课程名称︰普通物理学丙 课程性质︰森林系某些学群必修 课程教师︰李庆德 开课学院： 开课系所︰森林环资系 考试日期（年月日）︰April 22, 2009 考试时限（分钟）：120分钟 是否需发放奖励金：是的 （如未明确表示，则不予发放） 试题 : 前言：Do ...........一串英文，简单讲就是以下六题选五题写，每题20分总分100分 不一定要照题号顺序，可用中文或英文作答，可以使用计算机 斜体字上红色 1. A solid sphere and a disk both have the same mass M and radius R. (a) What are the moments of inertia of the solid sphere and the disk? Consider now that both the solid sphere and the disk are rolling without slipping up an incline. (b) Find the ratio of the heights, hs/hd, to which they rise if they have the same kinetic energy at the bottom of the incline. (c) Find the ratio of the heights, hs/hd, to which they rise if they have the same speed at the bottom of the incline. 2. A man of mass m=75 kg runs at a speed u=6m/s along the tangent to a diskshaped platform of mass M=150 kg and radius R=2m. The platform is initially at rest but can rotate freely about an axis through its center. Take I=MR2/2 for the moment of inertia of the platform. MR平方除以2 (a) Find the angular velocity of the platform after the man jump on the rim of the platform. (b) The man then walks to center of the platform. Find the new angular velocity. (c) What is the angular velocity of the platform when the man is midway between the rim and the center of the platfrm? 3. A mass M (either a solid sphere or a disk) of radius R moves at speed v0 without rolling. It encounters a rough surface whose coefficient is μ (a) Show that the angular momentium is conserved in the whole process of motion even though the mechanic energy is not conserved. (b) Take the mass to be a solid sphere with Icm =2MR2/5. Find the speed of the center of mass when pure rolling commences and evalute the distance the sphere travels on rough surface before pure rolling starts. (c) Take the mass to be a disk with I=MR2/2. Find the speed of the center of mass when pure rolling commences and evalute the distance the sphere travels on rough surface before pure rolling starts. 4. Fig1 shows a nonconducting disk of radius a with a uniform surface charge density σ(in unit C/m2) ╴ (a) Evaluate the electric field E at a distance y from the center along the central axis. (b) Use the result obtain for (a) to derive the eletric field strengh due to an infinite sheet of charge with uniform surface charge density. 图 一个半径a的圆盘，在圆心正上方y处 5. A conducting spherical shell of inner radius R1 and outer radius R2 carries an excess charge of -Q and a point charge 2Q is placed at its center. (a) What are the surface charge densities on the inner and outer surfaces of the conducting shell? ╴ (b) What is the eletric field╴E for r< R1? (c) Find the eletric field E for r>R2. (d) If the charge 2Q is moved off the center, one can no longer use Gauss's law to find the eletric field as in (b) and (c). However, if the charge is still in the cavity enclosed by the conducting shell, what can you say about the charge on the inner and outer surfaces of the conducting shell? 6. A uniform solid sphere of mass M and radius R is at the center of a thin uniform spherical shell of mass M and radius 2R. Find the force on a point particle of mass m if the particle is at the following distance from the center of the sphere and the spherical shell: (a)R/2; (b)3R/2; (c)5R/2. --

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