved along with it. If the level is smooth, then the maximum potential energy of the spring is(A) (B)(C) (D) [[]]4. (3 points)A child of the quality of M stands on the edge of a horizontal platform with a radius of R. The platform can rotate freely through a vertical, smooth, fixed axis through its center. The moment of inertia is J. Both the platform and the child are stationary at the start. When the child suddenly moves counter clockwise toward the edge of the platform at a rate of V relative to the ground, the angular velocity and the rotation direction of the platform relative to the ground are(A) clockwise.(B) counter clockwise.(C) clockwise.(D) counter clockwise. [...]5. (3 points)Two different ideal gases, if their most probable rates are equal, their(A) equal to the average rate, root mean square speed equal.(B) equal to the average rate, root mean square speed is not equal.(C) the average rate is not equal, the root mean square speed equal.(D) the average rate is not equal, not equal to the root mean square speed. [...]6. (3 points)According to the second law of thermodynamics:(A) work can be converted to heat, but heat can not be converted to power.(B) heat can be transferred from a hot object to a cryogenic substance, but not from a cryogenic object to a high temperature object.(C) irreversible processes are processes that cannot proceed in the opposite direction.(D) all spontaneous processes are irreversible. [...]7. (3 points)There are several explanations for the interpretation of Gauss's theorem:(A) if the Gauss surface is zero everywhere, there is no charge in the plane.(B) if the Gauss surface has no charge, then the Gauss surface is zero everywhere.(C) if there is no zero on the Gauss surface, there must be charges in the Gauss plane.(D) if there is a net charge in the Gauss plane, the electric flux through the Gauss surface must not be zero.(E) Gauss's theorem applies only to electric fields with high symmetry. [...]8. (3 points)The radius of the cross section of a long straight wire is a, and a thin cylinder with a radius of B is coaxially arranged outside the conductor, and the two of them are insulated from each other. And the outer cylinder is grounded as shown. The electric charge per unit length of the wire is +, and the potential of the earth is zero. Then the field strength and the electric potential of the P point (Op=r) between the twoconductors are respectively:(A)(B)(C)(D) [[]]9. (3 points)The square coils with side lengths are respectively represented by two modes of current I (wherein the AB and CD are coplanar with the square), and in these two cases, the magnetic induction intensity of the coil at the center of the coil is respectively(A)(B)(C)(D) [[]]10. (3 points)The picture shows four charged particles in the same direction perpendicular to the magnetic field line, and the deflection trajectory of the magnetic field is injected into the uniformmagnetic field. The direction of the magnetic field is perpendicular to the surface of the O,The trajectory of the four particles is equal in mass and the magnitude of the electric energy is equal. In that case, the trajectory of the negatively charged particles with the largest kinetic energy is(A) Oa (B) Ob(C) Oc (D) Od [...]11. (3 points)A mass of simple harmonic vibration on the X axis, the amplitude of A = 4cm, T = 2S cycle, its equilibrium position is taken as the origin of coordinates, if t=0 the first moment of the particle by x= 2cm, and to the negative direction of X axis motion is second 2cm particle by x= at the moment(A) 1s (B) (2/3) s(C) (4/3) s (D) 2S [[]]12. (3 points)Using wedge interference method can detect surface defects, when the wavelength of monochromatic parallel light vertical incident, if the interference fringes observed as shown in the figure, each part of the fringe vertex exactly with left fringeof the straight part of the tangent line, then the surface of the workpiece and bending at the corresponding part of the fringe(A) raised, and the height is (B) raised, and the height is...(C) depressions, and the depth is (D) depressions, and the depth is []13. (3 points)A beam of light is a mixture of natural light and polarized light, let it through a vertical polarizer, if this incident beam axis rotating polarizer, the measured transmission light intensity maximum is 5 times the minimum value, then the incident beam in natural light and polarized light intensity ratio is(A) 1 / 2 (B) 1 / 5(C) 1 / 3 (D) 2 / 3Two, fill in the blanks: (46 points)1. (3 points)Let the particles move along the X axis. When the initial condition is t=0, the initial velocity is v0=0, and the coordinate x0=10 is a=4t. Then the equation of motion is.2. (3 points)Under the action of constant force F, an object moves in a straight line. The equation of motion is x=A-Bt+ct2 (A, B, C is constant), and the mass of the object should be m=.3. (3 points)At a constant speed, the quality of M ship, respectively, forward and backward at the same time the level of two throws of equal mass (m) objects thrown two objects relative to the ship the same rate (U) expression of the ship and try to write in the process of the system of the law of conservation of momentum (don't have Jane, for reference).4. (5 points)As shown in the figure, a homogeneous consolidation in a thin rod end ball, and can rotate around a horizontal smooth fixed shaft O to rotate, there is a bullet along with the horizontal angle direction and embedded in the ball hit, then hit in the process of conservation, cricket, bullets, rod system, the reason is. The process of cricket bat and ball increased after being hit in the conservation on cricket, bullets, rod, earth system.5. (3 points)At room temperature, the pressure of the ideal gas of 1 moldiatomic molecules is P, and the volume is V, and the average kinetic energy of the gas molecule is.6. (3 points)If the pressure and volume of an ideal gas remain constant, but the mass and temperature change, then can the internal energy change?.7. (3 points)The thermodynamic temperature of a high temperature heat source is n times of the thermodynamic temperature of a low temperature heat source. In a Kano cycle, the heat delivered by a gas to a cryogenic heat source is twice as much as that obtained from a high temperature heat source.8. (3 points)A simple harmonic wave propagates along the positive direction of the X axis. The relation curves between the vibration velocity and time at two points of X1 and X2 are shown as follows (a) and (b), and the distance between X1 and X2 is known as (lambda lambda).9. (3 points)White light (4000-7000) vertical incidence of 4000 slits per centimeter of grating, can produce the level of the complete visible spectrum.10. (3 points)A charged metal ball, when it is surrounded by a vacuum, stores the electrostatic energy of Wo and keeps its energy constant,It is immersed in an infinite isotropic homogeneous dielectric with relative dielectric constant, when its electrostatic energy is We =.11. (6 points)The three basic assumptions of Bohr's theory of hydrogen atoms are:(1),(2),(3).12. (5 points)An electron at a rate of motion of 0.99c (electron rest mass