※ [本文轉錄自 crsie 信箱] 作者: michael9002 (土撥鼠) 看板: NTU-Exam 標題: [試題] 96上 陸駿逸 普通物理學甲上 期中考 時間: Wed Nov 7 00:20:53 2007 課程名稱︰普通物理學甲上 課程性質︰系訂必修 課程教師︰陸駿逸 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰96年11月6日 考試時限（分鐘）：130分 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. (8 pts) You are given a 2D force F = (Fx(x,y),Fy(x,y)) = (8y^3/255,3xy) where x,y are in meter and the force is in the Newton unit. (a) Calculate the work done by the force, from (0,0) to (1,2) along a straight line. (b) Calculate the work done by the force, from (0,0) to (0,2) along a straight line. (c) Calculate the work done by the force, from (0,2) to (1,2) along a straight line. (d) Based on the above calculations, is this force a conservative force? (e) With the help of the Stoke's theorem, is this force a conservative force? 2. (5 pts) Conservative force. (a) Write down the definition of a conservative force. (b) Why do you want to define it this way? 3. (5 pts) Write down the 1D work-kinetic energy theorem for a particle with the mass M. Prove the theorem without assuming a constant acceleration. 4. (6 pts) Suppose that you find a strange spring which has the force law F(x) = -k(x+x^3), where x is in meter and the force is in Newton unit. (a) What is the work done by this force if a particle connected to it is moved from x = 0.1m to x = 0.5m? (b) Define a potential energy V(x) for this spring. (c) Use the potential energy you defined in (b) to calculate the work done from x = 0.6m to x = 0.1m. 5. (4 pts) Set up a coordinate system, and calculate the center of the mass position of the water molecule H2O. Suppose that the bond length is 1.2埃, and the bond angle is 104.5度.(You can use cos 104.5度 = -0.25,sin 104.5度 = 0.97. Atomic mass: H, 1g/mol; O, 16g/mol.) 6. (10 pts) A car of 600kg is turning in a flat track in a circular arc of the radius R = 100m. The coefficient of the static friction between the tires and the track is 0.75. (a) When the car is turning with a constant speed 26m/s. Calculate the magnitude of the friction force. (b) If the driver tries to accelerate the car to have his speed to increase to 27m/s with the tangential acceleration aT=5m/sec^2 (for 0.2 sec). What will happen? Can he make the turn? 7. (10 pts) A ball of the mass 0.1kg is connected to a vertical rotating rod by two massless strings of the equal length L = 1m. The strings are tied to the rod with the separation d = 1m. The ball is rotating with the same angular speed as the rod. (a) Calculate the tensions of the two strings when the rotation motion has the period 1 sec. (b) Calculate the tensions of the two strings when the rotation motion has the period 2 sec. --

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