华工《大学物理》20112012试卷(B卷)答案.pdf
诚信应考,考试作弊将带来严重后果！华南理工大学期末考试 大学物理2011-2012(2)期末试卷（B 卷）注意事项：1.考前请将密封线内各项信息填写清楚；2.所有答案请直接答在答题纸上；3考试形式：闭卷；4.本试卷共 15 题，满分 100 分，考试时间 120 分钟。考试时间：2012 年 7 月 2 日 9：00-11：00 题 号 1 2 3 4 5 6 7 8 得 分 评卷人 题 号 9 10 11 12 13 14 15 总分 得 分 评卷人 Completion(Total 40 points,4 points/question)1.A particle leaves the origin with an initial velocity =(3.00i)m/sv and a constant acceleration 2=1.00i0.500j m/sa.When it reaches its maximum x coordinate,its velocity is=1.5/mvm s j.2.A force 2=3.00Fcxxi acts on a particle as the particle moves along an x axis,with F in newtons,x in meters,and c a constant.At =0 x,the particles kinetic energy is 20.0 J;at =3.00 mx,it is 11.0 J.Find =c 4.00 N/m .3.The figure shows a particle moving in a horizontal circle.A force)(0j yi xFF acts on the particle.During the particle moving from point O to(0，2R),the work done by Fis 202F R.4.A 4.0 kg bundle starts up a 30o incline with 128 J of kinetic energy.If the coefficient of kinetic friction between bundle and incline is 0.30,it will slide up the incline 4.3 m._ _ 姓名 学号 学院 专业 座位号 (密 封 线 内 不 答 题)密封线 x y R O 5.The angular acceleration of a wheel is 42=6.04.0tt,with in radians per second-squared and t in seconds.At time =0t,the wheel has an angular velocity of+2.0 rad/s and an angular position of+1.0 rad.Write expressions for (a)the angular velocity 531.21.332.0tt(rad/s);(b)the angular position 640.200.332.01.0ttt(rad).6.An iron anchor of density 7870 kg/m3 appears 200 N lighter in water than in air.The volume of the anchor is 232.04 10 m.Its weight in the air is 31.57 10 N.7.In the figure,two diverse springs of spring constant respectively 1k and 2k are in series attached to a block of mass m,the frequency of oscillation is 12121()2fm kkk k.8.A stationary motion detector sends sound waves of frequency 0.150 MHz toward a truck approaching at a speed of 45.0 m/s.The frequency of the waves reflected back to the detector is 0.195 MHz .9.The figure represents a closed cycle for a gas(the figure is not drawn to scale).The change in the internal energy of the gas as it moves from a to c along the path abc is-200 J.As it moves from c to d,180 J must be transferred to it as heat.An additional transfer of 80 J to it as heat is needed as it moves from d to a.As it moves from c to d,the work done on the gas is 60 J .10.The figure shows the Maxwell-Boltzmann velocity distribution functions of a gas for two different temperatures 1T and 2T,then 1T 2T(,or=).k1 m k2 p V a d b c Calculation(Total 60 points)11(Total 12 points,6 points/question)A person of mass M=32.5 kg on ice disdainfully throws a quantum text book weighing m=2.25 kg at bv=12 m/s.The book is thrown from zero height and the total distance between the book and the offender is 15.2 m when the book lands.(1)At what angle was this excellent book thrown?(2)How fast is the offender moving?Solution:(1)Since there are no external forces in the horizontal direction on the person-book system,the x component of the center of mass does not move while the book is in the air.We can use this fact to find how far the book travels before it hits the ground.0()cmbbbMXx mxx MxxmM Where 15.2 mx is the total final separation of the book and the person.Plugging in numbers,14.2 mbx.Take the book to be thrown at an angle with respect to the horizontal.Then the books initial velocity in the x direction is cosbv and that in the y direction is sinbv.In the x direction we know that cos cosbbbbxxv ttv.In the y direction,the book starts and ends the same height so,2110sin sin=22bbv tgtvgt Substitute t,we find 2sin2 =37.62bbgxv.(2)Taking the persons final velocity to be v,we know from conservation of momentum that cos cos.bbmMvmvvvM we find 0.66/vm s.Answer:(1)the book is thrown at angle=37.6;(2)the offender has a final velocity of 0.66/vm s.(Note:because of the double angle formula,for,there is a second solution when the angle is equal to 90).12.