of 9.11 * 1031kg), then the total electron energy is J, the kinetic energy of classical mechanics and relativistic electron kinetic energy ratio.13. (3 points)Static mass is me the potential for electronic, electrostaticfield accelerated U12, without considering the effect of relativity, the De Broglie wavelength lambda = E.Three. Calculation questions: (65 points)1. (10 points)The equation of motion of a known particle is (as a constant),Find (1) the trajectory equation and velocity of the particle(2) the velocity of a particle and the rotation direction ofa particle(3) the relation between the acceleration of a particle and the vector?2. (10 points)M was a short tube, with a length of hard straight rod suspension as shown in figure L, quality can be ignored, with ether droplets Sheng tube, pipe with mass m cork closed, when the heating tube cork in the ether vapor pressure to fly out, hanging around the tube O in the vertical plane for a complete circular motion, then the minimum speed of the cork flew out for? If you change a hard straight pole into a string, what if?3. (10 points)Having two concentric spherical shells with a radius of insulation for each other, and when the + Q is given to the inner ball:(1) the charge distribution and electric potential of the outer sphere;(2) re insulating the ball after grounding, the charge distribution and the electric potential of the outer sphere(3) then, the inner sphere is grounded, the charge distribution of the inner sphere and the potential of the outer sphere4. (10 points)As shown in the figure, the plane charged ring two coplanar, the inner and outer radius are respectively R1, R2 and R2, R3, the outside of the ring to a second N2 RPM clockwise, inside the ring to a second N1 rpm counterclockwise. If the charge surface density is the ratio of the N1 to the N2, the magnetic induction intensity at the center of the circle is zero.5. (10 points)As shown in the figure, the current long straight conductor for I, a B C D rectangular frame with a long straight conductorcoplanar, and the a D A D C / B a B edge D side is fixed, a and C B to speed without friction uniform translational t=0, a, B and C D side edge coincidence, set line inductance negligible.(1) for example, i=I0, seek the electromotive force in a B, a, B, two points, which point has high potential?(2) the total induced electromotive force in the wire frame when the a b t is moved to the position shown by i=I0cos omega.6. (10 points)A plane harmonic wave propagates along the negative direction of the Ox axis, the wavelength is lambda, and the vibration law of the particle at P is shown in figure.(1) seeking the vibration equation of particle at P;(2) find the wave equation of this wave;(3) in the figure, the vibration equation of the particle at the coordinate origin O is calculated.7. (5 points)In the experiment of single slit Fraunhofer diffraction for white, second bright fringe center is measured at the wavelength of third level bright fringe center and thewavelength for the red wavelength for overlap.Second pageThree hundred and thirty-oneSouth China University of TechnologyIn 2004, I studied the master's degree entrance examination papers(the answer to the test paper is invalid. Please answer it on the answer sheet. After the test, this volume must be returned with the answer sheet.)Subject name: General PhysicsApplicable profession: Philosophy of science and technology Common pageFirst page。
Fundamentals of Physics-Test 1EXAMINEE NAME:Solve 8 of the following 10 problems.1. A non-conducting rod of length L has charge q - uniformlydistributed along its length. (a)What is the linear chargedensity of the rod? (b) What is the electric field at point P, a distance a from the end of the rod? (c) What is the electric potential at point P with 0=V at infinity?2. A non-conducting sphere shell, of inner radius a and outer radius b , has a volumecharge density r A /=ρ (within itsthickness), where A is a constant and r is thedistance from the center of the shell. Inaddition, a point charge qis located at thecenter. What value should A have if theelectric field in the shell (br a ≤≤) is to be uniform?3. A long straight wire of radius R that carries a uniformly distributed current i directly out of page. What is the magnetic field B (a) inside and (b) outside the wire?4. A rectangular loop of N close-packedturns is positioned near a long straightwire. What is the mutual inductance Mfor the loop-wire combination?5. A broad beam of light of wavelength 600nm is sent directly downward through a glass plate (n=1.5) that, with a plastic plate (n=1.2), forms a thinwedge of air which acts as thin film. Anobserver looking down through the topplate sees the fringe pattern shows asthe Figure. With dark fringes centeredon ends A and B. (a) What is thethickness of the wedge at B? (b) How many dark fringes will the observer see if the air between the plates is replaced with water (n=1.33)?6. A diffraction grating is made up of slits of width 300nm with separation 900nm. The grating is illuminated by monochromatic plane waves of wavelength nm 600=λ at normal incidence. (a) How many diffraction maxima are there in the full pattern? (b) What is the width of a spectral line observed in the first order if the grating has 1000 slits?7. A clock moves along the x axis at a speed of 0.600c and reads zero as it passes the origin. (a) Calculate the Lorentz factor. (b) What time does the clock read as it passes x=180m?8. What is the speed of a particle (a) whose kinetic energy is equal to twice its rest energy and (b) whose total energy is equal to twice its rest energy?9. (a) If the work function for a certain metal is 1.8eV , what is its stopping potential for light of wavelength 400nm? (b) What is the maximum speed of electrons emitted via the photoelectric effect as they leave the metal surface (s m c C e s J h /100.3,106.1,1063.681934⨯=⨯=⋅⨯=--)?10. W hat is (a) the momentum and (b) the de Broglie wavelength of an electron whose kinetic energy is 120 eV (,1011.931kg m e -⨯= J eV 19106.11-⨯=)?。
Fundamentals of Physics-Test 2EXAMINEE NAME:I. Fill in each of the following blanks with an appropriate expression or quantity.