课程名称︰普通物理学甲上 课程性质︰机械系必修 课程教师︰蔡尔成 开课学院：理学院 开课系所︰物理系开给机械系 考试日期（年月日）︰101/1/13 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : → 1.[10%]In the following figure, what magnitude of (constant)force F applied horizonally at the axle of the wheel is necessary to raise the wheel over the obstacle oh height h? tThe wheel's radius is r, and its mass is m. (大家就行行好假装它是圆吧...) w───── / \ / \ │——r — │→F │ │────────── \ / │ ︱ \ / │ h ──────────── ︱ 2.[10%]what is the acceleration of a rising hot-air balloon if the ratio of the density outside the balloon to that inside is 1.39? Neglect the mass of the balloon fabric and the basket. 3.[10%]A uniform rope of mass m and length L hangs from a ceiling. (a)[5%] Show that the speed of a tranverse wave on the rope is a function of y, the distance from the lower end, and is given by v = (gy)^(1/2). (b)[5%] Show that the time a tranverse wave takes to travel the length if the rope is given by t = 2 (L/g)^(1/2) 4.[10%]A tuning fork of unknown frequency makes 3.00 beats per secind with a standard fork of frequency 384 Hz. The beat frequency decreases when a small piece of wax is out on a prong of the first fork. What is the frequency of this fork? 5.[10%]In the temperature range T1 to T2, the pressure p of a certain non ideal gas is related to volume V and temperature T by 2 T T p = α--- - β--- . V V How much work is done by the gas if its temperature is raised from T1 to T2 while the pressure p is held constant? 6.[10%]Air flows over the top of an airplane wing of area A with speed vt and past the underside of the wing (also of area A) with speed vu. Show that in this simplified situation Bernoulli's eqution predicts that the magnitude L of the upward lift force on the wing will be L = (1/2)ρA(vt^2-vu^2) 7.[10%]The orbit for a planet moving around the Sun is an ellipse whose semi- major axis (one half the major axis) and semi-minor axis (one half the minor axis) are a and b. If the speed of the planet is Vo at the perihelion (the point that is nearest to the Sun), what is the period of the orbiting planet? 8.[10%]The equation of motion for a damped oscillator under an external driven force is mx'' + bx' + kx = Fo cos(ωt + θ) and the steady state solution is x(t) = Xm cos(ωt + ψ) Prove that Fo Xm = ------------------------------ (1/2) ((mω^2 - k)^2 + b^2ω^2) 9.[10%]An inventor have constructed a heat engine that has an efficiency of 75% when operated between the boiling and freezing points of water. Is it possible? 10.[10%]The two isotherms of the Stirling engine cycle are connected, not by adiabatic processes as for the Carnot engine but by constant-volume dQ processes. Prove that ∫--- = 0 for an ideal Stirling engine cycke with the T working subtance assumed to be an ideal gas. P.S. 第八题中的ω於题目中有下标d，因排版因素故省略 第十题的积分符号中间应该是路径积分，不过因为我找不到这符号所以...(ry --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.7.214 ※ 编辑: peter506g 来自: 140.112.7.214 (01/13 12:39) ※ 编辑: peter506g 来自: 218.35.138.124 (01/13 22:29)