課程名稱︰普通物理學甲上 課程性質︰共同必修 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）︰98.1.15 考試時限（分鐘）：2小時40分 是否需發放獎勵金：是，謝謝 （如未明確表示，則不予發放） 試題 : General Physics Final Exam 2009/1/15 Instructor:Prof. CY Chao 1.Figure 1 shows an uniform solid cylinder of mass M, Radius R, and length L. What is the rotational inertia about the central diameter axis? Derive it in detail. (10%) 2.Figure 2 is a gyroscope consists of a wheel foxed to a shaft. Plese derive the precession rate of this device where the mass of the wheel is M (the mass of the shaft is ignored), the angular speed is ω, the rotational inertia about its shaft is I and the distance between the center of the wheel and the tip O is r. (10%) 3.Please derive the gravitational force between an uniform spherical sheel with total mass M and a particle with mass m witch is outside the shell. The distance between the particle and the center of the sphere shell is r. (do it by integration) (10%) 4.Figure 3 shows a dampeed oscillator with a block (mass m), a spring (spring constant k) and damping constant b between vane and liquid. The rod extending from block to the vane (assume massless) is also assumed massless. When the block start oscillating, a dragging force is generated and is proportional to the vane's velocity. (a) Write down the equation of motion of the system and solve it in terms of x(t). What are the frequency, the amplitude, and the mechanical energy of this damping system? (b) Draw a graph of the equation of motion, and denote the features on it. (6%,4%) 5. In fig. 4, an aluminum wire, of length L1 = 60.0cm, cross-sectional area 1.00×10^(-2)cm^2, and density 2.60g/cm^3, is joined to a steel wire, of density 7.80g/cm^3 and the same cross-sectional area. The compound wire, load with a block of mass m = 10kg, is arranged so that the distance L2 from the joint to the supporting pulley is 86.6cm. Transverse waves are set up on the wire by an external source of variable freqyency; a node is located at the pulley. (a) Find the lowest frequency that penerates a standing wave the joint as one of the nodes. (b)How many nodes are observed at this frequency? (6%, 4%) 6. Two trains are traveling toward each other at 30.5m/s relativeto the ground . One train is blowing a whistle at 500 Hz. (a) What frequency is heard on the other train in still air? (b) What frequency is heard in the ither train if the wind is blowing at 30.5m/s toward the whistle and away from the listener? (4%, 6%) 老師後來有補充 聲速是343m/s 7. Figure 5 shows the cross section of a wall made of three layers. The thickness of the layers are L1, L2 = 0.700 L1, and L3 = 0.350 L1. The thermal conductivities are k1, k2 = 0.900 k1, and k3 = 0.800 k1. The temperatures at the left and right sides of the wall are TH = 30.0度C and TC = -15度C, respectively. Themal conduction is steady. (a) What is the temperature difference ΔT2 across layer 2 (between the left and right sides of the layer)? If k2 were, insteadn equal to 1.1k1, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previous, and (c) what would be the value of ΔT2? (4%,3%,3%) 8.Show that the relation between the pressure and the volume during an adiabetic expansion of ideal gas is γ ρV^ = constan where γ = CP/CV (10%) 9. 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 2 (3/2) 2 (-Mυ^ /2RT) P(υ) = 4π(M/2πRT)^ υ^ e^ ∞ (-t) (z-1) (You may need this: ∫ e^ t^ dt = (z-1)! ) (10%) 0 10. Derive the vhange in entropy when n mole of an ideal gas doubles its volume in a free wxpansion. (you should derive the result by using statistical mechanics) (10%) 老師後來說將should 改成must 一定要用統計力學來解XD --

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