※ [本文轉錄自 NTU-Exam 看板] 作者: Danceaway (瑤小五) 看板: NTU-Exam 標題: [試題] 94上 梁啟德 普物期末考 時間: Sat Jan 14 09:55:40 2006 課程名稱︰普通物理學甲 課程性質︰ 課程教師︰梁啟德 開課系所︰物理系 考試時間︰2 HR 試題 : 1. Please prove that ofr an adiabatic(絕熱) expansion(膨脹) of an ideal gas, the pressure p and the volume V obey pV^γ= a constant, where γ =Cp/Cv is the ratioa of the molar specific heats(莫耳比熱) for the gas. Cp is the molar specific hea for a consant pressure process and Cv is the molar specific heat for a consant volume process, respectively(10%) 2. If the remperature fo a rod of length : is raised by an amount of ΔT, its length is found to increase by an amountΔL=LαΔT, where αis a constant called the coefficient of linear expansion. Please prove that the coefficient of volume expansionβ is given by β=3α.(10%) [Hint:ΔV =VβΔT] 3. A toy rocket moves at a speed of 242m/s directly toward a stationary pole while emitting sound waves at freauency f=1250Hz (a) What frenquency f' is sensed by a detector that is attached to the pole?[10%] (b) Some of the sound reaching the pole reflects back to the rocket, which has an onboard detector. What frequency f" does it detect?[10%][Hint: The speed of sound is 343m/s. Please consider the Doppler effect 都卜勒效應] 4. Determine the amplitude of the resultant wave when two sinusoidal string waves having the same frequency and travelling in the same direction are combined, if their amplitudes are 3.0 cm and 4.0 cm and they have phase constants of 0 and π/2 rad, respectively(10%). (Hint: use Phasors) 5. A block of mass m is connected to two spring of force constants k1 and k2 as shown in Figure 1. The block moves on a frictionless table after it is displaced from equilibrium and released. Show that the block exhibits simple harmonic motion with period T=2π(m/k1+k2)^1/2(10%) Figure 1: ├══●══┤ k1 m k2 6. An ideal gas is carried through a thermodynamic cycle consisting of two isobaric(等壓) and two isothermal(等溫) precesses as shown in Fig.2. Please show that the net work done on the gas in the entire cycle is given by Wnet=-P1(V2-V1)ln(P2/P1) Figure 2:P-V圖上有ABCD四點 A-B, C-D為等溫，B-C, D-A為等壓，A點、D點的溫、壓分別為P1V1和P2V2。 7. A block of wood floats in water with two-thirds(2/3) of its volume submerged(浸入). In oil the block floats with 0.90 of its volume submerged, Find the density of (a)the wood(5%) and (b) the oil.(5%) 8. Twho stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass(Fig 3). Show that each star has a period given by T^2=4π^2d^3/G(M+m) (10%) Hint: Apply Newton's second law to each star. Note that the center-of-mass condition requires that Mr2=mr1, where r1+r2=d. Figure 3: 如hint所描述的。 9. Big Ben(大笨鐘), the Parliament Building tower clock in London(倫敦) hour and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg and 100 kg, respectively. Calculate the total angylar momentum of these hands about the center point. Treat the hands as long thin uniform rods.(10%) -- 這個小孩好奇怪。 --

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