課程名稱︰普通物理學甲上
課程性質︰系定必修
課程教師︰李尚凡
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰97/1/19
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Suppose our Sun is about to explode. In an effort to escape, we depart
in a spacecraft at v=0.980c and head toward the star Tau Ceti, 20.0ly away.
When we reach one half of our journey from the Earth as seen in a frame of
reference in which the Sun and Tau Ceti are at rest, we see our Sun explode
and, unfortunately, at the same instant we see Tau Ceti explode as well. In
the spacecraft's frame of reference, which occurred first? By how many years?
2. A solid sphere of mass m and radius r(I=2/5mr^2)rolls without slipping
along the track shown in the figure. It starts from rest with the lowest
point of the sphere at height h above the bottom of the loop of radius R,
much larger than r. (a) What is the minimum value of h (in terms of R)
such that the sphere completes the loop? (b) What are the force components
on the sphere at the point P if h=3R?
3. From the Maxwell-Boltzmann speed distribution,(老師有給，但太難打了)，
show that the average speed and the most probable speed of a gas molecule are.
4 The oldest artificial satellite in orbit is Vanguard I, launched March
3, 1985. Its mass is 1.60kg. In its initial orbit its minimum distance from
the center of the Earth was 7.02 Mm and its speed at this perigee point was
8.23 km/s. (a)Find the total energy of the satellite-Earth system. (b)
Find the magnitude of the angular momentum of the satellite. (c) Find its
speed at apogee and its maximum (apogee) distance from the center of the
Earth. (d) Find the semi-major axis of its orbit. (e) Determine its period.
5. A 1.00-mol sample of an ideal gas(r=1.40) is carried through the
Carnot cycle described in the figure. At point A, the pressure is 25.0 atm
and the temperature is 600 K. At point C, the pressure is 1.00 atm and the
temperature is 400K. (a) Determine the efficiency of an engine operating in
this cycle. (b) Calculate the net work done per cycle.
6. A solid sphere (radius=R I=2/5 mR^2) rolls without slipping in a
cylindrical trough (radius=5R) as shown in the figure. Show that, for small
displacements from equilibrium perpendicular to the length of the trough, the
sphere executes simple harmonic motion with a period T=二拍根號(28R/5g)
7. Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from
initial volume Vi=1.00m^3 to final volume Vf=2.00m^3. At any instant during
the expansion, the pressure P and volume V of the gas are related by
P=5.00exp[(Vi-Vf)/a] with P in kilopascals, Vi and V in cubic meter, and
a=1.00m^3. (a) How much work is done by the gas during the expansion?
(b) What is the change in entropy S ?
8. Two waves are described by the wave functions y1(x,t)=5.0sin(2.0x-10t)
y2(x,y)=10cos(2.0x-10t) where y1,y2,and x are in meters and t is in seconds.
The wave resulting from their superposition is also sinusoidal. Determine
the amplitude and phase of this sinusoidal wave.
9. A stream of water flows steadily from a kitchen faucet as in the figure.
At the faucet the radius of the stream is R and the emerging speed is V0.
Find the diameter of the stream as a function of the vertical drop y.
10. To permit measurement of her speed, a skydiver carries a buzzer
emitting a steady tone at 1800Hz. A friend on the ground at the landing site
directly below listens to the amplified sound he receives. Assume that the
air is calm and that the sound speed is 343m/s, independent of altitude. While
the skydiver is falling at terminal speed her friend on the ground receives
waves of frequency 2150Hz. (a) What is the skydiver's speed of descent?
(b) Suppose the skydiver can hear the sound of the buzzer reflected from the
ground. What frequency does she receive?
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