(Total 12 points,4 points/question)(1)What is the rotational inertia CMI of a propeller with three blades(treated as rods)of mass m,length L at 120o relative to each other?(2)If a torque acts on this propeller,how long will it take to reach an angular velocity?(3)How many revolutions will it have made before reaching this?Solution(1)We know that the rotational inertia of a single rod rotating around its end is 213mL.Its not hard to convince oneself that if there are three of them rotating around the same axis and in the same plane,the rotational inertia is just three times this,2CMImL.(2)Since t and CMI,2CMImLt.(3)From our knowledge of constant acceleration problems,222222 222CMImL The number of revolution it made is 2224mLN 13(Total 12 points)A hollow spherical iron shell floats almost completely submerged in water.The outer diameter is 60.0 cm,and the density of iron is 7.87 g/cm3.Find the inner diameter.Solution For our estimate of submergedV we interpret“almost completely submerged”to mean 3submerged4 where 30 cm3ooVrr Thus,equilibrium of forces(on the iron sphere)leads to grgVgrrgmFowatersubmergedwaterioironironb 333343434 Where ir is the inner radius(half the inner diameter).Substitute into our estimate for submergedV as well as the densities of water(1.0 g/cm3)and iron(7.87 g/cm3),we obtain the inner diameter:31122ironwateroirr=57.3cm 14(Total 12 points,4 points/question)A progressive wave travelling along a string has maximum amplitude A0.0821 m,angular frequency =100 rad/sand wave number =22.0 rad/mk.If the wave has zero amplitude at =0tand =0 x for its starting conditions(1)State the wave function that represents the progressive wave motion for this wave travelling in the negative x-direction.(2)Find the wavelength,period T and the traveling speed v of this wave.(3)Find its amplitude at a time =2.5 st at a distance =3.2 mxfrom its origin,for this wave travelling in the negative x-direction.Solution(1)m 1000.22sin102.82txy(2)22221000.2856 m;0.0628 s;4.545 m/s2210022Tvkk(3)m 10-9.85.21002.30.22sin102.8-32y.15.(Total 12 points,4 points/question)One mole of an ideal diatomic gas goes from a to c along the diagonal path in Figure.The scale of the vertical axis is set by =5.0 kPaabpand =2.0 kPacp,and the scale of the horizontal axis is set by 3=4.0 mbcV and 3=2.0 maV.During the transition,(1)What is the change in internal energy of the gas?(2)How much energy is added to the gas as heat?(3)How much heat is required if the gas goes from a to c along the indirect path abc?a b c Va Vbc Volume(m3)Solution Two formulas(other than the first law of thermodynamics)will be used.It is straightforward to show,for any process that is depicted as a straight line on the pV diagram,the work is straight2ifppWV Which includes,as special cases,Wp V for constant-pressure process and 0W for constant-volume processes.Further int22ffEnRTpV Where we have used the ideal gas law in the last step.We emphasize that,in order to obtain work and energy in joules,pressure should be in pascals(N/m2)and volume should be in cubic meters.The degrees of freedom for a diatomic gas is 5f.(1)The internal energy change is pab Pc Pressure(kPa)3333int int 355()(2.0 10 Pa)(4.0 m)(5.0 10 Pa)(2.0 m)22 5.0 10 JcaccaaEEp Vp V (2)The work done during the process represented by the diagonal path is 333diag(3.5 10 Pa)(2.0 m)7.0 10 J2accappWVV Consequently,the first law of thermodynamics gives 333diagintdiag5.0 107.0 10 J2.0 10 JQEW .(3)The fact that intE only depends on the initial and final states,and not on the details of the“path”between them,means we can write 3intint int 5.0 10 JcaEEE for the indirect path,too.In this case,the work done consists of that done during the constant pressure part(the horizontal line in the graph)plus that done during the constant volume part(the vertical line):334indirect(5.0 10 Pa)(2.0 m)+01.0 10 JW Now,the first law of thermodynamics leads to 343indirectintindirect(5.0 101.0 10)J5.0 10 JQEW
