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）︰2016/01/15 考試時限（分鐘）：170 試題 : 圖片：http://imgur.com/D1hpj4o 1. Fig.1 shows a rigid assembly of a thin hoop (of mass m and radius R=0.150m) and a thin radial rod (of mass m and length L=2.00R). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the place of the rod and hoop, through the lower end of the rod. Assuming that the enrgy given to the assembly in such a nudge is negligible, what would be the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? (8%) 2. Two trains are traveling toward each other at 35.7 m/s relative to the ground. One train is blowing a whistle at 850 Hz. (a) What frequency is heard on the other train in still air? (b) What frequency is heard on the other train if the wind is blowing at 35.7 m/s toward the whistle and away from the listener? (c) What frequency is heard if the wind direction is reserved? (8%) 3. In Fig.2, an aluminum wire, of length L1 = 60.0 cm, cross-sectional area 1.25×10^-2 cm^2, and desity 2.60 g/cm^3, is joined to a steeel wire, of desity 7.80 g/cm^3 and the same cross-sectional area. The compound wire, loaded with a block of mass m = 10.0 kg, is arranged so that the distance L2 from the joint to the supporting pulley is 86.6 cm. Transverse waves are set up on the wire by an external source od variable frequency; a node is located at hte 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? (8%) 4. In Fig.3, a unifrom plank, with a length L of 10.5 m and a weight of 445 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 3.05 m. The plank remains in equilibrium for any value of ɵ≧70.0度, but slips if ɵ<70.0度. Find the coefficient of static friction between the plank and the ground. (8%) 5. What is the entropy change when n moles of an ideal gas doubles its volume in a free expansion? Please derive the answer with a statistical machanics. (8%) 6. A wave passes through an element, which moves along y axis, and travels along a horizontal x axis with velocity v. Please derive the wave equation. (10%) 7. In Fig.4, unifrom beams A and B are attached to a wall with hinges and loosely bolted together (there is no torque of one on the other). Beam A has length La = 2.40 m and mass 58.0 kg; beam B has mass 70.0 kg. The two hinge points are separated by distance d = 1.80 m. In unit-vector notation, what is the force on (a) beam A due to its hunge, (b) beam A due to the bolt, (c) beam B due to its hinge, and (d) beam B due to the bolt? (8%) 8. In the Fig.5, a 1.0 g bullet is fired into a 0.60 kg block attached to the end of a 0.75 m nonunifrom rod of mass 0.50 kg. The block-rod-bullat system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about that axis at A is 0.060 kg˙m^2. Treat the block as a particle. (a) What then is the rotatiomal inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 4.5 rad/s, what is the bullet's speed just before impact? (8%) 9. In Fig.6, block 2 of mass 2.00 kg oscillates on the end of a spring in SHM with a period og 14.10 ms. The position of the block is given by x = (1.0 cm) cos(ωt + π/2). Block 1 of mass 4.00 kg slides toward block 2 with a velocity of magnitude 6.0 m/s, directed along the spring's length. The two bocks undergo a completely inelastic collision at time t = 5.0 ms. (The duration of the collision is much less than the period of motion.) What is the amplitude of the SHM after the collision? (8%) 10. Container A in Fig.7 holds an ideal gas at a pressure 8.0×10^5 Pa and a temperature of 250 K. It is connected by a thin tube (and a closed valve) to containerB, with four times the value of A. Container B holds tha same ideal gas at a pressure of 1.0×10^5 Pa and a temperature of 450 K. The valve is opend to allow the pressuers to equalize, but the temperature of each container is maintained. What is then the pressure? (8%) 11. A 3.0 cm slab has fromed on an outdoor tank of water (Fig.8). The air is at -14℃. Find the rate of ice formation (centimeters per hour). The ice has thermal conductivity 0.0040 cal/s˙cm˙℃ and density 0.92 g/cm^3. Assume there is no energy transfer through the walls or bottom. (8%) 12. In the temperature range 310 K and 330 K, the pressure p of a certain nonideal gas is related to volume V and temperature T by T T^2 p = (24.9 J/K) － - (0.00662 J/K^2) －－ V V How much work is done by the gas if its temperature is raised from 315 K to 330 K while the pressure is held constant? (8%) --

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