(48)1. The position of an electron is given by k j t i t r 0.20.60.22+-= (where t is in seconds and the coefficients have the proper units for r to be in meters). (a) The velocity )(t v and the acceleration )(t a are (1) and (2) respectively for the electron. (b) In unit-vector notation, The velocity v and the acceleration a are, att=2.0s, (3) and (4) .2. A wheel rotates with an angular acceleration given by 2364bt at -=α, where t is the time and a and b are constant. If the wheel has an initial angular speed 0ω, then (a) the equation for the angular speed is (5) , and (b) the angular displacement of the wheel is (6) as functions of time.3. An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the position (measured from the system’s equilibrium location), velocity, and acceleration of the block are ,/6.13,100.0s m v m x -== and 2/123s m a -=. Then (a) the frequency of the oscillation is (7) , (b) the mass of the block is (8) , and the amplitude of the motion is (9) .4. The equation of a transverse wave traveling along a very long string is given by ),0.402.0sin(0.6t x y ππ+= where x and y are expressed in centimeters and t is in seconds. So (a) the amplitude is (10) , (b) the wavelength is (11) , (c) the frequency is (12) , (d) the speed is (13) , (e) the maximum transverse speed of a particle in the string is (14) ,5. Suppose 2.00 mol of an ideal diatomic gas, with molecular rotation but not oscillation, experiences a temperature increase of 60.0 K under constant-pressure conditions. (a) The heat added to the gas is (15) . (b) The increase in internal the kinetic energy is(16) .II. Solve the following problems. (52)1.Force j N i xN F )4()3(+=, with x in meters, acts on a particle, changing only the kinetic energy of the particle. (a) How much work is done on the particle as it moves from coordinates (2m, 3m) to (3m, 0m)? (b) How much the kinetic energy of the particle is changed during the motion? (8)2. A uniform spherical shell of mass Mand radius R rotates about a vertical axison frictionless bearings as shown in thefigure. A massless cord passes around theequator of the shell, over a pulley ofrotational inertia I and radius r, and isattached to a small object of mass m.There is no friction on the pulley ’s axle; the cord does not slip on the pulley. Whatis the speed of the object after it has fallen a distance h from rest? Use work-energy consideration. (14)3. A string oscillates according to the equation].)40cos[(])3)[sin(50.0('11t s x cm cm y --=ππ(a) What are the amplitude and speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (b) What is the distance between nodes? (c) What is the speed of a particle of the string at the position x = 1.5 cm when t = 9s/8? (15)4. One mole of an ideal gas is used as theworking substance of an engine thatoperates on the cycle shown as the rightfigure. BC and DA are reversibleadiabatic processes. (a) Is the gasmonatomic, diatomic, or poly-atomic? (b)the heat added to the gas in one cycle. (c)the heat leaving the gas in one cycle. (d)the efficiency of the cycle, and (e) thechange in entropy of the gas per cycle. (15)。
Exercise:1. A particle moving along x axis starts from x 0 with initial velocityv 0. Its acceleration can be expressed in a =-kv 2 where k is a knownconstant. Find its velocity function v =v (x ) with the coordinate x asvariable.2. A particle moves in xy plane with the motion function asj t i t t r )3sin 5()3cos 5()(+=(all in SI). Find (a) its velocity )(t v and (b)acceleration )(t a in the unit-vector notation. (c) Show that v r⊥.3. A bullet of mass m is shot into a sand hill along a horizontalpath, assume that the drag of the sand is kv f -=, find the velocityfunction v(t) if 0)0(v v = and the gravitation of the bullet can beignored.4. what work is done by a conservative force j i x f 32+= thatmoves a particle in xy plane from the initial position j i r i 32+= to the final position j i r f 34--=. All quantities are in SI.5. The angular position of a point on the rim of a rotating wheel isgiven by 320.30.4t t t +-=θ, where θ is in radians and t is inseconds. Find (a) its angular velocities at t=0s and t =4.0s? (b)Calculate its angular acceleration at t =2.0s. (c) Is its angularacceleration constant?6. A uniform thin rod of mass M and length L can rotate freelyabout a horizontal axis passing through its top end o (231ML I =). Abullet of mass m penetrates the rod passing its center of masswhen the rod is in vertical stationary. If the path of the bullet ishorizontal with an initial speed v o before penetration and 20v after penetration . Show that (a) the angular velocity of the rod just after the penetration is MLmv 430=ω. (b) Find the maximum angular max θ the rod will swing upward after penetration.7. A 1.0g bullet is fired into a block (M=0.50kg) that is mountedon the end of a rod (L=0.60m). The rotational inertia of the rodalone about A is 206.0m kg ⋅. The block-rod-bullet system thenrotates about a fixed axis at point A. Assume the block is smallenough to treat as a particle on the end of the rod. Question: (a)What is the rotational inertia of the block-rod-bullet system aboutA? (b) If the angular speed of the system about A just after thebullet ’s impact is 4.5rad/s , What is the speed of the bullet justbefore the impact?8. A clock moves along the x axis at a speed of 0.800c and readszero as it passes the origin. (a) Calculate the Lorentz factor γbetween the rest frame S and the frame S* in which the clock isrest. (b) what time does the clock read as it passes x =180m ?9. What must be the momentum of a particle with mass m sothat its total energy is 3 times rest energy?10. Ideal gas within a closed chamber undergoes the cycle shownthe Fig. Calculate Q net the net energy added to the gas as heatduring one complete cycle.11. One mole of a monatomic ideal gas undergoes the cycleshown in the Fig. temperature at state A is 300K.(a). calculate the temperature of state B and C.(b). what is the change in internal energy of the gas between stateA and state B? (int E )(c). the work done by the gas of the whole cycle .(d). the net heat added to the gas during one complete cycle.12. The motion of the electrons in metals is similar to the motionof molecules in the ideal gases. Its distribution function of speedis not Maxwell ’s curve but given by.⎩⎨⎧=0)(2Av v pthe possible maximum speed v F is called Fermi speed. (a)plot the distribution curve qualitatively. (b) Express the coefficientA in terms of v F . (c) Find its average speed v avg .13. Two containers are at the same temperature. The firstcontains gas with pressure 1p , molecular mass 1m , and rmsspeed 1rms v . The second contains gas with pressure 12p , molecularmass 2m , and average speed 122rm s avg v v =. Find the mass ratio21m m .14. In a quasi-static process of the ideal gas, dW =PdV andd E int =nC v dT . From the 1st law of thermodynamics show that thechange of entropy i f v i fT T nC V V nR S ln ln +=∆ .Where n is the numberof moles, C v is the molar specific heat of the gas at constantvolume, R is the ideal gas constant, (V i , T i ) and (V f , T f ) . are theinitial and final volumes and temperatures respectively.15. It is found experimentally that the electric field in a certainregion of Earth ’s atmosphere is directed vertically down. At analtitude of 300m the field is 60.0 N /C ; at an altitude of 200m , thefield is 100N /C . Find the net charge contained in a cube 100m onedge, with horizontal faces at altitudes of 200m and 300m .Neglect the curvature of Earth.16. An isolated sphere conductor of radius R with charge Q . (a)Find the energy U stored in the electric field in the vacuum outsidethe conductor. (b) If the space is filled with a uniform dielectrics ofknown r ε what is U * stored in the field outside the conductorthen?17. Charge is distributed uniformly throughout the volume of aninfinitely long cylinder of radius R. (a) show that, at a distance rfrom the cylinder axis (r<R), r E 02ερ=, where ρis the volume charge density. (b) write the expression for E when r>R .18. A non-uniform but spherically symmetric distribution ofcharge has a volume density given as follow:⎩⎨⎧-=0)/1()(0R r r ρρwhere 0ρ is a