課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰張顏暉
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰1/18 10:30~12:30
考試時限（分鐘）：2小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Final Exam. (EE 2007/01/18)
1.Two point-like particles, each of mass m ,are originally at rest seaparated
by a distance d. Find the time for them to come together under the influence
of the gravity.(10)
2.A fluid is rotating at constant angular velocity ω about the central
vertical axis of a cylindrical container, see Fig.1. The radius of the
container is R. Assuming that p(y_0,0) = p_c , (a) Find p(y_0,r), i.e. the
r-dependence of the pressure with fixed value of y. (b) Show that the liquid
surface is of paraboloidal form, a vertical cross section of the surface is
the curve y = ω^2*r^2 / 2g .(10) y
║* ↑ *║
║ * │ * ║
║ * │ * ║
<Fig.1 > ║ * │ * ║
║ *│* ║
─╨────┼────╨─→r
3.A tank is filled with water to height H. A hole is punched in one of the
walls at depth h below the surface,see Fig. 2. (a) Find x, the distance
between the foot of the wall and the place where the stream strikes the
floor. (b) At what depth should the hole be placed to maximize x.
╟────╢ ┬ ┬
<Fig.2> ║ ║ │ │
║ ║ │h │H
║ → v ┴ │
║ ║ │
╚════╩═════ ┴
├───┤
x
4. A wheel is free to rotate about its fixed axle. A spring is attached to one
its spokes at a distance r from the axle, as shown in Fig. 3. Assume that
the wheel is a hoop of mass m and radius R, obtain the frequency of the
small oscillations of this system in terms of M, R, r and the spring force
constant k. (rotational inertial of the wheel in this case is I = 0.5MR^2.)
(10)
< 因為可以大略想像出來,故圖省略 >
5. Write down the wave equation for a transverse plane wave propagating along
y-direction, oscillating along the z-direction, angular frequency ω,
velocity v, and amplitude A. Write down the wave equation for a longitudinal
plane wave propagating along z-direction with angular frequency ω,
wavelength λ and amplitude B. (5)
6. A uniform rope of mass m and length L hangs from the ceiling.
(a) Find the speed of the transverse wave in the string as a function of y,
where y is the distance from the free end of the string. (b) Find the time
needed for a pulse generated at one end of the rope to travel to the other
end.
7. A gas of N particles has the hypothetical speed distribution N(v) = 0 for
v > v_0 ,and N(v) = cv for 0 < v < v_0. (a) Express C in terms of N and v_0.
(b) Find the root mean square speed of the particles. (10)
8. The P-V diagram of a Stirling engine is shown is Fig.4. Find the efficiency
of the engine assuming V_a , V_b , T_H , T_L are known and the working gas
is a monoatomic gass. The definition of the efficiency of this engine is
the total work (both positive and negative) done by the engine divided by
the heat absorbed by the engine. (10)
P↑ A
│ * * ↓ Qh A-B is isothermal, at temperature T_H
｜ Q →* *
｜ D * C-D is isothermal, at temperature T_L
｜ * B
｜ * * →
｜ * * Q
│ QL ↓ * C <Fig.4>
└───────────→V
Va Vb
9. There are three different ways of stating the second law of thermodynamics.
State any two of them and prove that the two statements you chose are
equivalent. (10)
For O' moving with u with respect to O, x' = γ(x-ut) , t' = γ(t - ux/c^2)
10.A spaceship passes through planet A and then planet B iwth speed v = 0.8c
According to observer 1 who is in the spaceship, it took 30s to go from
planet A to planet B. For observer 2 who is in planet A and relative to him
,planet B is not moving, what is the distance between planets A nd B?
According to this observer how long does it take for the spaceship to
travel from planet A to planet B ?
Observer 3 is in another spaceship and is moving at 0.6c relative to the
first spaceship, and according to observer2, observer3 is moving in
opposite direction with observer 1. According to observer 3, what is the
time required for the first spaceship to pass through the two planets and
what's the distance between the two planets?
11. A particle, when at rest, has mass m, what are the momentum and kinetic
energy of this particle when it is moving with a very high speed v
(in positive direction, and the speed is measured in frame O).
For an observer in frame O' which is moving with a velocity u (also in
positive x direction) with respect to frame O, what is the momentum of the
particle? (10)
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※ 編輯: pcboy0831 來自: 140.112.240.231 (01/18 23:38)