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
考試時間︰2006.11.17 10:00~12:50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.When baseball player throw the ball in from the outfield, they usually allow
it to take one bounce before it reaches the infield, on the theory the ball
arrives sooner that way. Suppose the angle at which the outfielder threw it,
as shown in the figure(圖略), but that the ball's speed after the bounce is
√(2/3) times what it was before the bounce. (a) Assume that the ball is
always thrown with the same initial speed. At what angle θ should the
fielder throw the ball to make it go the same distance D with one bounce(
lower path) as a ball thrown upward at 45.0 with no bounce (upper path)?
(b) Determine the ratio of the time intervals required for the one-bounce
and no-bounce throws.
2.A rocket body of mass M will fall out of the sky with terminal speed Vt
after its fuel is used up. What power out put must the rocket engine produce
if the rocket is to fly (a) at it terminal speed straight up; (b) at three
the terminal speed straight down? In both case assume that the mass of the
fuel and oxidizer remaining in the rocket is negligible compared to M.
Assume that the force of air resistance is proportional to the square of the
rocket's speed.
3.Consider an object on which the net force is a resistive force proportional
to the square of its speed. For example, assume that the resistive force
acting on a speed is f=-kmV^2, where k is constant and m is the skater's
mass. The skater crosses the finish line of a straight-line race with speed
V and then slow down by coasting on his skates. The skater's speed at any
time t after crossing the finish line is v(t)=V/(1+ktV). (a) Find the
position x as a function of time for an object mass m, located at x=0 and
moving with velocity v^2 i(i代表x方向單位向量，向量符號打不出來) at time t=0
and thereafter experiencing a net force -kmv^2 i. (b) Find the object
velocity as a function of position.
4.Consider a thin uniform rod of length L. when the rod is straight, its
center of mass is at its center. Now bend the rod in a circle arc so that it
subtends an angle of 90.0 of the center of the arc, as shown in the figure(
圖略). In this configuration, how far outside the rod is the center of mass?
5.A plumb bob does not hang exactly along a line directed to the center of the
Earth's rotation. How much does the plumb bob deviate from a radial line at
35度 north latitude? Assume that the Earth is sperical.
6.A 2.00-kg block situated on a rough incline is connect to a spring of
negligible mass having a spring constant of 100N/m (圖略). The pulley is
frictionless. The block is released from rest when the spring is unstretched
. The block moves 20.0cm down the incline before coming to rest. (a) Find
the coefficient of kinetic friction between block and incline. Suppose the
incline is frictionless from rest with the spring initially unstretched.
(b) How far does it move down the incline before coming to rest? (c) What
is its acceleration at its lowest point? Is the acceleration constant?
(圖為37度的斜面上有一物，然後更上面接彈簧)
7.Tow particles with masses m and 3m are moving toward each other along the x
axis with the same initial speeds Vi. Particle m is traveling to the left,
while particle 3m is traveling to the right. They undergo an elastic
glancing collision such that the particle m is moving downward after the
collision at right angles from its initial direction. (a) Find the final
speeds of the two particles. (b) What is the angle θ at which the particle
3m is scattered?
8.Suzanne observes two light pulses to be emitted from the same location, but
separated in time by 3.00μs. Mark sees the emission of the same two pulses
separated in time by 9.00μs. (a) How fast is Mark moving relative to
Suzanne? (b) According to Mark, what is the separation in space of two
pulses?
9.A 5.00-g bullet is fired into and pass throuth a 1.00-kg, 10.0cm cubic block
, as in the figure(圖略). The block, initially at rest, is connected to a
massless spring of force constant 900N/m hanging from the roof. If the
initial speed of the bullet just before impact is 400m/s and the block moves
5.00cm upwards after impact, find (a) the speed at which the bullet emerges
from the block and (b) the mechanical energy converted into internal emergy
in the collision.
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