課程名稱︰普通物理學甲上
課程性質︰必帶
課程教師︰朱士維助理教授
開課學院：理學院
開課系所︰材料系
考試日期（年月日）︰10/01/11
考試時限（分鐘）：130(1020~1230)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.[5]During our entire lifetime, int4eractions with various people are
inevitable. It is vital to show mutual respect in these interactions.
One of the key components in successful interaction/communication is
to know others' names. So, please write down the names of our teaching
assistant in the General physics course(in Chinese or English, be sure
you spell correctly)
2.[25]A 60 kgw person is performing fast-spin during ice-skating. He starts
from slow-spin with stretched arms, and speeds up when he raises his arm
(a) assuming the weight of each arm is 5 kgw, and using the following
simplified model, what are the moments of inertia of the performer with
streched arms and raised arms, respectively? (b) The speed of slow-spin
is 1rev/sec. What is the spin speed when the performer raises his arms?
(c) What are the kinetic energies of the streched-arm and raised-arm
situation, respectively? (d)Apperantly, the rotation energy does not
conserve during this movement. Where does the additional kinetic energy
come from? (Note: even if you don't know how to calculate (a), you can
still finish the following by assuming the moment of inertia to be I1,I2
respectively.
3[15] In class, we have derived Kepler's law from Neewton's law, and found
that the equation of trajectory is (x+c)^2 (y)^2 (a^2=(GM)^2/4E^2
-------+----=1 b^2=L^2/=2mE
a^2 b^2 c=A/-2mE)
E is the total mechanical energy, L is the angular momentum, and A is
the Laplace-Runge-Lenz factor. (a) When the total mechanic energy E<0,
what is the shape and area of the trajectory? (b) What is the shape of
the trajectory when E->0 ? Please explicitly write down the equation of
the tracjectory.
4.[15] Remember the magic lid? By simply putting it on a cup, we were able to
lift the cup with the little mouse. (a) What is the principle of it?
(b) Assuming the initial volume inside the cup is 1000cm^3 with the lid
on, the area of the cup opening is 100cm^2, the weight of the cup is
500g, and the atmospheric pressure in the room is 1 atm, how much
volume change in the cup is necessary to allow us to lift this cup?
5.[10] In an in-class demonstration, we put 1ml water inside a 600ml plastic
bottle and boiled the water. After the water vapor at 373K filled the
bottle, we tightened the bottle cap. When it was cooled down to ambient
temperature at 293K, the bottle crushed. Please estimate the remaining
volume of the bottle at this temperature.(The vapor pressure of water is
760 mmHg at 373K and drops to 17.54 mmHg at 293K)
6.[10] (adapted from prob. 17-103, waterfall accoustics) The turbulent impact
of the water in a waterfall causes the surrounding ground to oscillate
in a wide range of low frequencies. If the water falls freely(no rock
in the way), the oscillations are greatest in amplitude at a particular
frequency fm. This fact suggests that acoustic resonance is involved
and fm is fundamental frequency. The following table ends (1/2) are
effectively involved in waterfall resonance. (Hint: The speed of the
turbulent water is about 1100m/s)
fm(Hz) 2.8 3.7 4.4 11.2 35
L(m) 100 75 64 25 8
7.[20] (a) A propogating sinusoidal wave is expressed as s'=socos(x-t), with
x in meter and t in second. Please find out the value of its frequency
and angular wave number. (b) What is the speed of s'=socos(x-t)? (c)
When two waves s1=5cos((2000pi/340)x-2000pi*t) and s2=5cos((2002pi/340)x
-2002pi*t) propogate together, beating happens. Please derive the beating
frequency mathemetically summing these two propogating waves.
8.[10] (a) Define "reversible" and "irreversible"
(b) Explain why the effciency of a reversible Carnot engine is higher
than an irreversible one?
9.[10] An ideal gas is taken reversibly from state i, at temperature T1, to any
of the other states labeled, I, II, III, IV, V on the P-V diagram. All
are at the same temperature T2. Rank the five processes according to the
change in entropy of gas, least to greatest. Be sure to explain the
reason.(Since the diagram is hard to draw, I will explain that below.
The path I is vertically going up from i(T1) to an isothermal curve(T2)
and V is an isobaric process from i(T1) to another point on the
isothermal curve(T2), and II, III, IV are between I and V)
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