课程名称︰普通物理学甲上 课程性质︰系必修 课程教师︰张宝棣 开课学院：电机资讯学院 开课系所︰资工系 考试日期（年月日）︰2008/10/24 考试时限（分钟）：130 min , 10:20-12:30 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. A 200-m-wide river has a uniform flow speed of 1.1m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.0 m/s with respect to the water. There is a clearing on the north bank 82 m upstream from a point directly opposite the clearing on the south bank. (a) In what direction must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing? (10%) 2. A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk(Fig. 1) The coefficient of friction between block and disk are 0.750 ( static) and 0.640 (kinetic) while those for the penny and block are 0.520 ( static) and 0.450 (kinetic). What is the maximum rate of rotation in revolutions per minute that the disk can have, without the block or penny sliding on the disk? (10%) 3. A 250 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.5 N/m (Fig. 2) The block becomes attached to the spring and compressess the spring 12 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring (Assume that friction is regligible.) (d) If the speed at impact is doubled, whate is the maximum compression of the spring? (20%) 4. A 4.0-kg block is stacked on top of a 12.0 kg block, which is accelerating along a horizontal table at a = 5.2 m/s2 (Fig. 3). Let μk = μs = μ. (a) What minimum coefficient of friction μ between the two blocks will prevent the 4.0-kg block from sliding off? (b) If μ is only half of this minimum value, what is the acceleration of the 4.0-kg block with respect to the table, and (c) with respect to the 12-kg block? (d) What is the force that must be applied to the 12.0 kg block in (a) and in (b), assuming that the table is frictionless? (15%) 5. A small mass m is set on the surface of a sphere (Fig. 4). If the coefficient of the static friction is μs = 0.60, at what angle ψ would the mass start sliding? (5%) 6. Two curved inclines of two identical wedge-shaped masses M smoothly merge with a horizontal frictionless surface as indicated in Fig. 5. The curved surfaces of the inclines are also frictionless. Another mass m is released at rest from a height h on one of the inclines. (a) When m reaches the horizontal plane, is the mechanical energy of m and M conserved? Is the total momentum of m and M conserved when m reaches the horizontal surface? Why? (5%) (b) After m reaches the horizontal plane, it encounters the righthand wedge and ascends it to some height h'. Are both total energy and total momentum conserved when m reaches height h'? Please explain.(5%) (c) Please express h'? in terms of m, M, and h using the ideas in (a) and (b). (10%) 7. An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90 degree. (a) At what angle does the target particle move after the collision? (b) What are the final speed of the two particles? (c) What fraction of the initial kinetic energy is transferred to the target particle? (15%) 8. A block of mass m1 = 2.0 Kg slides along a frictionless table with a speed of 10 m/s. Dirctly in front of it, and moving in the same direction, is a block of mass m2 = 5.0 Kg moving at 3.0 m/s. A massless spring constant k = 1120 N/m is attached to the near side of m2, as shown in Fig. 6. When the blocks collide, what is the maximum compression of the spring? (5%) --

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