※ [本文轉錄自 NTU-Exam 看板] 作者: SummerWind86 (不能寒訓...) 看板: NTU-Exam 標題: [試題] 94上 李尚凡普物甲 期末考 時間: Fri Jan 13 03:06:01 2006 課程名稱︰普通物理學甲上 課程性質︰ 課程教師︰李尚凡 開課系所︰機械 考試時間︰2006-1-12 試題 : 8. Imagine that a tunnel is drilled through the Earth , Mass M, as shown in Figure. An object of mass m at a distance r from the center of the Earth experiment gravitation attraction only by the mass within the sphere of radius r (the reddish region in the Figure). (a)Write Newton's law of gravitation for an object at the distance r from the center of the Earth, and show that the force on it is of Hooke's law form, F=-kr, find k . G is the gravitational constant. (b)Show that m follows simple harmonic motion if it moves without friction, and follows the differential equation d^2x/dt^2 + (g/r)x = 0, where g = GM/R^2. (c)A sack of mail is dropped into the tunnel. How many minutes will it arrive at the other side? R=6370km, g=9,80m/s^2 9. A train whistle (f=400Hz) sounds higher or lower in frequency depending on whether it approaches or recedes. (a)prove that the difference in frequency between the approaching and receding train whistle is Δf= 〔(2u/v)/(1-u^2/v^2)〕f where u is the speed of the train and v is the speed of sound. (70%) (b)Calculate this difference for a train moving at a speed of 130km/h. Take the speed of sound in air to be 340km/h.(30%) 10.When a metal pipe closed at one end is cut into 2 pieces, the lowest resonance frequency for the air column in one-end-closed piece is 256Hz that for the other is 440Hz . What resonant frequency would have been produced by the original length of pipe? 11.A cylinder is closed at both ends and has insulating walls. Starting with the expression w = -∫PdV and using the conding PV^γ = constant, we can show that the work done on the gas is W=〔1/(γ-1)〕(PfVf-PiVi) for an adiabatic process, which is also equal to nCv(Tf-Ti). When the cyclinder is devided into two compartments by a perectly insulating partition that is perpendicular to the axis of the cyclinder. Each compartment contains 1.00mol of oxygen, which behaves as an ideal gas with γ=7/5. Initially the two compartments have equal volumes, and their temperatures are 550K and 250K. The partition is then allowed to move slowly until the pressures on its two sides are equal. Find the final temperatures in the two compartments. 12.A sample consisitng of n mol of an ideal gas undergoes a reversible isobaric expansion from volume Vi to volume 3Vi. Find the change in entropy of the gas. 13.An idealized idesel engine operates in a cycle known as the air-standard diesel cycle, shown in Figure. Fuel is sprayed into the cyclinder at the point of maximum compression, B.Combustin occurs during the expansion B→C which is modeled as an isobaric process. Show that the efficiencyof an engine operating in this idealized diesel cycle is e = 〔1-(1/γ)〕〔(Td-Ta)/(Tc-Tb)〕 此篇與上篇相聯...2,4,5,8,13題有圖...抱歉無法提供... 老師的答題方式為13選10題來做...沒題10分. --

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