課程名稱︰ 普通物理學甲上 課程性質︰ 資工系大一必修 (物化生三選一) 課程教師︰ 王名儒 開課學院： 開課系所︰ 考試日期（年月日）︰ 2015/01/16 考試時限（分鐘）： 基本上是兩節課 但寫不完助教都會通融 試題 : 1. A solid cylinder with mass M & radius R is attached to a horizental spring with force constant k. If it is perturbed a bit, it will roll without slipping along the horizental surface. Find out the period of this simple harmonic oscillation. 2. Three string waves propagating towards +x direction with functional forms Asin(kx-ωt-π/3), Asin(kx-ωt) and Asin(kx-ωt+π/6). Find out the functional form of the combined wave. 3. What is the rate of energy transmission of the following wave: y(x,t)=Asin(kx-ωt) on a string with linear density μ? It is known that the potnetial energy is the same as the kinetic energy of a simple harmonic wave traveling on a string. 4. Two trains are traveling toward each other with a fixed speed ±30m/sec relative to the ground. One train is blowing a whistle at 500Hz. What frequency is heard on the other train? 5. Describe three different heat transfer mechanism. If there is theorical formula to describe the heat transfer property of a material or related mechanisms, you should write them down. 6. What is the maximum efficiency of a heat engine to operate between the warm layer (30*C) of sea water and the cold deep layer (5*C)? 7. Write down the Maxwell distribution of the molecular speed of an ideal gas. Determine the ratio of the probability for gas molecules at 250K to have a speed of 250m/s to the probability of gas molecules at 150K to have the same speed. The molar mass of the gas molecules is 39.9g/mol. 8. A small piece of metal with temprature Tx is put in contact with a heat reservoir (temperature T). Prove that the above process is irreversible if Tx is not equal to T. 9. What is the entropy change for an ideal gas undergoing free expansion to four times of its original volume? 10. Find the electric field at a point (x,y,z) due to a charge q located at d/2 and a charge -q at -d/2 on the Z axis. Is the field strength still proportianal to r^(-2)? (z>>d) --

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