課程名稱︰普通物理學甲上
課程性質︰大一必修
課程教師︰李慶德
開課學院：電資學院
開課系所︰電機工程學系
考試日期（年月日）︰2015/1/8
考試時限（分鐘）：30分鐘
試題 :
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General Physics A — Final Simulation — January 8, 2015
Do any 5 problems given below!
1. A harmonic oscillator consisting of a block with mass m and a spring with
spring constant k is damped by a damping force that is proportional to the
velocity v, i.e., Fd = -bv. Thus, the displacement function x(t) satisfies
the equation 2
d x dx
m ─── + b ── + kx = 0.
2 dt
dt
The solution of this equation is
2
-bt/2m k b
X(t) = Xm e cos(ω't+ψ), with ω' = √( ─ - ── ),
m 2
4m
where Xm is the amplitude and ω' is the angular frequency of the damped
oscillator. Assume that m = 250 g, k = 85 N/m, and b = 70 g/s for this
damped oscillator.
(a) What is the period of the motion?
(b) How long does it take for the amplitude of the damped oscillator to
half its initial value?
(c) How long does it take for the mechanical energy to drop to half its
initial value?
2. Three identical stars of mass M form an equilateral triangle that rotates
around the triangle's center as the stars move in a common circle about the
center. The triangle has edge length L. Find the speed of the stars.
3. Three sinusoidal waves of the same frequency travel along a string in
positive direction of an x-axis. Their amplitudes are y1, y1/2, and y1/3,
and their phase constants are 0, π/2, and π, respectively.
(a) What are the amplitude and phase constant of the resultant wave?
(b) Plot the wave form of the resultant wave at t = 0, and discuss its
behavior as t increases.
4. Two 50 g ice cubes are dropped into 200 g of water in a thermally
insulated container. Suppose that the water is initially at 25°C, and the
ice comes directly from a freezer at -15°C.
(a) What is the final temperature at thermal equilibrium?
(b) What is the final temperature if only one ice cube is used?
Note that the heat of fusion of water is LF = 79.5 cal/g and 1cal = 4.1868J.
5. A block weighing 15.0 N, which can slide without friction on an incline
at angle θ = 37.0°, is connected to the top of the incline by a massless
spring of unstretched length 0.480 m and spring constant 125 N/m.
(a) How far from the top of the incline is the block's equilibrium point?
(b) If the block is pull slightly down the incline and released, what is
the period of the resultant oscillations?
6. A girl is sitting near an open window of a train that is moving at a
velocity of 10.0 m/s to the east. The girl's uncle stands near the tracks
and watches the train move away. The locomotive whistle emits sound at
frequency 500.0 Hz. The air is still.
(a) What frequency does the uncle hear?
(b) What frequency does the girl hear?
Now a wind begins to blow from the east at 10.0 m/s.
(c) What frequency does the uncle hear?
(d) What frequency does the girl hear?
7. Initially, 1 mol of oxygen has temperature 300 K and volume 12 L. We will
allow it to expand to volume 20 L. Oxygen (O2) is diatomic and here has
rotation but not oscillation. Here, we will also assume it to be an ideal
gas.
(a) What would be the final temperature if the gas expands adiabatically?
(b) What would be the final temperature and pressure if, instead, the gas
expands freely to the new volume, from an initial pressure of 2.0 Pa?
=============================== 試題完 ====================================
備註：
雖然考卷上面寫挑五題作就好，但當時教授只要求我們挑兩題寫。