課程名稱︰普通物理學甲上
課程性質︰系訂必修
課程教師︰李尚凡
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰97/1/18
考試時限（分鐘）：約240分鐘(略少)
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, 10.0 ly away.
When we reach one half of our journey from the earth as seen in a frame
of reference in which the Sun and the Tau Ceti are at rest, we see our Sun
explode and, unfortunately, at the same instant we see Tau Ceti explode as
well. Inthe spacecraft's frame of reference, whice occured first? By how
many years?
2. In the figure below, the fresh water behind a reservior dam has depth D=15m
. A horizontal pipe 4.0cm in diameter passes through the dam at depth
d=6.0m. A plug secures the pipe opening. (a) Find the magnitude of the
frictional force between plug and pipe wall. (b) The plug is removed. What
water volume exits the pipe in 3 hours?
3. Consider the particles in a gas centrifuge, a device used to seperate
particles of different mass by whirling them in a circular path of radius r
at angular speed w. The force acting toward the center of the circulr path
on a given particle is m(w^2)r. Show that the density of the particles as a
function of r is
n(r) =n0 e^{[(m(r^2)(w^2) ]/2(kB)T}
4. A plank with a mass M=6.00kg rides on top of two identical solid
sylindrical rollers that have R=5.00cm and m=2.00kg. The plank is pulled
by a horizontal force F=6.00N applied to the end the plank and perpendicula
-r to the axis of the cylinders(which are parallel). The cylinders roll wit
-hout slipping on a flat surface. There is also no slipping between the cyl
-inders and the plank. (a)Find the acceleration of the plank and of the rol
-lers. (b)What friction forces are acting?
5. A projectile of mass m moves to the right with a speed vi. The projectile s
-trikes and sticks to the end of a stationary rod of mass M, length d, pivo
-ted about a frictionless axle through its center. (a)Find the angular spee
-d of the system right after the collision. (b)Determine the fractional los
-s in machanical energy due to the collision.
6. A 1.00-mol sample of a diatomic ideal gas, initially having pressure P and
volume V, expand so as to have pressure 2P and volume 2V. Determine the en
-tropy change of the gass in the pricess.
7. Two sinusoidal waves with the same amplitude of 9.00mm and the same wavelen
-gth travel along a string that is stretch along an x axis. Their resultant
is shown twice in the figure below, as valley A travels in the negative dir
-ection of the x axis by distant d=56.0cm in 8.0 ms. The tick marks along
the axis are seperated by 10 cm. Let the equation for one wave be of the
form y(x,t)=ym sin(kx±wt+φ1), whereφ1=0 and you must choose the correct
sign infront of the w. for the equation of the other wave, what are
(a)ym (b)k (c)w (d)φ2, and (e)the sign infront of w
8. A 1.00-mol of an ideal monatomic gas is taken through the cycle shown in
the figure. The process A→B is a reversible isothermal expansion. Caculate
(a)the net work done by the gas (b)the energy added to the gas by heat (c)
the energy exhausted from the gas by heat (d)the efficiency of the cycle.
9. Ablock of mass M is connected to a spring of mass m and oscillates in SHM
on a horizontal, frictionless track. The force constant of the spring is k
and the equilibrium length is l. Assume that all portions of the spring
oscillate in fhase and that the velocity of a segment dx is proportional
to the distance x from the fixed end; that is, vx=(x/l)v. Also, note that
the mass of a segment of the spring is dm=(m/l)dx. Find (a)the kinetic
energy of the system when the block has a speed v, and (b)the period
of oscillation.
10. At the Winter Olympics, an athlete rides her lude down the track while a
bell just above the wall of the chute rings continuously. When her sled
passes thr bell she hears the frequency of the bell fall by the musical
interval called a minor third. That is, the frequency she hears drops to
five sixths of its original value. (a)Find the speed of sound in air at
the ambient temperature -10.0度C. (b)Find the speed of the athlete.
11. Three identical stars of mass M from an equilateral triangle that rorates
around the triangle's center as the stars move in a common circle about
that center. The triangle has edge length L. What is the speed of the
stars?
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