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︰機械系 考試日期（年月日）︰103年1月9日 考試時限（分鐘）：170 mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Fig: http://ppt.cc/~Xnw 1. (a) Describe the working principle of a strain gauge for small strain measurements. (b) Design an experiment to accurately measure the moment inertia of any-shaped object. (4%, 4%) 2. Two cylinders with radius R1 and R2 and rotational inertias I1 and I2 about their central axis are supported by axes perpendicular to plane of Fig. 1. The large cylinder is initially rotating with angular velocity w0. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually, slipping ceases, and the two cylinders rotate at constant rates in the opposite directions. Find the final angular velocity w2 of small cylinder in term of I1, I2, R1, R2, and w0. (8%) 3. Find the gravitational force between a circular plate and a particle of mass m, a distance h from the center of the plate as shown in Fig. 2. The circular plate has a mass M and radius R. (8%) 4. (a) How to detect the universe background radiation. (b) What’s the evidence of the universe expansion. (4%, 4%) 5. Show that (a) there is no perfect engine, (b) there is no perfect refrigerator. (4%, 4%) 6. Proof that the sound wave intensity, which is the average transmitted wave power per unit area, is given by: P = 1/2(pvw^2 Sm^2) Where p is density of mass, v is speed of wave, and Sm is amplitude of wave. (9%) 7. Four bricks of length L, identical and uniform, are stacked on top of one another (Fig. 3) in such a way that part of each extends beyond the one beneath. Find, in term of L, the maximum values of (a) a1, (b) a2, (c) a3, (d) a4, and (e) h, such that the stack is in equilibrium. (10%) 8. Fig. 4 shows a stream of water flowing through a hole at depth h = 12 cm in a tank holding water to height H = 40 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a second hole be made to give the same value of x? (c) At what depth should a hold be made to maximize x? 9. In the overhead view of Fig. 5, a long uniform rod of mass 0.600 kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k = 1530 N/m is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. What is the period of the small oscillations that result when the rod is rotated slightly and released? (8%) 10.Two identical piano wires have a fundamental frequency of 600 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 8.0 beat/s when both wires oscillate simultaneously? 11.Container A in Fig. 6 holds an ideal gas at the pressure of 5.0 x 10^5 Pa and a temperature of 300 K. It is connected by a thin tube ( and a closed calve ) to container B, with four times the volume of A. Container B holds the same idea gas at a pressure of 1.0 x 10^5 Pa and temperature of 400 K. The valve is opened to allow the pressure to equalize, but the temperature of each container is maintained. What then is the pressure? (8%) 12.Fig. 7 shows two paths that may be taken by a gas from an initial point i to a final point f. Path 1 consists of an isothermal expansion ( work is 50 J in magnitude ), an adiabatic expansion ( work is 40 J in magnitude ), an isothermal compression ( work is 30 J in magnitude ), and then an adiabatic compression ( work is 25 J magnitude ). What is the change in the internal energy of the gas if the gas goes from point i to point f along path 2? (8%) --

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