課程名稱︰普通物理甲上 課程性質︰必修 課程教師︰趙治宇 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2012/1/12 考試時限（分鐘）：170min 是否需發放獎勵金：是 謝謝:D （如未明確表示，則不予發放） 試題 : 1.Prove that the speed v of a sound wave in a medium with bulk modulus B and density ρ is given by v=(B/ρ)^(1/2) (8%) 2.A system with a container which is filled with an unknown gas of molar mass M is maintained at temperature T. Please derive the average speed (Vavg) of the gas molecules. The probability distribution function is P(v)=4π*(M/2πRT)^(3/2)*(v^2)*(e^(-Mv^2/2RT)). ∞ [You may need this: ∫ e^(-t)*t^(Z-1) dt=(z-1)!] (8%) 0 3.Design an experiment to measure the inertia of a irregular object precisely. (8%) 4.(a)How to detect the universe background radiation. (4%) (b)What's the evidence of the universe expansion. (4%) 5.Show that the relation between the pressure and the volume during an adiabatic expansion of ideal gas is pV^γ= constant, where γ=Cp/Cv (8%) 6.Derive the change in entropy △S when n mole of an ideal gas doubles its volume in a free expansion.(you must derive the result by using statistical machanisms.) (8%) 7.Two identical piano wires have a fundamental frequency of 600 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurence of 8.0 beats/s when both wires oscillate simultaneously? (8%) 8.Derive the change in entropy △S between the initial state (Vi,Ti) and final state (Vf,Tf) of an ideal gas in a reversible process (Fig.1) (Express your answer with Vi,Ti,Vf,Tf) (6%) T | .(Vi,Ti) | | | . (Vf,Tf) | |＿＿＿＿＿＿＿ V Fig.1 9.Figure 2 shows a rigid assembly of a thin hoop (of mass m and radius R=0.150m ) and a thin radius rod (of mass m and length L=2.00R ). The assembly is upright,but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly im such a nudge is negligible, what would be the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? (8%) 10.Two 2.00kg balls are attached to the ends of a thin rod of length 50.0cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal.(Fig3), a50.0g wad of wet putty drops onto one of the balls, hitting it with a speed of 3.00m/s and the sticking to it. (a)What is the angular speed of the system just after the putty wad hits? (b)What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c)Through what angle will the system rotate before it momentarily stops? (4%,4%,4%) putty wad 　*　　 　rotation axis　　　　　 | | 　＿＿＿＿＿＿＿＿＿＿ Ｏ＿＿＿＿Ｘ＿＿＿＿Ｏ Fig.3 11.For the stepladder shown in Fig.4, sides AC and CE are each 2.44m long and hinged at C. Bar BD is a tie-rod 0.762m long, halfway up. A man weighing 854N climbs 1.80m along the ladder. Assuming that the floor is frictionless and neglecting the mass of the ladder, find (a)the tension in the tie-rod (b)the magnitudes of the forces on the ladder from the floor at A (C)the magnitudes of the forces on the ladder from the floor at E (4%,3%,3%) 12.In Fig.5, a 2.50kg disk of diameter D=42.0cm is supported by a rod of length L=76.0cm and negligible mass that is pivoted at its end. (a)With the massless torsion spring unconnected, what is the period of oscillation? (b)With the torsion spring connected, the rod is vertical at equilibrium. What is the torsion constant of the spring if the period of oscillation has been decreased by 0.500s? (4%,4%) *考試可攜帶工程計算機與電子辭典 --

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