positive constant, r is the distance to the symmetric center O and R is theradius of the charge distribution. Within the charge distribution (r <R ), show that (a) the charge contained in the co-center sphere ofradius r is )34(31)(430r Rr r q -=πρ, (b) Find the magnitude of electricfield E (r ) within the charge (r < R ). (c) Find the maximum field E max =E (r *) and the value of r *.19. In some region of space, the electric potential is the followingfunction of x,y and z: xy x V 22+=, where the potential is measuredin volts and the distance in meter . Find the electric field at thepoint x=2m, y=2m . (express your answer in vector form)20. The Fig. shows a cross section of an isolated spherical metalshell of inner radius R 1 and outer radius R 2. A point charge q is located at a distance 21R from the center of the shell. If the shell is electrically neutral, (a) what are the induced charges (Q in , Q out )on both surfaces of the shell? (b) Find the electric potential V(0) atthe center O assume V (∞)=0.21. Two large metal plates of equal areaare parallel and closedto each other with charges Q A , Q B respectively. Ignore the fringingeffects, find (a) the surface charge density on each side of bothplates, (b) the electric field atp 1, p 2 . (c) the electric potentialA and B)22.In a certain region of space, the electric potential is ()2=-+where A,B,C are positive constant. The ,,,V x y z Axy Bx Cyelectric field is ; at which point is the electric field equal to zero .23. A 9.60-μC point charge is at the center of a cube with sides of length 0.500m. The electric flux through one of the six faces of the cube is ; the answer would be if the sides were of length 0.250m.。
2009─2010学年第一学期 《力学》(双语)课程考试试卷(A 卷)专业:物理学 年级:08级 考试方式:闭卷 学分:4 考试时间:120分钟引力常量 G=6.67×10-11N 2·m 2·kg -2 重力加速度 g=9.8m/s -2 真空中光速 c=3.00×10m/s一Choose the Correct Answer (3’ ⨯10=30’)Note: Please fill answers in the following table1. A particle moves in a circle with radius R at variable-speed, the magnitude of the acceleration is (v is the speed at any one time) d v/d t .(B) v 2/R .(C) d v/d t + v 2/R .(D) [(d v/d t )2+(v 4/R 2)]1/2.2. A projectile initial velocity v 0 and projectile angle θ , the centripital acceleration and the tangential acceleration at highest point , respectively are:(A) g cos θ , 0 , (B) g cos θ , g sin θ , (C) g sin θ , 0,(D) g , g , 3. Shown in Figure 1, a cylindrical cage with radius R, rotates along the central axis OO ' . A block A is stick to the cylinder block wall with the friction coefficient μ between the block A and cylinder.To make block A do not fall, the angular velocity ω of cylinder should be at least(A) R g μ. (B) gμ.(C)()R g μ.Fig 1(D)R g .4. The mass of particle B is four times of that of Particle. At the beginning the speed of particle A and B is respectively (3i +4 j), (2i-7j). Due to the interaction between the two particles, the speed of A becomes (7i-4j). At this time the speed of particle B is(A) 2i -7j . (B) i -5j . (C) 0.(D) 5i -3j .5. Shown in Figure 2, a smooth, thin rod, rotating along the OO ′at constant angular velocity,is fixed at point O, with a small ring set in the upper end of rod.. At the beginning the pole in a cone movement, and then the small ring along the rod fell from the stationary. In the course of ring drop,the small ring, rod and the Earth are composed of a systemwhose mechanical energy and angular momentum are(A) Mechanical energy, angular momentum are notconserved(B) Mechanical energy is conserved, while angular momentum is not. (C) angular momentum is conserved, while mechanical energy is not. (D) Mechanical energy, angular momentum are conserved6. There are two same radius fine quality ring A with uniform mass distribution and B of the unevenmass distribution. Their rotational inertia along the axis which is perpendicular to ring plane, are respectively J A and J B , then the(A) J A >J B . (B) J A <J B . (C) J A =J B . (D) Not sure.7. In figure 3, the masses of Pulley, rope are negligible. Ignoring all the friction, if the m 1 of the object A, is greater than the m 2 of object B, during the movement, the spring balance reading is(A) (m 1+m 2 )g . (B) (m 1-m 2)g .(C) 2m 1m 2g/(m 1+m 2). (D) 4m 1m 2g/(m 1+m 2).Fig 2Fig 38. A simple harmonic wave propogating in elastic medium, in one instant, an element is in a position of equilibrium, this time its energy is(A) Zero kinetic energy, maximum potential energy. (B) Zero kinetic energy, Zero potential energy.(C) Maximum kinetic energy, maximum potential energy. (D) Maximum kinetic energy, Zero potential energy. 9. A locomotive is running away from a observer at rest at a speedof 25ms -1, with the whistle frequency of 600Hz , then the observer will receive the voice with the frequency of (assuming the speed of voice in the air is 340 m/s)(A) 558Hz . (B) 646 Hz . (C) 555 Hz . (D) 649 Hz .10. Two incidents happen at the same time while two different places inan inertial reference frame, then will they happen at a same time in another inertial reference frame? Which of the following is correct?(A) They must happen at different time. (B) They must happen at same time.(C) They might happen at a same time or different time. (D) It’s uncentain二. Fill in the Blanks (2’ ⨯10=20’)1.An object osciooate in thevertical direction isconnected to a spring. The vibration equation is y=A sin ω t , in which A 、ω are constant, then(1)The speed of an object relationship with a function of time is ;(2) The speed of an object relationship with a function of coordinate is .2. A particle subject to two constant force has a displacement of∆r =3i+8j (SI), and its kinetic energy increases by 24J, if one of the constantforce F 1=12i -3j (SI), then the work done by the other force is3. A particle oscillates simple harmonic motion, with period of T. Along the positive x-axis, it moving from the equilibrium position to one-half the maximum displacement will cost time .4. The two basic assumptions of special relativity are and5. Altair (牛郎星) is 16 light years away from the Earth, if a spacecraft travelwith a velocity of , it will take the spacecraft 4 years (time shown in the spacecraft ) to arrive Altair.6. The so-called vacuum degree of fluid, means the difference with fluid inside pressure and the atmospheric pressure , as the mercury vacuum gauge shown inthe figure, let h= 50cm, then the vacuum degree inside the container B isthe N/m 2?7. The homogeneous pole, with length L, make it stand upright to smooth the desktop, and then release hands, as the pole can not be locatedabsolute along the vertical direction, so then it fall. Let the pole move in the o-xy plane.Atthe beginning, the pole coincides with the axis, then the center of mass moves along the horizontal direction. Then the pole trajectory equation for the endpoint is三. (15 points)There is a mass of m 1, length l uniform thin rods, located onthe desktop with coefficient of sliding friction μ. It canrotates in the desk plane, about the fixed axis at O. Another block of the mass m 2 collides with the end of rod the other end. Before and after the collision the speed of block are respectively v 1 and v 2, such as the as shown in Figure 5. If the collision time is very short, (1) what is the rotational inertia of the rod about point A?