复旦大学力学系 2006~2007学年第一学期期终考试试卷 口A卷口B卷 课程名称:大学物理上课程代码:PHYS120001.06 开课院系:物理系考试形式:闭卷 姓名 学号: 专业 题号1 3 4 6 8总分 得分 L. Fill the blank and choose the correct answer (33") 1. The equation of a transverse wave traveling along a very long string is given by y=(6.0 cm) sin((2.0T rad/m)x+(4.0 rad/s)z]. The amplitude is the frequency is the speed is the direction of propagation of the wave the maximum transverse speed of a particle in the string is 2. A crate with mass m is resting on a platform scale() Ft). The gravitational constant at the place 装订线内不要答题 is g. After considering the Earths rotation( with angular speed o), we can read the weight of the crate from the scale with the value of 3. A mass(m)on a spring(k)that obeys Hooke's law has a period of 0.50 seconds when hung vertically and allowed to oscillate freely. The mass/spring system is placed on a frictionless incline plane, as shown below. The natural period for this system is (a)less than 0.50 seconds (b) greater than 0.50 seconds (c) Need to know angle of incline to determine answer (d)equal to 0.50 seconds 4. A sound source produces a certain intensity. If you were to double your distance from it, the new intensity would be (a)the same as before (b)twice the original intensity (c)one-quarter times the original intensity (d)half as much as it was originally (e)1. 41 times less the original intensity 5. A bird flying directly away from a birdwatcher and directly toward a distant cliff(&i)at a speed of 15 m/s. The bird produces a shrill cry whose frequency is 800 Hz. The frequency in the sound that the bird watcher hears directly from the bird The frequency that the birdwatcher hears in the echo(a )that is reflected from the cliff (Sound speed is 340 m/s)
1 复旦大学力学系 2006～2007 学年第一学期期终考试试卷 □A 卷 □B 卷 课程名称：_ 大学物理上 课程代码：_PHYS120001.06_ 开课院系：__物理系_______ 考试形式： 闭卷 姓 名： 学 号： 专 业： 题 号 1 2 3 4 5 6 7 8 总 分 得 分 I. Fill the blank and choose the correct answer (33’) 1. The equation of a transverse wave traveling along a very long string is given by y=(6.0 cm) sin[(2.0π rad/m)x+(4.0π rad/s)t]. The amplitude is_________,the wavelength is __________, the frequency is ___________, the speed is ___________,the direction of propagation of the wave is__________, the maximum transverse speed of a particle in the string is_____________.(6’) 2. A crate with mass m is resting on a platform scale(磅秤). The gravitational constant at the place is g. After considering the Earth’s rotation (with angular speed ω), we can read the weight of the crate from the scale with the value of ___________________. 3. A mass (m) on a spring (k) that obeys Hooke's law has a period of 0.50 seconds when hung vertically and allowed to oscillate freely. The mass/spring system is placed on a frictionless incline plane, as shown below. The natural period for this system is ______________________________. (a) less than 0.50 seconds. (b) greater than 0.50 seconds. (c) Need to know angle of incline to determine answer. (d) equal to 0.50 seconds. 4. A sound source produces a certain intensity. If you were to double your distance from it, the new intensity would be ______________. (a) the same as before. (b) twice the original intensity (c) one-quarter times the original intensity (d) half as much as it was originally (e) 1.41 times less the original intensity. 5. A bird flying directly away from a birdwatcher and directly toward a distant cliff(悬崖) at a speed of 15 m/s. The bird produces a shrill cry whose frequency is 800 Hz. The frequency in the sound that the bird watcher hears directly from the bird is_______________;The frequency that the birdwatcher hears in the echo (回声) that is reflected from the cliff is__________________. (Sound speed is 340 m/s) …………………………..………………………………………………………………………………………………………………………………………………………. ( 装 订 线 内 不 要 答 题 )
6. A nickel-steel rod at 21 C is 0.62406 m in length. Raising the temperature to 31C produces an elongation of 121.6 uam. The coefficient of linear expansion is 7. The specific heat of many solids at very low temperatures varies with absolute temperature T according to the relation c=AT, where A is a constant. The heat energy needed to raise the temperature of a mass m of such a substance from T=0 to T=20K is 8. Which type of ideal gas will have the largest value for Cp-Cv? (a)Monatomic (b) Diatomic (c)Polyatomic (d) The value will be the same for all 9. Which of the following states can not express the second law of thermodynamics? (a) You can not change completely heat energy into work (b)The entropy of an irreversible process never decreases (c) You can not transfer heat energy from a low-temperature reservoir to a higher temperature reservoir without doing work (d)The entropy of a closed system never decreases Il. An observer is standing on a platform of length 65 m. a train passes at a relative speed of 0. 