課程名稱︰普通物理學甲上 課程性質︰必帶 課程教師︰陳智泓 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰102/10/24 考試時限（分鐘）：110分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 普通物理學期中考 Exam hours: 10:20am ~ 12:10pm on 10/24/2013 1. (10%) A vertical container with base area of length L and width W is being filled with identical pieces of candy, each with a volume of v and a mass m. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at a certain rate per unit time dH/dt, at what rate per unit time does the mass of the candies in the container increase? 2. (10%) A rock is thrown vertically upward from ground level at time 0. At time t it passes the top of a tall tower, and later, at time t , it 1 2 reaches its maximun height. What is the height of the tower? Give your answer in terms of the given variables and g. 3. (10%)A ball is to be shot from level ground with a certain speed v at 0 various angles θ. The launch angle determines both the time of flight t and the minimum speed v the ball will have during its flight, min which means they can be related to each other. At some angle, the ball will have a maximum possible time of flight. Call this time t . max Find a formula which gives the ratio of v to v in terms of t, t , min 0 max and g. 4. The acceleration of a particle moving only on a horizontal xy plane is → ︿ ︿ → given by a = (3t) i+ (4t) j, where a is in meters per second-squared and t → ︿ ︿ is in seconds. At t=0, the position vector is r = (20m) i+ (40m) j and the → ︿ ︿ velocity is v = (5m/s) i+ (2m/s) j. Find expressions for the (a) (10%) x component (in meters) of the position of the particle at time t. (b) (10%) y component (in meters) of the position of the particle at time t. (c) (10%) What is the angle between its velocity and the positive direction of the x axis at time t? 5. A lamp hangs vertically from a cord in a descending elevator with a constant deceleration a. (a) (10%) If the tension in the cord is T, what is the lamp's mass? (b) (10%) What is the cord's tension when the elevator ascends with upward acceleration a? State your answers in terms of the given variables and g. 6. The figure shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pjlley (also of negligible mass). At time t=0 container 1 has m and container 2 has mass 1 m with m <m , but container 1 is losing mass (through a leak) at the 2 1 2 constant rate r. (a) (10%) At what rate is the magnitude of acceleration of the container changing at time t? (b) (10%) When will container 2 reach maximum acceleration? Express your answers in terms of the variables given and g. 第六題的圖 http://ppt.cc/bfjt --

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