課程名稱︰普通物理學甲上 課程性質︰物理系大一必帶 課程教師︰邱雅萍 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰2018/01/09 考試時限（分鐘）：110分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 國立臺灣大學物理系106-1學年度普通物理學期末考 2018.01.09 答題須知： 一、作答時，請標明題號，考試時間為10:20~12:10。 二、請詳列相關公式及計算過程，記得寫上單位，並以M.K.S制表示。 1.(5%)[Coriolis Force] This week, as the "bomb cyclone" hits the Northest in the United States, conditions steadily worsen in Long Island, New York.(See Figure.1) The air moves and the rotation of the Earth creates a cyclone effect. Explain why the air rotates by the counterclockwise direction in the Northern hemisphere (when viewed from above) by the Coriolis Force. 2.(10%)[The motion of liquid: Bernoulli's equation] (1)(10%) You can use a hairdryer to do the following experiment. A strong wind blows two pieces of papers. However, the space between these two pieces of papers will close. Explain the phenomenon. (See movie 1) 3.(20%)[Rolling and Precession] (1)(5%) Why does a rolling bicycle have greater stability than one at rest? (2)(5%) Explain why in precessional motion, the torque changes the direction of the spin angular momentum without changing its magnitude. (3)(10%) Cylinder C (mass 10.0 kg and radius 0.070 m) rolls without slipping on hill H as shwon in Figure 2. THe string does not strtch and is wrapped around the cylinder C. What are the magnitude and direction of the accel- eration? 4.(20%)[Oscillation] (1)(10%) A long rod (length= L) is pivoted freely about an axis that does not pass through its center of mass. Such an arrangement forms a physical pendulum that executes SHM for small angular displacements. Compare the period of the oscillation when we have a simple pendulum (length= L) and set into oscillation. (See movie 2) (2)(10%) When displaced and released, the 2kg mass in Figure 3 oscillates on the frictionless horizontal surface with period π/6 seconds. If a small mass is placed on the 2kg block and the coefficient of static friction between the small mass and the 2kg block is 0.1, what is the maximum amp- litude of oscillation before the small mass slips? (Assume the period is unaffected by adding the small mass.) │ ┌─┐ │ │ m│ │ k ┌┴─┴┐ Fig.3 ├----─┤ 2kg │ └───┴───┴── 5.(20%)[Free expansion] A thermally insulated box is seperated into two compa- rtments (volume V_1 and V_2) bu a membrane. One of the compartments contains an ideal gas at temperature T; the other is empty (vacuum). (See Figure 4) The membrane is suddenly removed, and the gas fills up the two compartments and reached equilibrium. (1)(10%)(a) What is the final temperature of the gas? (2)(10%)(b) Show that the gas expansion process is irreversible. ↙insulated walls ╔══╤══╗ V_1→║....│ V_2║ ╚══╧══╝ ↓ Fig.4 ╔═════╗ ║..........║ ╚═════╝ 6.(25%, 5% for each)[Carnot Cycle] (1) If W and W' represent work done by 1 mole of monatomic and diatomic gas respectively, calculate W'/W. Now, n= 0.081 kmol of He gas initially (point 1 in P-V diagram) at 27°C, volume= 1.0 m^3 and pressure= 2×10^5 N/m^2 is taken over the Carnot cycle. For He C_v = 3R/2, C_p = 5R/2. Assume the ideal gas law. (2) What is the change in internal energy of the helium from 1 →2? (3) How much heat is absorbed in going from 1→3? (4) The path from 2→3 is adiabatic, prove the entropy change is zero. (5) Calculate the efficiency of the cycle. 7.(20%)[Kinetic theory of gas] Given the Maxwell speed distribution function f(v) = N(m/(2πkT))^(3/2)4πv^2e^{-mv^2/(2kT)}, the average value of speed v_av is, v_av = ∫^∞_0 vf(v)dv/N Where N is the total number of particles. (1)(10%) Show that the average speed is 8kT v_av = √── (Note that: ∫^∞_0 x^3e^(-ax^2)dx = 1/(2a^2)) πm (2)(10%) The mass of a hydrogen molecule is m= M/N_A= 3.36×10^(-27) kg. Calculate the rms speed. --

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