80c moving parallel to the edge of the platform. The observer S notes that the front and back of the train simultaneously line up with the ends of the platform at a particular instant. (12) (a)According to S, what is the time necessary for the train to pass a particular point on the train? (b)What is the rest length of the train? (c)According to an observer S on the train, what is the length of the platform? Ill. The force of interaction between two atoms in certain diatomic molecules can be represented by F=-ar+b/r in which a and b are positive constants and r is the separation distance of the atoms. Then(a)find the separation at equilibrium; (b) for small oscillations about this equilibrium separation,write out the equation of the motion(Hint: expand the force at equilibrium separation and do the first order approximation) and find the solution for the equation;(c) find the period of the motion.(12
2 6. A nickel-steel rod at C D 21 is 0.62406 m in length. Raising the temperature to C D 31 produces an elongation of 121.6 μm. The coefficient of linear expansion is __________________. 7. The specific heat of many solids at very low temperatures varies with absolute temperature T according to the relation c=AT3 , where A is a constant. The heat energy needed to raise the temperature of a mass m of such a substance from T=0 to T=20K is ________________________. 8. Which type of ideal gas will have the largest value for Cp – Cv ?_________________________ (a) Monatomic (b) Diatomic (c) Polyatomic (d) The value will be the same for all. 9. Which of the following states can not express the second law of thermodynamics?___________ (a) You can not change completely heat energy into work. (b) The entropy of an irreversible process never decreases. (c) You can not transfer heat energy from a low-temperature reservoir to a higher temperature reservoir without doing work.. (d) The entropy of a closed system never decreases. II. An observer is standing on a platform of length 65 m. A train passes at a relative speed of 0.80c moving parallel to the edge of the platform. The observer s notes that the front and back of the train simultaneously line up with the ends of the platform at a particular instant. (12’) (a) According to s, what is the time necessary for the train to pass a particular point on the train? (b) What is the rest length of the train? (c) According to an observer s’ on the train, what is the length of the platform? III. The force of interaction between two atoms in certain diatomic molecules can be represented by F= -a/r2 +b/r3 in which a and b are positive constants and r is the separation distance of the atoms. Then (a) find the separation at equilibrium; (b) for small oscillations about this equilibrium separation, write out the equation of the motion (Hint: expand the force at equilibrium separation and do the first order approximation) and find the solution for the equation; (c) find the period of the motion. (12’)
IV. Sources separated by 20 m vibrate according to the equations y=0.06singr t)(m) y2=0.02sinGr t)(m). They send out waves along a rod of speed first source and 8 m from the second? (8) 12m 装订线内不要答题 V. The equation for a particular standing wave on a string is y=0. 15sin(5x)cos(300n)m. Find the (aJamplitude of vibration at the antinode, (b)distance between nodes,(c)wavelength, and (d)frequency. (8)
3 IV. Sources separated by 20 m vibrate according to the equations ' 0.06sin( ) 1 y = π t (m), ' 0.02sin( ) 2 y = π t (m). They send out waves along a rod of speed 3 m/s. What is the equation of motion of a particle 12m from the first source and 8 m from the second? (8’) V. The equation for a particular standing wave on a string is y=0.15sin(5x)cos(300t) m. Find the (a)amplitude of vibration at the antinode, (b)distance between nodes, (c)wavelength, and (d)frequency. (8’) x 20m 12m 8m …………………………..………………………………………………………………………………………………………………………………………………………. ( 装 订 线 内 不 要 答 题 )
VI. The figure shows a hypothetical speed distribution of n gas molecules with N(v)=Cv for 0vo. Find(a)an expression for C in terms of N and vo,(b)the average speed of the particles, and(c) the rms speed of the particles VIl. One mole of an ideal diatomic gas is caused to pass through the cycle shown on the pl diagram in below figure, where V2=3V1 Determine, in terms of pl, VI, T1, and R:(a)AEint, and AS for all three processes, (b) the efficiency of the cycle (15) Isotherm Adiabatic Constant volume
4 VI. The figure shows a hypothetical speed distribution of N gas molecules with 2 N(v) = Cv for 0v0. Find (a) an expression for C in terms of N and v0, (b) the average speed of the particles, and (c) the rms speed of the particles. (12’) VII. One mole of an ideal diatomic gas is caused to pass through the cycle shown on the pV diagram in below figure, where V2=3V1. Determine, in terms of p1,V1, T1, and R: (a) ∆Eint, and ∆S for all three processes, (b) the efficiency of the cycle. (15’) Adiabatic Isotherm V1 V2 Constant volume
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