(2)how long have process from thin rod starting rotate to stop after the collision?P 2 (Fig 5四. (15 points)A skierfree falls from point A, when he arrives at platform C across a trench of width d via point B, his velocity v c is just in the horizontal direction. The vertical distance between point A and B is40 m. The tangential direction of the slope at point B is 30º to the horizon, the friction is neglected. (1) What ’s the skier ’s velocity v B leaving point B? (2) What ’s vertical distance between B and C? What about the trench width d ? (3) What ’s the skier ’s velocity v c arriving at C?五. (10 points)shows The waveform of simple harmonic wave at t = 0moment is shown in figure 7(1)What is the wave equation?(2) What is the vibration equation at point P.六. (10 points) A railway bridge of length L , the length of a train at rest is l . When the train is passing the bridge with high speed of 0.6c , what will be the bridge ’s lengthmeasured by the observer on the train? How long will it take him to measure the time that the whole train through the bridge?-Fig 72009─2010学年第一学期《力学》课程考试试卷(A 卷) 参考答案及评分标准一Choose the Correct Answer. (3’ ⨯10=30’)二. Fill in the Blanks. (2’ ⨯10=20’)1. v=A ωcos ωt , v=22y -A ω2. 12J.3. T /12 .4. relativity, c=constant.5. c c 97.017/16=.6. 426.66410/N m ⨯7. no ,4x 2+y 2=L 2三. (15points)Solution : (1) the rotational inertial of the rod about point A is J =()⎰lx l m x 012d /=m 1l 2/3Or J =()⎰212d /2lx l m x + m 1l 2/4=m 1l 2/3 (5 points)(2)Due to a very short time collision , M μ<<M F , The angular momentum of the thin rod and slider is approximate conserved. So we can getm 2v 1l=- m 2v 2l+ (m 1l 2/3)ωm 1ωl 2/3= m 2 ( v 1+v 2) l (4 points ) ,yielding M μ=()⎰lx l /m g 01d μ=μ m 1gl/2After the impact, the Impulse theorem reduces⎰=-tt M 0d μ-μm 1glt/2=0-m 1ωl 2/3=-m 2( v 1+v 2)l (4 points )So we can obtaint=2m 2( v 1+v 2)/(μ m 1g ) (2 points )四. (15points)解:Solution :⑴ The mechanical energy of the skier is conserved, taking point B aszero potential energy.∵mgH = mv B 2/2∴28.00/B v m s == (4 points )⑶The skier dose projectile motion from B to C, and C is known as the maximum point. Sov c = v B cos30º = 19.80m/s (4 points )⑵∵mv B 2/2 = m v c 2/2+mgh ∴h = (v B 2-v c 2)/2g = 20.00m ; (4 points ) The transit time :∵0 = v B sin30º-gt ∴t = v B /2g =1.43sThe transit distance d = v B cos30ºt = 28.29m. (3 points ) 五. (10 points)解:(1)When wave is at t =0 y 0=A cos ϕ0=0 v 0=-A ωsin ϕ0>0 so we can get ϕ0=-π/2.(2 points )and we know T=λ/v=0.40/0.08=5(s) (1points )So the wave equation isy=0.04cos[2π( t/5-x/0.4)-π/2] (SI) (3 points )(2) The vibration equation at point P is y P =0.04cos[2π( t/5-0.2/0.4)-π/2] = 0.04cos(0.4π t -3π/2)(SI)(4points )六. (10 points)Solution : L '=L (1-v 2/c 2)1/2 =0.6L (5分) ∆t '=( L '+l )/v =(0.6 L +l )/0.8c (5分)-。
Chapter 1 Particle KinematicsI) Choose one correct answer among following choices1. An object is moving along the x-axis with position as a function of time given byx=x(t). Point O is at x=0. The object is definitely moving toward O when2. An object starts from rest at x=0 when t=0. The object moves in the x direction with positive velocity after t=0. The instantaneous velocity and average velocity are related byA. v vB. v vC. v vdx x can be larger than, smaller than, or equal to3. An object is moving in the x direction with velocityA. Negative.B. Zero.C. Positive.D. Not determined from the information given. 4. An object is moving on the xy-plane with position as a function of time given by r = 2 2 a t i + b t j (a and b are constant). Which is correct?A. The object is moving along a straight line with constant speed.B. The object is moving along a straight line with variable speed.C. The object is moving along a curved path with constant speed.D. The object is moving along a curved path with variable speed.5. An object is thrown into the air with an initial velocity v 0 (4.9i 9.8 j)m/s.Ignore theair resistance (空气阻力 ). At the highest point the magnitude of the velocityis ( )(A) 0 (B) 4.9m/s (C) 9.8m/s (D) (4.9)2 (9.8) 2 m/s6. Two bodies are falling with negligible air resistance, side by side, above a horizontalplane. If one of the bodies is given an additional horizontal acceleration during its descent, it A. dx 0 dt B. dx 0 dt C. d(x 2) dt D. d(x 2) dtD.v x (t), and x is nonzero x dtconstant. With v x 0 when t=0, then for t>0 the quantity v x dv x v xdt isA.strikes the plane at the same time as the other body.B.strikes the plane earlier than the other body.C.has the vertical component of its velocity altered.D.has the vertical component of its acceleration altered.7. A toy racing car moves with constant speed around the circle shown below. When it is at point A its coordinates are x=0, y=3m and its velocity is 6m/s i . When it is atpoint B its velocity and acceleration are:22A.-6m/s j and 12m/s i , respectively.B. 6m/s j and -12m/s i , respectively.22C. 6m/s j and 12m/s i , respectively.D. 6m/s j and 2m/s i , respectively.8. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0m/s in a vertical circle. Its acceleration at the bottom of the circle is:2 2 2 2A. 9.8m/s , upB. 9.8m/s , downC. 8.0m/s , upD. 32m/s , up9. A boat is able to move through still water at 20m/s. It makes a round trip to a town3.0 km upstream. If the river flows at 5m/s, the time required for this round trip is:B.150 sC. 200 sD. 320 sA. 120 sII)Fill in the empty space with correct answer1. A particle goes from x=-2m, y=3m, z=1m to x=3m, y=-1m, z=4m. Its displacement is : .2.The x-component of the position vector of a particle is shown in the graph in Figureas a function of time.(a)The velocity component v x at the instant 3.0 s is .(b)When is the velocity component zero ? The time is .(c)Is the particle always moving in the same direction along the x-axis? .23.The angle turned through by a wheel is given byθ =at+bt , where a and b are constants. Its angular velocityω =, and its angular accelerationβ =4.When a radio wave impinges on the antenna of your car, electrons in the antennamove back and forth along the antenna with a velocitycomponent v x as shown schematically in Figure . Roughly sketchthe same graph and indicate the time instants when(a)The velocity component v x is zero;(b)The acceleration componenta x is zero;(c)The acceleration has its maximum magnitude.5. A car is traveling around a banked, circular curve of radius 150 m on a test track. At the instant when t=0s, the car is moving north, and its speed is 30.0 m/s but decreasing uniformly, so that after 5.0 s its angular speed will be 3/4 that it was when t=0s. The angular speed of the car when t=0s is , the angular speed 5.0 s lateris , the magnitude of the centripetal acceleration of the car when t=0s is , the magnitude ofthe centripetal acceleration of the car when t=5.00s is , the magnitude of the angular acceleration is , the magnitude ofthe tangential acceleration is .6. A projectile is launched at speed v 0 at an angle θ (withthe horizontal) from the bottom of a hill of c onstant slope asshown in Figure. The range of the projectile up the slope is .III) Calculate Following Problems:1. An object with mass m