課程名稱︰普通物理學甲上 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）︰2013/1/10 考試時限（分鐘）：170mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 請搭配圖片服用：http://i.imgur.com/UUngXtU.jpg 1. Show that the relation between the pressure and the volume during an adiabatic expansion of ideal gas is p‧(V^γ) = constant, where γ=Cp/Cv. (10%) 2. Design an experiment to measure the inertia of an irregular object precisely. (10%) 3. (a) What's the principle and the application of a strain gauge; (b) Describe the principle of equivalence for general theory of relativity. (5%, 5%) 4. Show that (a) there is no perfect engine, (b) there is no perfect refrigerator. (5%, 5%) 5. Calculate the gravitational force between the two objects m, M (a uniform disc with radius R) shown in Fig.1. (10%) 6. In Fig.2, a small 50g block slides down a frictionless surface through height h=15cm and then sticks to a uniform rod of mass 100g and length 35cm. The rod pivots about point O through angle θ before momentarily stopping. Find θ. (10%) 7. In Fig.3, an aluminum wire, of length L1=60.0cm, cross-sectional area 1.25×10^-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, loaded with a block of mass m=10.0kg, 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 frequency; a node is located at the pulley. (a) Find the lowest frequency that generates a standing wave having the joint as one of the nodes. (b) How many nodes are observed at this frequency? (10%) 8. Two identical piano wires have a fundamental frequency of 600Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 8.0beat/s when both wires oscillate simultaneously? (10%) 9. Figure 4 shows (in cross section) a wall consisting of four layers, with thermal conductivities k1=0.060W/m.k, k3=0.040W/m.k, k4=0.12W/m.k (k2 is not known). The layer thicknesses are L1=1.5cm, L3=2.8cm, and L4=3.5cm (L2 is not known). The known temperatures are T1=30℃, T12=25℃, and T4=-10℃. Energy transfer through the wall is steady. What is interface temperature T34? (10%) 10. Figure 5 shows a hypothetical speed distribution for particles of a certain gas: P(v)=C‧v^2 for 0＜v≦V0 and P(v)=0 for v＞V0. Find (a) an expression for C in terms of V0, (b) the average speed of the particles, and (c) their rms speed. (10%) 11. In Fig.6, a plank with a mass M rides on top of two identical solid cylindrical rollers that have radius R and mass M. The plank is pulled by a constant horizontal force F applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on a flat surface. There is also no slipping between the cylinders and the plank. (a) Find the acceleration of the plank and of the rollers. (b) Find the friction force between one cylinder and the plank? (10%) 12. 兩條很輕，長度同為l的平行繩子，繫住一質量為m，長度為2a的均勻直桿的兩端， 使其鉛直懸掛如下圖7所示。不考慮任何因摩擦而損失的能量，輕敲直桿的一端， 　　使其繞通過直桿質心的鉛直軸轉動，起始的角速度為ω0。假設在運動過程中， 　　繩子的長度維持不變，問： 　　(a)當直桿質心到達最高點時，直桿共轉過多少角度？ _＿_＿ 　　(b)試證，若ω0＜＜√lg/a ，則直桿的運動為簡諧運動，並求出其週期。(10%) --

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