[試題] 100上 蔡爾成 普通物理學甲上 期末考
課程名稱︰普通物理學甲上
課程性質︰機械系必修
課程教師︰蔡爾成
開課學院：理學院
開課系所︰物理系開給機械系
考試日期（年月日）︰101/1/13
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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1.[10%]In the following figure, what magnitude of (constant)force F applied
horizonally at the axle of the wheel is necessary to raise the wheel over
the obstacle oh height h? tThe wheel's radius is r, and its mass is m.
(大家就行行好假裝它是圓吧...)
w─────
/ \
/ \
│——r — │→F
│ │──────────
\ / │ ︱
\ / │ h
──────────── ︱
2.[10%]what is the acceleration of a rising hot-air balloon if the ratio of
the density outside the balloon to that inside is 1.39? Neglect the mass of
the balloon fabric and the basket.
3.[10%]A uniform rope of mass m and length L hangs from a ceiling. (a)[5%]
Show that the speed of a tranverse wave on the rope is a function of y,
the distance from the lower end, and is given by v = (gy)^(1/2). (b)[5%]
Show that the time a tranverse wave takes to travel the length if the rope
is given by t = 2 (L/g)^(1/2)
4.[10%]A tuning fork of unknown frequency makes 3.00 beats per secind with
a standard fork of frequency 384 Hz. The beat frequency decreases when a
small piece of wax is out on a prong of the first fork. What is the
frequency of this fork?
5.[10%]In the temperature range T1 to T2, the pressure p of a certain non
ideal gas is related to volume V and temperature T by
2
T T
p = α--- - β--- .
V V
How much work is done by the gas if its temperature is raised from T1 to T2
while the pressure p is held constant?
6.[10%]Air flows over the top of an airplane wing of area A with speed vt and
past the underside of the wing (also of area A) with speed vu. Show that in
this simplified situation Bernoulli's eqution predicts that the magnitude L
of the upward lift force on the wing will be L = (1/2)ρA(vt^2-vu^2)
7.[10%]The orbit for a planet moving around the Sun is an ellipse whose semi-
major axis (one half the major axis) and semi-minor axis (one half the minor
axis) are a and b. If the speed of the planet is Vo at the perihelion (the
point that is nearest to the Sun), what is the period of the orbiting planet?
8.[10%]The equation of motion for a damped oscillator under an external driven
force is
mx'' + bx' + kx = Fo cos(ωt + θ)
and the steady state solution is
x(t) = Xm cos(ωt + ψ)
Prove that
Fo
Xm = ------------------------------
(1/2)
((mω^2 - k)^2 + b^2ω^2)
9.[10%]An inventor have constructed a heat engine that has an efficiency of 75%
when operated between the boiling and freezing points of water. Is it
possible?
10.[10%]The two isotherms of the Stirling engine cycle are connected, not by
adiabatic processes as for the Carnot engine but by constant-volume
dQ
processes. Prove that ∫--- = 0 for an ideal Stirling engine cycke with the
T
working subtance assumed to be an ideal gas.
P.S. 第八題中的ω於題目中有下標d，因排版因素故省略
第十題的積分符號中間應該是路徑積分，不過因為我找不到這符號所以...(ry
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