課程名稱︰普通物理學甲
課程性質︰大一必修
課程教師︰梁啟德
開課系所︰for生機系
考試時間︰2005.1.12
試題 :
1.Please prove that for an adiabatic(絕熱) expansion(膨脹) of an ideal gas,the
pressure ｐ and the volume Ｖ obey ｐ^Ｖ^γ(ｐ的Ｖ^γ次方)=a constant,where
γ=Ｃp/Ｃv is the ratio of the molar specific heats(莫耳比熱) for the gas.
Ｃp is the molar specific heat for a constant pressure process and Ｃv is
the molar specific heat for a constant volume process,respectively.(10%)
2.If the temperature of a rod of length is raised by an amount of ΔＴ,its
length is found to increase by an amount ΔＬ=ＬαＴ,where αis a constant
called the coefficient of linear expansion.Please prove that the coefficient
of the volume expansion β is given by β=3α.(10%)
3.Determine the amplitude of the resultant wave when two sinusoidal string
waves having the same frequency and traveling in the same direction are
combined,if their amplitudes are 3.0cm and 4.0cm and they have phase
constants of 0 and π/2 rad,respectively.(10%)(Hint:use the Phasors)
4.A block of wood float in water with two-thirds(2/3) of its volume submerged
(浸入).In oil the block floats with 0.90 of its volume submerged.Find the
density of (a) the wood(5%) and (b) the oil.(5%)
5.A vertical(垂直) spring stretches 9.6cm when a 1.3kg block is hung from its
end.(a) Calculate the spring constant(5%).The block is then displaced an
additional 5.0cm downward and released from rest.Find (b) the period (5%)
(c) the frequency (5%) and (d) the amplitude (5%) of the resulting Simple
Harmonic Motion (SHM)(簡諧運動).
6.A cockroach(蟑螂) of mass ｍ runs counterclockwise(反時鐘) around the rim of
a lazy Susan(a circular dish mounted on a vertical axle) of radius Ｒ and
the rotational inertia Ι and having frictionless bearings.The cockroach's
speed(relative to ground)is ｖ,whereas the Lazy Susan turns clockwise
(順時鐘) with angular speed ω0.The cockroach finds a bread crumb and stops
(a) What is the angular speed of the Lazy Susan after the cockroach stops?
(5%) (b)Is mechanical energy 機械能 conserved as they stop?(5%)
7.Please prove Bernoulli's equation ｐ+ρ(ｖ^2)/2+ρｇｈ= a constant(常數)
along any tube or flow where ｐ is the pressure(壓力) ρ is the fluid
density,ｖ is the fluid velocity,ｇ is the free-fall accelaration and ｙ is
the vertical position(垂直位置),respectively.(10%)
8.A toy rocket moves at a speed of 242m/s directly toward a stationary pole
while emitting sound waves at frequency ｆ=1250Hz (a)What frequency ｆ' is
sensed by a detector that is attached to the pole?(5%) (b)Some of the sound
reaching the pole reflects back to the rockets,which has an onboard detector
.What frequency ｆ'' does it detect?(5%)(Hint:The speed of the sound is
343m/s.Please consider the Doppler effect 都卜勒效應)
9.In terms of the gravitational constant(萬有引力常數) Ｇ and the mass of the
Earth Ｍ,please express the total mechanical energy 機械能(動能加位能) of a
satellite 人造衛星(with the mass of ｍ) going around the Earth in a circular
orbit with a radius Ｒ.(Hint:ｍ and Ｒ must be included in your answer to
this question)(10%)
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