課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰蔡爾成
開課系所︰物理系開給大氣系
考試時間︰95/01/09
試題 :
(10% for each problem)
1.In the first stage of a two-stage Carnot engine, energy is absorbed as heat
Q1 at temperature T1, work W1 is done, and energy is expelled as heat Q2 at
a lower temperature T2. The second stage absorbs that energy as Q2, does work
W2, and expels energy as Q3, at a still lower temperature T3. Prove that
efficiency of the engine is (T1-T3)/T1
2.Derive the average speed of the molecule in a gas at temperature T from the
Maxwell's probability distribution function of molecular speeds:
M 3/2 2 -Mv^2/2RT
P(v) = 4π(───) v e
2πRT
∞ -ax
Hint: Try x=v^2 and make use of the integral ∫ xe dx = 1/a^2
0
3.The first law of termodynamics for an ideal gas is
dE = dQ - PdV,
where dQ represents the energy exchanged as heat between the system and its
surroundings. Show that the amount of heat exchanged between two state may
be path dependent by providing an example. Q therefore can not be a state
function of the ideal gas.
4.(a)What is the equation of continuity for the flow of an ideal fluid?
(b)What is Bernoulli's equation?
5.A standing wave may be represented as
y(x,t) = y_m cos(ωt - kx) + y_m cos(ωt + kx)
Show that the Maximum kinetic energy in each loop of the above standing wave
is "2π^2 μ y_m^2 fυ", where μ is the mass density, f is the frequency,
and υ is the wave speed.
6.A physical pendulum consists of a uniform solid disk of radius R supported
in a vertical plane by a pivot located at a distance d from the center of
the disk. The disk is displaced by a small angle and released. What is the
period of the resulting simple harmonic motion? Express your answer in terms
of R, d and the free-fall acceleration g.
7.A bowler throws a bowling ball of radius R along a lane. The rotational
inertia of the ball is (2MR^2)/5. The ball slides on the lane with initial
speed υ0 and zero initial speed ω0 = 0. The kinetic friction force acting
on the ball causes a linear acceleration of the ball while producing a
torque that causes an angular acceleration of the ball. When the linear
speed υ has decreased enough and angular velocity has increased enough, the
ball stops sliding and then rolls smoothly. What is the linear speed of the
ball when smooth rolling begins?
8.It is known that the rotational inertia foa s uniform thin spherical shell
of mass m about any radius is (2mR^2)/3. Show that the rotational inertia
for a uniform solid sphere of mass M about any radius is (2MR^2)/5.
9.The orbit for a planet moving the Sun is an ellipse whose semi-major axis
and semi-minor axis are a and b. If the speed of the planet is υ0 at the
perihelion, what is the speed of the planet at the aphelion? Express your
answer in terms of a, b, υ0.
10.The equation of motion for a damped oscillator under an external driven
force is
‥ ‧
mｘ + bｘ + kｘ = Fcos(ω_d + θ).
Find the resonant solution ｘ(t) when mω_d^2 = k.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.34.224.122