課程名稱︰普通物裡甲 課程性質︰必修 課程教師︰趙治宇 開課學院：理學院 開課系所︰化工系 考試日期（年月日）︰2011/11/17 考試時限（分鐘）：170 min 是否需發放獎勵金：是 感謝囉:) （如未明確表示，則不予發放） 試題 : 1.Describe the principle of Scan Tunneling Microscope(STM). 6% 2.A single conservative force F(x) acts on a 1.0kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is giveb by U(x)=-4x*e^(-x/4)J, where x is in meters. At x=5.0m the particle has a kinetic energy of 2.0J. (a)What's the maximum kinetic energy of the particle and the value of x at which it occurs? 4% (b)Determine an expression for F(x) as a function of x and for what value of x does F(x)=0? 4% 3.Find the moment inertia of a hollow sphere (mass M) with inner and outer radius R1 and R2, respectively. 8% 4.Find the gravitational force between a uniform disc(mass M and radius R) and a particle (mass m). The distance between the particle and the disc is d, and the particle is right on the top of the centre of this disc. 8% 5.Consider the air friction is proportional to object's velocity. Now, we throw ball 1 (mass m) up with initial velocity v0, and sumultaneously we drop ball 2 (mass m) right on the top of ball 1, falling from rest at the height h. Find the meet time, the height when two balls meet, and the velocities of these two balls at that moment. 12% 6.(a)Describe the principle and operation of laser. 4% (b)Briefly explain the occurrence of low-temperature superconductor. 4% 7.A football kicker can give the ball an initial speed of 25 m/s. What are the (a)least and (b)greastest elevation angles at which he can kick the ball to score a field goal from a point 50m in front of goalposts whose horizantal bar is 3.44m above the ground? (4%,4%) 8.In Fig.1, 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= 6.0 N 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)angleβ? (4%,4%) Fig.1 Fig.2 Fig.3 ◢◣m █ 彈簧 M ＼◥◤ ↑ ￣○╲ █╴﹏﹏﹏╴█╴╴ ＼ ＼ h∣ ██ ＼ █ 　█ ○ ＼ ＼ ∣ █ ＼ █▇▇▇▇▇▇▇▇ ︱ β╭＼○ ↓ █ ＼↖T　　　█ █ ︱ ￣￣￣￣|｜ █ █ x　　█　 █ █ 2M |｜ ￣￣￣￣￣￣ █ █ █ |█m2 ∣ ∣ █ █ |↑→ x2 x1 █ █ |｜F 9.Fig.2 shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h=1.25m, so the cart slides from x1=3.00m to x2=1.00m. During the move, the tension in the cord is a constant 28.0N. What is the change in the kinetic energy of the cart during the move? 8% 10.Two blocks, of masses M=2.0kg and 2M, are connected to a spring of spring constant k=200N/m that has one end fixed, as shown in Fig.3. The horizantal surface and the pulley are frictionless,and the pulley has negligible mass. The blocks are released from rest with the spring relaxed.(a)What is the combined kinetic energy of the two blocks when the hanging block when it has fallen that 0.090m? (b)What is the kinetic energy of the hanging block when it has fallen that 0.090m? (c)What maximum distance does the hanging block fall before momentarily stopping? (3%,3%,3%) 11.A uniform soda can of mass 0.140kg is 12.0cm tall and filled with 0.354kg of soda(Fig.4). Then small holes are drilled in the top and bottom (with negligible loss of metal) to drain the soda. What is the height h of the com(質心) of the can and contents (a)initially and (b)after the can losses all the soda? (c)What happens to h as the soda drains out? (d)If x is the height of the remaining soda at any given instant, find x when the com reaches its lowest point. (2%,2%,2%,3%) Fig.4(圓柱狀) 　 Fig.5 *xw之w為下標。 ╭──╮ ╰──╯ █ │ │ → █ ╴ │ │ 1○ ○2 █ ↑ │ │ ▇▇▇▇▇▇▇▇▇▇ x↓ │ │ ———————————x(cm) — ╰──╯ ︱ ︱ 0 xw 12.In Fig.5, particle 1 of mass m1=0.30kg slides rightward along x axis on a frictionless floor with a speed of 2.0m/s.When it reaches x=0,it undergoes a one-dimensional elastic collision with stationary particle 2 of mass m2=0.40kg. When particle 2 then reaches a wall at xw=70cm, it bounces from the wall with no loss of speed.At what position on the x axis does particle 2 then collide with particle 1? 8% 　＊考試可攜帶工程計算機及電子辭典。 --

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