initially at rest is acted by a force F k 1i k 2tj , where k 1and k 2 are constants. Calculate the velocity of the object as a function of time.2. You are operating a radio-controlled model car on a vacant tennis court. Your position is the origin of coordinates, and the surface of the court lies in the xy-plane. The car, which we represent as a point, has x- and y-cooridnates that vary with time2 23 3 according to x=2.0m-(0.25m/s )t , y=(1.0m/s)t+(0.025m/s )t . a. Find the car's instantaneous velocity at t=2.0s.b. Find the instantaneous acceleration at t=4.0s.23. An object moves in the xy-plane. Its acceleration has components a x =2.50t and a y =9.00-1.40t. At t=0 it is at the origin and has velocity v 0 1.00i 7.00 j .Calculate the velocity and position vectors as functions of time.24. An automobile whose speed is increasing at a rate of 0.600 m/s travels along a circular road of radius 20.0 m. When the instantaneous speed of the automobile is 4.00 m/s, find (a) the tangential acceleration component, (b) the radial acceleration component, and (c) the magnitude and direction of the total acceleration.25. Heather in her Corvette accelerates at the rate of (3.00i -2.00 j ) m/s , while Jill in2her Jaguar accelerates at (1.00i +3.00 j ) m/s . They both start from rest at the originof an xy coordinate system. After 5.00 s, (a) what is Heather ' s speed with respect to Jill, (b) how far apart are they, and (c) what is Heather ' s acceler atoti oJnill ?re lativeChapter 2 Newton 's laws of motionI) Choose one correct answer among following choices1. In the SI, the base units (基本单位 ) for length, mass, time are ( )(A) meters, grams, seconds. (B) kilometers, kilograms, seconds.(C) centimeters, kilograms, seconds. (D) meters, kilograms, seconds.2. Which one of the following has the same d imension (量纲) as time ( )3. Which of the following quantities are independent (无关 ) of the choice of inertialx (A) (D) vx(B) (C)frame(惯性系 )?(A)v (B) P (C)F (D) W4.Suppose the net force F on an object is a nonzero constant. Which of the following could also be constant?A. Position.B. Speed.C. Velocity.D. Acceleration.5.An object moves with a constant acceleration a. Which of the following expression is also constant? ( )(A) dvdt(B)dvdt(C)d(v2)dt dt6. An object moving at constant velocity in an inertial frame must:A. have a net force on it.B. eventually stop due to gravity.C. not have any force of gravity on it.D. have zero net force on it.7. A heavy ball is suspended as shown. A quick jerk on the lower string will break that string but a slow pull on the lower string will break the upper string. The first result occurs because:A. the force is too small to move the ballB. action and reaction is operatingC. the ball has inertiaD. air friction holds the ball back8. A constant force of 8.0 N is exerted for 4.0 s on a16-kg object initially at rest. The change in speed of this object will be:A. 0.5m/sB. 2m/sC. 4m/sD. 8m/s9. A wedge rests on a frictionless horizontal table top. Anobject with mass m is tied to the frictionless incline of thewedge as shown in figure. The string is parallel to theincline. If the wedge accelerates to the left, when the objectleaves the incline, the magnitude of its acceleration isA. gsinθB. gcosθC. gtanθD. gcotθ10. A crane operator lowers a 16,000-N steel ball with a downward acceleration of 23m/s . The tension force of the cable is:A. 4900NB. 11, 000NC. 16, 000ND. 21, 000N 11. A 1-Npendulum bob is held at an angle θ from the vertical by a 2-Nhorizontal force F as shown. The tension in the string supportingthe pendulum bob (in newtons) is:A. cos θB. 2/ cos θC. 5D. 1212. A car moves horizontally with a constant acceleration of 3m/s . A ball is suspended by a string from the ceiling of the car. The ball does not swing, being at rest with respect to the car. What angle does the string make with the vertical?A. 17?B. 35?C. 52?D. 73?13. A 32-N force, parallel to the incline, is required to push a certain crate at constant velocity up a frictionless incline that is 30? above the horizontal. The mass of the crate is:A. 3.3kgB. 3.8kgC. 5.7kgD. 6.5kg II) Fill in the empty space with correct answer1. A2.5 kg system has an acceleration a (4i )m s2 . There are two forces acting on the system, and One of the forces is F1 (3i 6j)N . The other force is .2. Two masses, m1 and m2, hang over an ideal pulley and the system is free to move. The magnitude of the acceleration a of the system of two masses is Themagnitude of the tension in the cord is .3. You are swinging a mass m at speed v around on astring in circle of radius r whose plane is 1.00 m abovethe ground as shown in Figure. The string makes anangle θ with the vertical direction.(a) Apply Newton' s econd law to the horizontal andvertical direction to calculate theangle θ is .(b) If the angle θ = 47.4 a°nd the radius of the circle is1.50 m, the speed of the mass is .(c) If the mass is 1.50 kg, the magnitude of the tensionin the string is(d) The string breaks unexpectedly when the mass is movingexactly eastward. The location the mass will hit the ground is .III) Calculate Following Problems:1. A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge, and a horizontal force F isapplied to the wedge. What must be the magnitude of F if the block is toremain at a constant height above the table top?2. The mass of blocks A and B in Figure are 20.0kg and 10.0kg, respectively.The blocks are initially at rest on the floor and are connected by a masslessstring passing over a massless and frictionless pulley. An upward force F isapplied to the pulley. Find the accelerations a1 of block A and a2 of block Bwhen F is(a) 124N ; (b) 294N ; (c) 424N.3. An object is drop from rest. Find the function of speed with respect to timeand the terminal speed. Assuming that the drag force2is given by D = bv .4. A small bead can slide without friction on a circular hoop that is ina vertical plane and has a radius of 0.100m. The hoop rotates at aconstant rate of 4.00rev/s about a vertical diameter.(a) Find the angleβ at which the bead is in vertical equilibrium.(b) Is it possible for the bead to “ride” at the same elevation as thecenter of the hoop?(c) What will happen if the hoop rotates at 1.00rev/s.Chapter 3 Linear momentum, Conservation of momentumI)Choose one correct answer among following choices1.An object is moving in a circle at constant speedv . The magnitude of the rate of change of momentum of the object23A.is zero.B. is proportional to v.C. is proportional to v .D. is proportional to v .2.If the net force acting on a body is constant, what can we conclude about its momentum?A. The magnitude and/or the direction of P may change.B.The magnitude of P r remains fixed, but its direction may change.C.The direction of P remains fixed, but its magnitude may change.D.P remains fixed in both magnitude and direction.3.If I is the impulse of a particular force, what is dI /dt ?A. The momentumB. The change in momentumC.The forceD. The change in the force4. A variable force acts on an object from t i 0 to t f . The impulse of the force is zero. One can conclude thatA. r 0 and P 0.B. r 0 but possibly P 0.C. possibly r 0 but P 0.D. possibly r 0 and possibly P 0.5. A system of N particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?A. It must be zero.B. It could be non-zero, but it must be constant.C. It could be non-zero, and it might not be constant.D.The answer depends on the nature of the internal forces in thesystem.6.The x and y coordinates of the center of mass of the three-particle system shown below are:A. 0, 0B. 1.3m, 1.7mC. 1.4m, 1.9mD. 1.9m, 2.5m7.Block A, with a mass of 4 kg, is moving with a speed of 2.0m/swhile block B, with a mass of 8 kg, is moving in the oppositedirection with a speed of 3m/s. The center of mass ofthe two block-system is moving with a velocity of:A. 1.3m/s in the same direction as A.B.1.3m/s in the same direction as B.C.2.7m/s in the same direction as A.D.1.0m/s in the same direction as B.8. A large wedge with mass of 10kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block 's velocity is 3.0m/s and the horizontal component is 6.0m/s. At that instant the velocity of the wedge is:A. 3.0m/s to the leftB. 