推 aesopcjm:帥氣!! 01/18 23:03
※ 編輯: yulunchen 來自: 203.73.172.151 (01/18 23:05)
課程名稱︰普通物理學甲(上)
課程性質︰系定必修
課程教師︰梁啟德
開課學院：工學院
開課系所︰材料科學與工程學系
考試日期（年月日）︰2007/1/15
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
1. Please prove that for an adiabatic (絕熱) of an ideal gas, the pressure p
and the volune V obey pV^γ = a constant, where γ= Cp/Cv is the ratio of
the molar spcific heats (莫耳比熱) for the gas. Cp is the molar specific
heat for a constant pressure process and Cv is the molar specific heat for
a constant volume process, respectively (10%)
2. A toy rocket moves at speed of 242 m/s directly toward a stationary pole
while emitting sound waves at frequency f = 1250 Hz
(a) What frequency f' is sensed by a detector that is attached to
the pole? (10%)
(b) Some of the sound reaching the pole reflects back to the rocket,
which has an onboard detector. What frequency f'' does it detect? (10%)
[Hint: The speed of sound is 343 m/s. Please consider the Doppler effect.]
3. A cabin of volume V is filled with air (which we consider to be an ideal
diatomic gas) at an initial low temperature T1. After you light a wood
stove, the air temperature increases to T2. What is the resulting change
in the store of internal energy of the air in the cabin?(10%)
4. A sealed spherical shell of diameter d is rigidly attached to a cart, which
is moving horizontally with an acceleration a as in Fig 1. When the sphere
is at rest, it is nearly filled with a fluid having density ρ, and also
contains one small bubble of air at atmospheric pressure Po. Determine the
pressure P at the center of the sphere when the cart is moving with an
acceleration a as shown in Fig 1. (10%)
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Figure 1
5. The rell shown in Fig 2 has radius R and moment of inertia I. One end of the
block of mass m is connected to a spring of force constant k, and the other
is fastened to a cord wrapped around the reel. The reel axle and the incline
are frictionless. The reel is wound counterclockwise so that the spring
stretches a distance d from its unstretched position and is then released
from rest. Find the angular spped of reel when the spring is again
unstretched in terms of I, m the free-fall acceleration g, R, k, d and θ.
(10%)
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Figure 2
6. A 50.0-g object connected to a spring with a force constant of 35.0 N/m
oscillates on horizontal, frictionless surface with an amplitude of 4.00 cm.
Find (a) the total energy of the system (5%) and (b) the speed of the object
when the position is 1.00 cm (5%). Find (c) the kinetic energy (5%) and (d)
the potential energy when the position is 3.00 cm (5%).
2
7. y=x is a solution of x y" + xy'-y=0. Please find the general solution (通解)
of x y" + xy'-y=0.(10%)
8. Find the net torque (淨力矩) on the wheel in Fig 3 about the axle through
O if a=10.0 cm and b=25.0 cm (10%).
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Figure 3
圖只是大概畫出來,畫得不好請見諒!
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◆ From: 203.73.172.151
※ 編輯: yulunchen 來自: 203.73.172.151 (01/18 23:02)