課程名稱︰ 普通物理學甲上
課程性質︰ 大一必修
課程教師︰ 張顏暐
開課系所︰ 電機工程學系
考試時間︰ 2006/01/12
試題 :
1.Write down the wave equation for a transverse plane wave propagating along
y-direction, oscillating along x-direction, angular frequency ω, velocity v
and amplitude A. Write down the wave equation for a longtitudinal plane wave
propagating along z-direction with angular frequency ω, wavelength λ and
amplitude B. Write down the wave equation for a spherical transverse wave
propagating along radial direction with frequency f, and wave number k. Define
the amplitude and oscillating direction of the spherical wave yourself.
(10)
2.The gravittational force between two particles with mass of m and M,
initially at rest at great separation, pulls them together. Find the speed
of either particle relative to the other when the separation between the two
particles is d. Express your answer in term of m, M, G and d.
(10)
3.The potential energy between nitrogen atoms in a N2 molecule is given by
U(x) = a/x^12 - b/x^6, where x is the distence between nitrogen atoms. Assume
the mass of the nitrogen atom is m, find the oscillation frequency of a small
vibration of N2.
(10)
Taylor expansion: U(x) = U(x0) + dU/dx (x-x0) + 1/2 d^2U/dx^2 (x-x0)^2, where
x0 is the equilibrium position.
4.Explain why when a body is fully or partially immersed in a fluid it is
buoyed by a force that is equal to the weight of the fluid that body
displaces. (Archimedes' principle)
(5)
5.Assume that the density of the air is proportional to the air pressure in
earth's atmosphere. Find the air pressure as a function of altitude(height).
Assume that at sea level the air pressure is P0 and the air density is ρ0.
(10)
6.Find the average power transported by a sinusodical string wave with
velocity v and angular frequency ω. Assume the string linear density of the
string is μ.
(10)
7. Two rectangular metal rods of identical shape have thermal conductivity k
and 2k respectively are welded end to end, and side to side together as shown
in Fig. 1-a and Fig. 1-b. Fid the ratio of heat conduction rate of these two
arrangements.
(10)
Fig. 1-a
0℃ ■■■■■■ 100℃
Fig. 1-b
100℃
■■■
■■■
0 ℃
8.The cycles in Fig. 2 represents the operation of an internal combustion
engine. Assume the gasoline-air intake mixture is an ideal gas with γ=1.30.
(a) What are the ratios T2/T1, T3/T1, T4/T1, P3/P1 and P4/P1?
(b) What is the engine efficiency?
(15)
Fig. 2
3.00 p1┤２～﹐ 2->3 and 4->1 are adiabatic
｜│ ～３
｜│ │
p1┤１～﹐│
｜ ～４
｜
└┬──┬─
v1 4.00v1
9.Fig. 3 represents a Carnot engine that works between temperature T1 = 400K
and T2 = 150K and drives a Carnot refrigerator that works between temperature
T3 = 325K and T4 = 225K. What is the ratio Q3/Q1?
(10)
Fig. 3
│ T1 │ │ T3 │
╰┬─┬╯ ╰┬─┬╯
Q1│ │ │ │Q3
│ ╰────╯ │
│╭──────╮│
Q2││ W ││Q4
╭┴┴╮ ╭┴┴╮
│ T2 │ │ T4 │
10.In Fig 4-a, particle P is to move parallel to the x and x' axes of
reference frames S and S'; at a certain velocity relative to frame S. Frame S'
is to move parallel to the x axis of Frame S at velocity v. Fig 4.b gives the
velocity u' of the particle relative to frame S' for a range of values for v.
What value will u' have if (a) v = 0.9c and (b) v -> c.
(10)
Fig. 4-a
y y'
│ ├─→
│S │S'
│ │ ˙P
└─x└───x'
Fig. 4-b
0.8c├─▂
u' │ ▇︸︷▂▁
0.4c│ ￣
│
└──┴──┴──
0 0.2c 0.4c v
--
「我們愛星星至深無懼於黑暗。」
"We have loved the stars too fondly to be fearful of the night."
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.228.81.67