课程名称︰普通物理学甲上 课程性质︰必修 课程教师︰赵治宇 开课学院：工学院 开课系所︰化工系 考试日期（年月日）︰2013/1/10 考试时限（分钟）：170mins 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 请搭配图片服用：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. 两条很轻，长度同为l的平行绳子，系住一质量为m，长度为2a的均匀直杆的两端， 使其铅直悬挂如下图7所示。不考虑任何因摩擦而损失的能量，轻敲直杆的一端， 　　使其绕通过直杆质心的铅直轴转动，起始的角速度为ω0。假设在运动过程中， 　　绳子的长度维持不变，问： 　　(a)当直杆质心到达最高点时，直杆共转过多少角度？ _＿_＿ 　　(b)试证，若ω0＜＜√lg/a ，则直杆的运动为简谐运动，并求出其周期。(10%) --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 58.114.182.38 ※ 编辑: chan4 来自: 58.114.181.159 (11/24 19:10)