課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰蔡爾成
開課學院：物理系開給化工系
開課系所︰化工系
考試日期（年月日）︰2009/1/12
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. [10%]In the figure in (12-21),what magnitude of (constant)force F applied
horizontally at the axle of the wheel is necessary to raise the wheel over
an obstacle of height h? The wheel's radius is r and its mass is m.
(本題圖可參考foundamental of physics 8e 習題12-21)
2. [10%]A uniform rope of mass m and length L hangs from a ceiling.
(a)[5%]show that the speed of a transverse wave on the rope is a function of y,
the distance from the lower end,and is given by ____
/gy
(b)[5%]show that the time a transverse wave takes to travel the length of
the rope is given by ____
/ L
---------*2
____
/ g
3. [10%]A tuning fork of unknown frequency makes 3.00 beats per second with a
standard fork of frequency 384Hz.The beat frequency decreases when a small
piece of wax is put on a prong of the first fork.What is the frequency of
this fork?
4. [10%]The pressure p of a certain non ideal gas is related to volume V and
temperature T by
p = a*T/V +b*T*T/V
How much work is done by the gas if its temperature is raised from T1 to
T2 while the pressure is held constant?
5. [10%]A bowler throws a bowling ball of radius R along a lane.The rotational
inertia of the ball wuth respect to its center is Icm =2*M*R*R/5.The ball
slides on the lane with initial speed Vo and zero initial angular speed
Wo=0.The kinetic friction force acting on the ball causes a linear
acceleraion of the ball while producing a torque that causes an anguler
accelertion of the ball.When the linear speedv hasdecreased enough and
anguler velosity has increased enough,the ball stops slidind and then
rolls smoothly.What is the linear speed of the ball when smooth rolling
begins?
6. [10%]The orbit for a panet moving around the sun is an elliose whose
semi-major axis(one half the major axis)and semi-minor axis(one half
the minor axis) are a and b.If the speed of the planet is Vo at the
perihelion(the point that is nearest to the sun),what is the speed of the
planet at the aphelion(the point that is farest from the sun)?
Express your answer in terms of a,b,Vo.
7. [10%]The equation of motion for a damped oscillator under an external driven
force is
.. .
m x + b x + kx = Fo cos(Wdt+日).
Find the steady-state solution X(t) when 2
mWd = k.
8. It is known that the Maxwell's probability distribution of molecular speeds
in a gas at temperature T is
3
----- M 2
2 ----V
M 2 - 2RT
P(v) = 4π(------) V e
2πRT
(a)[5%]what is the most probable speed vp?
(b)[5%]what is the average speed Vavg?
9. [10%]An ideal gas carnot engine operatesbetween teo reservoirs:one at higher
temperaure TH and theother at lower temperature TL.Show that the efficiency
of carnot engine
TH-TL
ec= -----------
TH
10. [10%]On conditon that (delta S) >=0 is taken as the 2nd law of
thermaldynmics,prove that the efficiency of any heat engine,which operates
between two temperature TH and TL,cannot exceed
TH-TL
ec= -----------
TH.
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