課程名稱︰普通物理學甲上
課程性質︰
課程教師︰李尚凡
開課系所︰機械
考試時間︰2006-1-12
試題 :
8. Imagine that a tunnel is drilled through the Earth , Mass M, as shown in
Figure. An object of mass m at a distance r from the center of the Earth
experiment gravitation attraction only by the mass within the sphere of
radius r (the reddish region in the Figure). (a)Write Newton's law of
gravitation for an object at the distance r from the center of the Earth,
and show that the force on it is of Hooke's law form, F=-kr, find k .
G is the gravitational constant. (b)Show that m follows simple harmonic
motion if it moves without friction, and follows the differential equation
d^2x/dt^2 + (g/r)x = 0, where g = GM/R^2. (c)A sack of mail is dropped into
the tunnel. How many minutes will it arrive at the other side? R=6370km,
g=9,80m/s^2
9. A train whistle (f=400Hz) sounds higher or lower in frequency depending on
whether it approaches or recedes. (a)prove that the difference in frequency
between the approaching and receding train whistle is
Δf= 〔(2u/v)/(1-u^2/v^2)〕f
where u is the speed of the train and v is the speed of sound. (70%)
(b)Calculate this difference for a train moving at a speed of 130km/h.
Take the speed of sound in air to be 340km/h.(30%)
10.When a metal pipe closed at one end is cut into 2 pieces, the lowest
resonance frequency for the air column in one-end-closed piece is 256Hz
that for the other is 440Hz . What resonant frequency would have been
produced by the original length of pipe?
11.A cylinder is closed at both ends and has insulating walls. Starting with
the expression w = -∫PdV and using the conding PV^γ = constant, we can
show that the work done on the gas is W=〔1/(γ-1)〕(PfVf-PiVi)
for an adiabatic process, which is also equal to nCv(Tf-Ti). When the
cyclinder is devided into two compartments by a perectly insulating partition
that is perpendicular to the axis of the cyclinder. Each compartment contains
1.00mol of oxygen, which behaves as an ideal gas with γ=7/5. Initially the
two compartments have equal volumes, and their temperatures are 550K and
250K. The partition is then allowed to move slowly until the pressures on its
two sides are equal. Find the final temperatures in the two compartments.
12.A sample consisitng of n mol of an ideal gas undergoes a reversible isobaric
expansion from volume Vi to volume 3Vi. Find the change in entropy of the gas.
13.An idealized idesel engine operates in a cycle known as the air-standard
diesel cycle, shown in Figure. Fuel is sprayed into the cyclinder at the
point of maximum compression, B.Combustin occurs during the expansion B→C
which is modeled as an isobaric process. Show that the efficiencyof an engine
operating in this idealized diesel cycle is
e = 〔1-(1/γ)〕〔(Td-Ta)/(Tc-Tb)〕
此篇與上篇相聯...2,4,5,8,13題有圖...抱歉無法提供...
老師的答題方式為13選10題來做...沒題10分.
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