3.0m/s to the rightC. 6.0m/s to the rightD. 6.0m/s to the left9. A 1.0-kg ball moving at 2.0m/s perpendicular to a wall rebounds from the wall at1.5m/s. The change in the momentum of the ball is:A. zeroB. 0.5N s· away from wallC. 0.5N s· toward wallD. 3.5N s· away from wallII)Fill in the empty space with correct answer1.Two objects, A and B, collide(碰撞). A has a mass of m A 2kg , and B has a mass of m B4kg. The velocities before the collision are v A (2i 3j)m/s and v B (4i 2j)m/s. After the collision, v A (3i 2 j ) m/s. The final velocity of Bv B m/s.2. A stream of water impinges on(撞击) a stationary “dished”turbine blade, as shown in Fig.8. The speed of the water is v, bothbefore and after it strikes the curved surface of the blade, and themass of water striking the blade per unit time is constant at thevalue dm/dt . The force exerted by the water on theblade is ______________ .o3. A 320g ball with a speed v of 6.22m/s strikes a wall at angle θ of 30.0o and then rebounds with the same speed and angle. It is in contact with the wall for 10.4 ms.(a)The impulse was experienced by the wall is .(b)The average force exerted by the ball on the wall is .4.The muzzle speed of a bullet can be determined using a device calleda ballistic pendulum, shown in Figure. A bullet of mass m moving atspeed v encounters a large mass M hanging vertically as a pendulum atrest. The mass M absorbs the bullet. The hanging mass (now consisting ofM + m) then swings to some height h above the initial position of thependulum as shown. The initial speed v′ of the pendulum (with theembedded bullet) after impact is . The muzzlespeedv of the bullet is .III)Calculate Following Problems:1. A block of mass m 1=1.60kg initially moving to the right with a speed of 4.00 m/s on a frictionless horizontal track collides with a spring attached to a second block of massm2=2.10kg initially moving to the left with a speed of 2.50 m/s, as shown in Figure. The spring constant is 600 N/m.(a) At the instant block 1 is moving to the right with a speed of 3.00 m/s, as in Figure, determine the velocity of block 2.(b) Determine the distance the spring is compressed at that instant.Chapter 4 Work and EnergyI) Choose one correct answer among following choices1. The work done by gravity during the descent of a projectile:A. is positiveB. is negativeC. is zeroD. depends for its sign on the direction of the y axis2. A particle has a constant kinetic energyE k . Which of the following quantities must also be constant? ( )(A) r (B) v (C) v (D) P3. A 0.2kg block slides (滑行) across a frictionless floor with a speed of 10m /s. Thenet work done on the block is ( )(A) -20J (B) -10J (C) 0J (D) 20J4. A 0.50kg object moves in a horizontal circular track with a radius of 2.5m. An external force of 3.0N, always tangent to the track, causes the object to speed up as it goesaround. The work done by the external force as the mass makes one revolution is:A. 24 JB. 47 JC. 59 JD. 94 J2. A3.00-kg steel ball strikes a wall with a speed of 10.0m/s at an angle of 60.0 with t °he surface. It bounces offwith the same speed and angle. If the ball is in contact withthe wall for 0.200 s, what is the average force exerted onthe ball by the wall?3. A small ball with mass m is released from rest at the top of a container which inside wall is semicircle-shapedand frictionless. The container with mass M and radius horizontal surface, as shown. When the ball slides to point B at the bottom of thecontainer, find the normal force exerted by the container on the ball.R rests on a frictionless5. A man pushes an 80-N crate a distance of 5.0m upward along a frictionless slope that makes an angle of 30? with the horizontal. His force is parallel to the slope. If the 2speed of the crate decreases at a rate of 1.5m,/ sthen the work done by the man is: A. -200 J B. 61 J C. 140 J D. 200 J6.When a certain rubber band is stretched a distance x, it exerts a restoring force of 2 magnitude F = ax+bx , where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:2 3 2 2 3A. aL2 + bLx3B. aL + 2bL2C. a + 2bLD. aL2/2 +bL3/37.An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it the spring is extended 6.0cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10cm. While the spring is being extended by the force, the work done by the spring is: A. -3.6J B. -3.3J C. 3.6 J D. 3.3J8.Two objects with masses of m1 and m2 have the same kinetic energy and are both moving to the right. The same constant force F is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is:A. 1:4B. 4:1C. 1:2D. 1:19.At time t = 0 a 2-kg particle has a velocity of (4m/s) i - (3m/s) j . At t = 3s its velocity is (2m/s) i + (3m/s) j . During this time the work done on it was:A. 4 JB. -4JC. -12 JD. -40 J10. A 2-kg block starts from rest on a rough inclined plane that makes an angle of 6o0 with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0m down the plane, the mechanical energy of the Earth-block system changes by: A. 0 B. -9.8J C.9.8J D. - 4.9 JII)Fill in the empty space with correct answer1. A chain(链条) is held on a frictionless table with one-fourth ofits length hanging over the edge, as shown in figure. If the chainhas a lengthL and a massm , the work required to pull the hangingpart back on the table is J.2. A 0.1kg block is dropped from a height of 2m onto a spring offorce constant k = 2N/m, as shown. The maximum distance thespring will be compressed is ____________ m . (g=10m/2s)3. A single constant force F 3i 5j N acts on a4.00-kg particle.(a) If the particle moves from the origin to the point having the vector position r 2i 3j m, the work down by this force is .(b) If its speed at the origin is 4.00 m/s, the speed of the particle at r is .(c)The change in the potential energy of the system isIII)Calculate Following Problems:1. A 3.00-kg mass starts from rest and slides a distance d down africtionless 30.0 incline°. While sliding, it comes into contact withan unstressed spring of negligible mass, as shown. The mass slidesan additional 0.200 m as it is brought momentarily to rest bycompression of the spring (k=400N/m). Find the initial separation d between the mass and thespring.2.Two masses are connected by a light string passing over a light frictionless pulley as shown. The 5.00-kg mass is released from rest.