課程名稱︰普通物理甲
課程性質︰化工系必修
課程教師︰趙治宇
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰96/1/18
考試時限（分鐘）：170分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Describe briefly (a) the evidence of universe expansion and (b) the
working principle of laser cold trapping invented by Steven Chu(5%,5%)
2.Derive the Newton gravitational force between a particle of mass m located
on the central axis of a uniform thin disc of mass M and radius R? Note that
the particle is at distance d away from the disc center.(10%)
3.(a)Show that there is no perfect refrigerator in the real world.(6%)
(b)What are the four universe physical constants?(4%)
4.(a)Describe the working principle of a strain gauge for small strain
measurements.(5%)
(b)Design an experiment to accurately measure the moment inertia of
any-shaped object.(5%)
5.In Fig. 1, a 2.50 kg disk of diameter D = 42.0cm is supported by a rod
of length L= 76.0cm and negligible mass that is pivoted at its end.
(a) With the massless torsion spring unconnnected, what is the period
of oscillation? (b)With the torsion spring connected, the rod is vertical
at equilibrium. What is the torsion constant of the spring if the period
of oscillation has been decreased by 0.500s? (4%;6%)
6.In Fig. 2, a 30 kg child stands on the edge of a stationary merry-go-round
of mass 100 kg and radius 2.0m. The rotational inertia of the merry-go-round
about its rotation axis is 150 kg*m^2 . The child catches a ball of mass 1.0kg
thrown by a friend. Just before the ball is caught, it has a horizontal
velocity v of magnitude 12m/s, at angle Θ=37度 with a line tangent to
the outer edge of merry-go-round, as shown in Fig.2. What is the angular
speed of the merry-go-round just after the ball is caught?(10%)
7.Several planets(Jupitar, Saturn, Uranus) are encircled by rings, perhaps
composed of material that failed to form a satellite. In addition, many
galaxies contain ring-like structures. Consider a homogeneous the ring of
mass M and outer radius R.(see Fig.3)
(a)What gravitational attraction does it excert on a particle of mass m
located on the ring's central axis a distance x from the ring center?
(b)Suppose the particle falls from rest as a result of the attraction of
the ring of matter. What is the speed with which it passes through the
center of the ring? (5%;5%)
8.For the stepladder shown in Fig.4, sides AC and CE are each 2.44m long and
hinged at C. Bar BD is a tie-rod 0.762m long, halfway up.A man weighing 854N
climbs 1.80m along the ladder. Assuming that the floor is frictionless and
neglecting the mass of the ladder, find (a) the tension in the tie-rod and
the magnitudes of the forces on the ladder from the floor at (b) A.(7%;3%)
9.A uniform rope of mass m and lenghth L hangs from a ceiling. (a)What is the
speed of a transverse wave traveling on the rope? (As a function of y, the
distance from the lower end) And (b) how long does a transverse wave take
to travel over the rope? (5%;5%)
10.In Fig.5, a French submarine and a U.S. submarine move toward each other
during maneuvers in motionless water in the North Atlantic. The French sub
moves at a speed Vf=50.0 km/h, and the U.S. sub at Vus=70km/h. The French
sub sends out a sonar (sound wave in water) at 1000 Hz. Sonar waves travel
at 5470km/h. What the signal's frequency is detected by the French sub in
the signal reflected back to it by the U.S. sub?(10%)
11.Figure 6 shows a hypothetical speed distribution for a sample of N gas
particles(note that P(V)=0 for speed V>2Vo). What are the values of
(a) Vrms/Vo, (b) Vavg/Vo ,and (c)What fraction of the particle has a
speed between 1.5Vo and 2.0Vo? (3%;3%;4%)
12.The cycle in Fig. 7 represents the operation of a gasoline internal
combustion engine. Assume the gasoline-air intake is an ideal gas with
r(gamma)=1.30. What are the ratio (a)T3/T1 (b)P3/P1, and (c) What is the
engine efficiency? (3%;2%;5%)
註 All figures comes from Fundamentals of Physics (Halliday 7th)
Fig.1 P408--56
Fig.2 P301--58
Fig.3 P358--96
Fig.4 P324--35
Fig.5 P471--54
Fig.6 P532--39
Fig.7 P558--33
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