※ [本文转录自 NTU-Exam 看板] 作者: TassTW (为文载道尊於势) 看板: NTU-Exam 标题: [试题] 94上 电机系 普通物理甲上　张颜暐 期末考 时间: Fri Jan 13 19:30:14 2006 课程名称︰ 普通物理学甲上 课程性质︰ 大一必修 课程教师︰ 张颜暐 开课系所︰ 电机工程学系 考试时间︰ 2006/01/12 试题 : 1.Write down the wave equation for a transverse plane wave propagating along y-direction, oscillating along x-direction, angular frequency ω, velocity v and amplitude A. Write down the wave equation for a longtitudinal plane wave propagating along z-direction with angular frequency ω, wavelength λ and amplitude B. Write down the wave equation for a spherical transverse wave propagating along radial direction with frequency f, and wave number k. Define the amplitude and oscillating direction of the spherical wave yourself. (10) 2.The gravittational force between two particles with mass of m and M, initially at rest at great separation, pulls them together. Find the speed of either particle relative to the other when the separation between the two particles is d. Express your answer in term of m, M, G and d. (10) 3.The potential energy between nitrogen atoms in a N2 molecule is given by U(x) = a/x^12 - b/x^6, where x is the distence between nitrogen atoms. Assume the mass of the nitrogen atom is m, find the oscillation frequency of a small vibration of N2. (10) Taylor expansion: U(x) = U(x0) + dU/dx (x-x0) + 1/2 d^2U/dx^2 (x-x0)^2, where x0 is the equilibrium position. 4.Explain why when a body is fully or partially immersed in a fluid it is buoyed by a force that is equal to the weight of the fluid that body displaces. (Archimedes' principle) (5) 5.Assume that the density of the air is proportional to the air pressure in earth's atmosphere. Find the air pressure as a function of altitude(height). Assume that at sea level the air pressure is P0 and the air density is ρ0. (10) 6.Find the average power transported by a sinusodical string wave with velocity v and angular frequency ω. Assume the string linear density of the string is μ. (10) 7. Two rectangular metal rods of identical shape have thermal conductivity k and 2k respectively are welded end to end, and side to side together as shown in Fig. 1-a and Fig. 1-b. Fid the ratio of heat conduction rate of these two arrangements. (10) Fig. 1-a 0℃ ■■■■■■ 100℃ Fig. 1-b 100℃ ■■■ ■■■ 0 ℃ 8.The cycles in Fig. 2 represents the operation of an internal combustion engine. Assume the gasoline-air intake mixture is an ideal gas with γ=1.30. (a) What are the ratios T2/T1, T3/T1, T4/T1, P3/P1 and P4/P1? (b) What is the engine efficiency? (15) Fig. 2 3.00 p1┤２～﹐ 2->3 and 4->1 are adiabatic ｜│　～３ ｜│　　│ p1┤１～﹐│ ｜　　～４ ｜ └┬──┬─ v1 4.00v1 9.Fig. 3 represents a Carnot engine that works between temperature T1 = 400K and T2 = 150K and drives a Carnot refrigerator that works between temperature T3 = 325K and T4 = 225K. What is the ratio Q3/Q1? (10) Fig. 3 │ T1 │ │ T3 │ ╰┬─┬╯ ╰┬─┬╯ Q1│ │ │ │Q3 │ ╰────╯ │ │╭──────╮│ Q2││ W ││Q4 ╭┴┴╮ ╭┴┴╮ │ T2 │ │ T4 │ 10.In Fig 4-a, particle P is to move parallel to the x and x' axes of reference frames S and S'; at a certain velocity relative to frame S. Frame S' is to move parallel to the x axis of Frame S at velocity v. Fig 4.b gives the velocity u' of the particle relative to frame S' for a range of values for v. What value will u' have if (a) v = 0.9c and (b) v -> c. (10) Fig. 4-a y y' │ ├─→ │S │S' │ │ ˙P └─x└───x' Fig. 4-b 0.8c├─▂ u' │ ▇︸︷▂▁ 0.4c│ ￣ │ └──┴──┴── 0 0.2c 0.4c v -- 「我们爱星星至深无惧於黑暗。」 "We have loved the stars too fondly to be fearful of the night." --

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