課程名稱︰普通物理學甲
課程性質︰
課程教師︰梁啟德
開課系所︰物理系
考試時間︰2 HR
試題 :
1. Please prove that ofr an adiabatic(絕熱) expansion(膨脹) of an ideal
gas, the pressure p and the volume V obey pV^γ= a constant, where γ
=Cp/Cv is the ratioa of the molar specific heats(莫耳比熱) for the gas.
Cp is the molar specific hea for a consant pressure process and Cv is
the molar specific heat for a consant volume process, respectively(10%)
2. If the remperature fo a rod of length : is raised by an amount of ΔT,
its length is found to increase by an amountΔL=LαΔT, where αis a
constant called the coefficient of linear expansion. Please prove that
the coefficient of volume expansionβ is given by β=3α.(10%) [Hint:ΔV
=VβΔT]
3. A toy rocket moves at a speed of 242m/s directly toward a stationary
pole while emitting sound waves at freauency f=1250Hz (a) What frenquency
f' is sensed by a detector that is attached to the pole?[10%] (b) Some of
the sound reaching the pole reflects back to the rocket, which has an onboard
detector. What frequency f" does it detect?[10%][Hint: The speed of sound
is 343m/s. Please consider the Doppler effect 都卜勒效應]
4. Determine the amplitude of the resultant wave when two sinusoidal string
waves having the same frequency and travelling in the same direction are
combined, if their amplitudes are 3.0 cm and 4.0 cm and they have phase
constants of 0 and π/2 rad, respectively(10%). (Hint: use Phasors)
5. A block of mass m is connected to two spring of force constants k1 and
k2 as shown in Figure 1. The block moves on a frictionless table after it
is displaced from equilibrium and released. Show that the block exhibits
simple harmonic motion with period T=2π(m/k1+k2)^1/2(10%)
Figure 1:
├══●══┤
k1 m k2
6. An ideal gas is carried through a thermodynamic cycle consisting of
two isobaric(等壓) and two isothermal(等溫) precesses as shown in Fig.2.
Please show that the net work done on the gas in the entire cycle is given
by Wnet=-P1(V2-V1)ln(P2/P1)
Figure 2:P-V圖上有ABCD四點
A-B, C-D為等溫，B-C, D-A為等壓，A點、D點的溫、壓分別為P1V1和P2V2。
7. A block of wood floats 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%)
8. Twho stars of masses M and m, separated by a distance d, revolve in
circular orbits about their center of mass(Fig 3). Show that each star
has a period given by T^2=4π^2d^3/G(M+m) (10%)
Hint: Apply Newton's second law to each star. Note that the center-of-mass
condition requires that Mr2=mr1, where r1+r2=d.
Figure 3: 如hint所描述的。
9. Big Ben(大笨鐘), the Parliament Building tower clock in London(倫敦) hour
and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg
and 100 kg, respectively. Calculate the total angylar momentum of these
hands about the center point. Treat the hands as long thin uniform rods.(10%)
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這個小孩好奇怪。
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