(a)Determine the speed of the 3.00-kg mass just as the 5.00-kg mass hits the ground.(b)Find the maximum height to which the 3.00-kg mass rises.Chapter 5 Angular momentum and Rigid bodyI)Choose one correct answer among following choices1. A particle moves with position given by r 3ti 4j , where r is measured in meters when t is measured in seconds. For each of the following, consider only t > 0. The magnitude of the angular momentum of this particle about the origin is A. increasing in time. B. constant in time. C. decreasing in time. D. undefined2. A solid object is rotating freely without experiencing any external torques. In this caseA. Both the angular momentum and angular velocity have constant direction.B.The direction of angular momentum is constant but the direction of the angular velocity might not be constant.C.The direction of angular velocity is constant but the direction of the angular momentum might not be constant.D.Neither the angular momentum nor the angular velocity necessarily has a constant direction.3. A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. The magnitude of its angular momentum about the center of the circle is:2 2 2 2 2A. 6.0kg m·2/sB. 12 kg m·2/sC. 48 kg/m2· sD. 72 kg m·2/s24. A 6.0-kg particle moves to the right at 4.0m/s as shown. Themagnitude of its angular momentum about the point O is:22A. zeroB. 288 kg·m /sC. 144 kg·m /sD.24kg·m2/s5.Two objects are moving in the x, y plane as shown. Themagnitude of their total angular momentum (aboutthe origin O) is:A. zeroB. 6kg m·2/sC. 12kg m·2/sD. 30kg m·2/s6. A 2.0-kg block starts from rest on the positive x axis 3.0m from the origin and2thereafter has a constant acceleration given by a 4i 3j(m/s2). At the end of 2s itsangular momentum about the origin is:2 2 2A. 0B. (-36 kg ·2/sm) kC. (+48 kg m·2/s) kD. (-96 kg ·2/sm)k7.As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of12rad/s. The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75m from the origin. The z component of the angular momentum around the origin is:2 2 2 2A. 6.0kg m·2/sB. 9.0kg m·2/sC. 11kg m·2/sD. 14kg m·2/sII)Fill in the empty space with correct answer1. A particle located at the position vector r (2i j) m is acted by a forceF (i 3j)N. The torque about the origin should be _______________ N m.2.The velocity of a m=2kg body moving in the xy plane is given by v (i 2j) m/s.Its position vector is r (2i j)m. Its angular momentum L about the origin shouldbe _____________ kg m2s.3.Two particles each of mass m and speed v, travel inopposite directions along parallel lines separated by a distanced. The total angular momentum of the system about any originis .4. A particle is located at r = (0.5m) i + (-0.3m) j + (0.8m) k . A constant force ofmagnitude 2N acts on the particle. When the force acts in the positive x direction, the components of the torque about the origin is , and when the force acts in the negative x direction, the components of the torque about the origin is .5. A uniform beam of length l is in a vertical position with its lower end on a rough surface that prevents this end from slipping. The beam topples. At the instant before impact with the floor, the angular speed of the beam about its fixed end is .6. A disk of mass m and radius R is free to turn about a fixed, horizontal axle. Thedisk has an ideal string wrapped around its periphery from which another mass m (equal to the mass of the disk) is suspended, as indicated in Figure. Themagnitude of the acceleration of the falling mass is , the magnitude of theangular acceleration of the disk is .III)Calculate Following Problems:21.The pulley has radius 0.160m and moment of inertia 0.480kg·m . The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.2. A block with mass m slides down a surface inclined 30 to the horizontal. The coefficient of kinetic friction is μ. A string attached to the block is wrapped around a wheel on a fixed axis. The wheel has massm and radius R with respect to the axis of rotation. The string pulls without slipping.a) What is the acceleration of the block down the plane? b)What is the tension in the string?3. A wooden block of mass M resting on a frictionless horizontal surface is attachedto a rigid rod of length l and of negligible mass. The rod is pivotedat the other end. A bullet of mass m traveling parallel to thehorizontal surface and normal to the rod with speedv hits the blockand becomes embedded in it. What is the angular momentum ofthe bullet–block system?Chapter 9 Mechanic oscillationI)Choose one correct answer among following choices1. A particle on a spring executes simple harmonic motion. If the mass of the particle and the amplitude are both doubled then the period of oscillation will change by a factor ofA. 4.B. 8.C. 2.D. 22. A particle is in simple harmonic motion with amplitude A. At time t=0 it is at x=-A/2 and is moving in the negative direction, then the initial phase is:A. 2π3/ radB. 4π3/ radC. π radD. 3 π /2 rad3. A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. Of the following times, at which time is it furthest from the equilibrium point?A. 0.5TB. 0.7TC. TD. 1.4T4. A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:A. TB. 2TC. T/2D. 4T5.The displacement of an object oscillating on a spring is given by x(t) = A cos( ω t + φ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phasec onstant φ is:A. 0B. π /2 radC. π radD. 3 π/2 rad6.An object is undergoing simple harmonic motion with period T, amplitude A and1initial phase . Its graph of x versus t is:7.An object of mass m, oscillating on the end of a spring with spring constant k, has amplitude A. Its maximum speed is:A. A k /mB. A2k/mC. A m/ kD. Am/kII)Fill in the empty space with correct answer1. The total energy of a s imple harmonic oscillato(r谐振子) with amplitude A and force constant k is _________________ .2. Find the initial phases(初相) of the simple harmonic motion as shown in figure.12III)Calculate Following Problems:1. An object oscillates with simple harmonic motion along the x axis. Its displacement from the origin varies with time according to the equation: x (4.00m)cos( t 4 ). where t is in seconds and the angles in the parentheses are in radians.(a) Determine the amplitude, frequency, and period of the motion.(b) Calculate the velocity and acceleration of the object at any time t.(c)Determine the maximum speed and maximum acceleration of the object.2. A 50.0-g mass connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with amplitude of 4.00 cm.Find (a) the total energy of the system and (b) the speed of the mass when the displacement is 1.00cm.Find (c) the kinetic energy and (d) the potential energy when the displacement is 3.00cm.Chapter 10 WavesI) Choose one correct answer among following choices1. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:A. f = 1/TB. f = v + TC. f = vTD. f = v/T2. Water waves in the sea are observed to have a wavelength of 300m and a frequency of0.07 Hz. The speed of these waves is:A. 0.00021m/sB. 2.1m/sC. 21m/sD. 210m/s3.The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:A. upward。