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︰化工系 考試日期（年月日）︰2012/11/16 考試時限（分鐘）：170mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 請搭配圖片服用：http://i.imgur.com/126TjNf.jpg 1. Derive the moment inertia of the object shown in Fig. 1. (10%) Notice: this is NOT a thin rod problem. 2. Derive the first rocket equation shown in the class. (8%) 3. A ball with mass m is launched vertically from the ground with an initial velocity V0. Consider the air friction is proportional to the velocity square (f=μ‧ν^2). Find the velocity of this ball when it hits back to the ground again. (12%) 4. (a) Briefly describe the physical principle of He-Ne gas laser and how it works? (6%) (b) Briefly describe the principle of Polymer Chain Reaction (PCR) technique. (6%) 5. Briefly describe the principle of the time-to-flight mass spectroscopy. (8%) 6. A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in Fig.2, where t=0 at the instant the ball is struck. The scaling on the vertical axis is set by Va=19m/s and Vb=31m/s. (a) How far does the golf ball travel horizontally before returning to ground level? (b) What is the maximum height above ground level attained by the ball? (10%) 7. In Fig.3, a box 1 (m1=1.0kg) on a frictionless inclined surface is connected to a box 2 (m2=2.0kg). The pulley is massless and frictionless. An upward force of magnitude F=6.0N acts on the box 2, which has a downward acceleration of 5.5m/s^2. What are (a) the tension in the connecting cord and (b) angle β? (10%) 8. In Fig.4, blocks A and B have weights of 44N and 22N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if μs between A and the table is 0.15. (b) Block C suddenly is lifted off A. What is the acceleration of block A if μk between A and the table is 0.15? (10%) 9. A can of sardines is made to move along an x axis from x=0.25m to x=2.25m by a force with a magnitude given by F=x‧exp(-4x^2), with x in meters and F in newtons. (Here exp is the exponential function.) (a) Show that, in this system, the change of the work will still obey the work-kinetic energy theorem. (b) How much work is done on this can by the force? (10%) 10. In Fig.5, a block slides along a path that is without friction until the block reaches the section of length L=0.65m, which begins at height h=2.0m on a ramp of angle θ=30°. In that section, the coefficient of kinectic friction is 0.40. The block passes through point A with a speed of 8.0m/s. If the block can reach point B (where the friction ends), what is its speed there, and if it cannot, what is its greatest height above A? (10%) 11. The reel shown in Fig.6 has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and is then released from rest. Find the angular speed ω of the reel when the spring is agin unstretched. (10%) Note: Please show the answer with ω, R, I, m, k, d, θ, and g. 12. As shown in Fig.7, in a smooth and frictionless table, a rigid ball A elastically collides with other three indetical rigid balls B, C and D with initial velocity V0. These three balls initially contact with each other before collision, and move independently after collision. The velocity V0 of ball A is along with the direction of line L, which is the perpendicular bisector of the line connecting the centers of balls C & D. Find the velocities of these four rigid balls after collision. (10%) --

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