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課程名稱︰普通物理學丙
課程性質︰森林系某些學群必修
課程教師︰李慶德
開課學院：
開課系所︰森林環資系
考試日期（年月日）︰April 22, 2009
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是的
（如未明確表示，則不予發放）
試題 :
前言：Do ...........一串英文，簡單講就是以下六題選五題寫，每題20分總分100分
不一定要照題號順序，可用中文或英文作答，可以使用計算機
斜體字上紅色
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.
圖 一個半徑a的圓盤，在圓心正上方y處
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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