課程名稱︰普通物理學丙
課程性質︰
課程教師︰葉平老師
開課系所︰物理系
考試時間︰2005/01/12
試題 :(這是開給森林系的課)
1a. Use the second law of thermal dynamics to explain why theat naturally flow
from high temperature region to low temperature region.
1b. Some people dream of travelling near a black hole to make observations.
One difficulty such travellers have to face is the tidal force near the black
hole. Assume a spaceship goes to 1000km away from a black hole with 10 solar
masses, find the tidal force on the pilot with feet toward the black hole. Use
the following numbers: pilot's height=2m, 1 solar mass=2*10^30kg,
G= 6.7*10^(-11)N/m^2/kg^2. Also assume the mass of his head and feet are both
5kg.
2. A room of 3m*4m*5m size sits alone in an open field. The outside
temperature is -3C. The inside temperature is 27C.
a. Assume the thermal conducitivity of the wall is 0.1W/m/K and the thicness
of the wall is 0.2m. Find the rate of heat transfer from in side to outside
by conduction.
b. Find the rate of heat transfer by radiation. Stefan's constant=5.7*10^(-8).
Assume that emissivity =1.
c. Assume that the total heat lose is the sum of the above. How much power is
needed to keep the room at constant temperature by an electrical heater?
d. Again, if we replace the heater by a heat pump with coefficient of
performace 4, how much power is needed?
3. In prof. t' Hoof's Nobel lecture in 1901, he said how he started working
on osmotic pressures. He mentioned that is was found in the 1860's that a sap
containing 1% sugar (C12H22O11) in weight at room temperature causes a osmotic
pressure greater than 0.66atm.
a. Find the osmotic pressure assuming temperature= 300K. The gas constant R=
8.31 J/mole/K.
b. Find the hight the sap rises due to this osmotic pressure.
4. Find the room-mean-square velocity of hydrogen (H2) at temperature 27C.The
mass of hydrogen is 2u, and the Boltzmann constant is 1.38^10^(-23) J/K.
5. An ideal monatomic gas with volume 8 liters is first compressed
isothermally to 4 liters,then expanded to adiabatically back to 8 liters.
a. Is the final pressure higher or lower than the initial pressure?
b. Plot the P-V diagram qualitatively.
6. A gun fires a bullet with mass m1 with an inclination angle theta and
initial velocity v and hits an ice cube with mass m2 suspended by a string.
Here are the numbers: m1=0.1kg, m2=1.9kg, cos(theta)=0.6, v=200m/s.
a. Where should the ice cube be placed in (x,y) if it is to be hit at the
hightest point of the bullet's trajuctory? Assume the gun is at the origin
(0,0) and x is horizontal and y is vertical. Neglect the air resistence.
b. Assume the bullet is stopped in the ice cube. Fide the energy loss.
c. Assume that before the bullet hits the ice cube. The temperature of the
bullet and the ice are 100C and -10C, respectively. Find the final temperature
assuming the bullet and ice reaches the same temperature. The specific heat
capacity of the bullet is 0.5kJ/kg/K and of the ice is 2kJ/kg/K.
d. The ice cube moves with the bullet inside. With the string attached, it
becomes a penulum and starts swining. Find the maximum height of the ice cube
relative to its original position.
e. The string is long enough such that the maximum swing angle phi is
arccos(0.9). Fine the period of the pendulum.
7. The motorists in a racing make turns by lowering his body and the motorcycle
to the side like the picture.(此騎士壓車過彎。面對此圖片，往你的左手邊彎過去)
This can be understood by analyzing the change of angular momentum. Use the
following quantities: each wheel has a radius r and a momentent of inertia I,
the speed of the motorcycle is v, the angle of the inclination is theta, the
height of the center of gravity of motorist+motorcycle is h when theta=0, the
total mass of motorist+ motorcycle is m.
a. Write down the angular momentum of 2 wheels combined.
b. Write down the torque exterted on the motorist+ motorcycle.
c. Explain why the motorcycle turns.
d. Use: torque=dL/dt=w*L. Write down the magnitude of the precession angular
frequency w. For a ramp with know radius of curature, if the motorcycle runs
faster, should the motorist incline more or incline less to make the turn?
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話說得太大，書看得太少，這就是問題所在。
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