课程名称︰普通物理学甲上 课程性质︰必带 课程教师︰朱士维助理教授 开课学院：理学院 开课系所︰材料系 考试日期（年月日）︰10/01/11 考试时限（分钟）：130(1020~1230) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.[5]During our entire lifetime, int4eractions with various people are inevitable. It is vital to show mutual respect in these interactions. One of the key components in successful interaction/communication is to know others' names. So, please write down the names of our teaching assistant in the General physics course(in Chinese or English, be sure you spell correctly) 2.[25]A 60 kgw person is performing fast-spin during ice-skating. He starts from slow-spin with stretched arms, and speeds up when he raises his arm (a) assuming the weight of each arm is 5 kgw, and using the following simplified model, what are the moments of inertia of the performer with streched arms and raised arms, respectively? (b) The speed of slow-spin is 1rev/sec. What is the spin speed when the performer raises his arms? (c) What are the kinetic energies of the streched-arm and raised-arm situation, respectively? (d)Apperantly, the rotation energy does not conserve during this movement. Where does the additional kinetic energy come from? (Note: even if you don't know how to calculate (a), you can still finish the following by assuming the moment of inertia to be I1,I2 respectively. 3[15] In class, we have derived Kepler's law from Neewton's law, and found that the equation of trajectory is (x+c)^2 (y)^2 (a^2=(GM)^2/4E^2 -------+----=1 b^2=L^2/=2mE a^2 b^2 c=A/-2mE) E is the total mechanical energy, L is the angular momentum, and A is the Laplace-Runge-Lenz factor. (a) When the total mechanic energy E<0, what is the shape and area of the trajectory? (b) What is the shape of the trajectory when E->0 ? Please explicitly write down the equation of the tracjectory. 4.[15] Remember the magic lid? By simply putting it on a cup, we were able to lift the cup with the little mouse. (a) What is the principle of it? (b) Assuming the initial volume inside the cup is 1000cm^3 with the lid on, the area of the cup opening is 100cm^2, the weight of the cup is 500g, and the atmospheric pressure in the room is 1 atm, how much volume change in the cup is necessary to allow us to lift this cup? 5.[10] In an in-class demonstration, we put 1ml water inside a 600ml plastic bottle and boiled the water. After the water vapor at 373K filled the bottle, we tightened the bottle cap. When it was cooled down to ambient temperature at 293K, the bottle crushed. Please estimate the remaining volume of the bottle at this temperature.(The vapor pressure of water is 760 mmHg at 373K and drops to 17.54 mmHg at 293K) 6.[10] (adapted from prob. 17-103, waterfall accoustics) The turbulent impact of the water in a waterfall causes the surrounding ground to oscillate in a wide range of low frequencies. If the water falls freely(no rock in the way), the oscillations are greatest in amplitude at a particular frequency fm. This fact suggests that acoustic resonance is involved and fm is fundamental frequency. The following table ends (1/2) are effectively involved in waterfall resonance. (Hint: The speed of the turbulent water is about 1100m/s) fm(Hz) 2.8 3.7 4.4 11.2 35 L(m) 100 75 64 25 8 7.[20] (a) A propogating sinusoidal wave is expressed as s'=socos(x-t), with x in meter and t in second. Please find out the value of its frequency and angular wave number. (b) What is the speed of s'=socos(x-t)? (c) When two waves s1=5cos((2000pi/340)x-2000pi*t) and s2=5cos((2002pi/340)x -2002pi*t) propogate together, beating happens. Please derive the beating frequency mathemetically summing these two propogating waves. 8.[10] (a) Define "reversible" and "irreversible" (b) Explain why the effciency of a reversible Carnot engine is higher than an irreversible one? 9.[10] An ideal gas is taken reversibly from state i, at temperature T1, to any of the other states labeled, I, II, III, IV, V on the P-V diagram. All are at the same temperature T2. Rank the five processes according to the change in entropy of gas, least to greatest. Be sure to explain the reason.(Since the diagram is hard to draw, I will explain that below. The path I is vertically going up from i(T1) to an isothermal curve(T2) and V is an isobaric process from i(T1) to another point on the isothermal curve(T2), and II, III, IV are between I and V) --

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