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︰化學系
考試日期（年月日）︰103/1/9
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 :
普通物理學期末考
Exam hours: 10:20am ~12:10pm on 1/9/2014
1. Hunting a black hole. Observations of the light from a certain star
indicate that it is part of a binary (two-star) system. This visible star
has moves in a circle of radius r and has orbital period T. Variations in
1
the brightness of nearby stars suggest that the unseen companion moves in a
circle of radius r (see the Fig. (1)). Find the approximate masses
2
(a) (10%) m of the visible star and
1
(b) (10%) m of the dark star.
2
Express your answer in terms of r , r , T, and G.
1 2
2. Assume a planet is a uniform sphere of radius R that (somehow) has a narrow
radial tunnel through its center. Also assume we can position an apple
anywhere along the tunnel or outside the sphere. Let F be the magnitude
R
of the gravitational force on the apple when it is located at the planet's
surface. How far from the surface is there a point where the magnitude of
the gravitational force on the apple is F /2 if we move the apple
R
(a) (5%) away from the planet and
(b) (5%) into the tunnel?
Express your answer in terms of the variables given.
3. In the Fig. (2), water flows through a horizontal pipe and then out into
the atmosphere at a speed v . The diameter of the left and right sections
1
of the pipe are d and d , respectively.
1 2
(a) (5%) What volume of water flows into the atmosphere during a time t?
In the left section of the pipe, what are
(b) (5%) the spped v , and
2
(c) (10%) the gauge pressure?
State your answers in terms of the given variables, using (the density
of water) and π when necessary.
4. A thin uniform rod with mass m swings about an axis that passes through
one end of the rod and is perpendicular to the plane of the swing. The rod
swings with a period T and an angular amplitude of φ (assume this angle
M
is sufficiently small to allow for the use of the equations in this chapter).
(a) (10%) What is the length of the rod?
(b) (10%) What is the maximum kinetic energy of the rod as it swings?
State your answer in terms of the given variables, using g and π when
applicable.
5. A uniform rope of mass m and length l hangs from a ceiling
(a) (5%) Find the spped of a transverse wave on the rope at h from the
lower end.
(b) (10%) Find a time a transverse wave takes to travel the length of the
rope.
6. (5%) A plane flies at n times the speed of sound. Its sonic boom reaches a
man on the ground a time t after the plane passes directly overhead.
What is the altitue of the plane? Give your answer in terms of the given
variables, using v for speed of sound.
s
7. A tube of length L is closed at one end. A streched wire is placed near the
open end. The wire has length l and has mass m. It is fixed at both ends
and oscillates in its fundamental mode. By resonance, it sets the air
column in the tube into oscillation at that column's fundamental frequeny.
Find
(a) (5%) that frequency and
(b) (5%) the tension in the wire.
State your answer in terms of the given variables, using v for the
s
speed of sound if necessary.
第一題的圖 Fig .1 第三題的圖 Fig. 2 http://ppt.cc/xhDE
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