課程名稱︰普通物理學甲上
課程性質︰系必修
課程教師︰張寶棣
開課學院：電機資訊學院
開課系所︰資工系
考試日期（年月日）︰2008/10/24
考試時限（分鐘）：130 min , 10:20-12:30
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A 200-m-wide river has a uniform flow speed of 1.1m/s through a jungle and
toward the east. An explorer wishes to leave a small clearing on the south
bank and cross the river in a powerboat that moves at a constant speed of
4.0 m/s with respect to the water. There is a clearing on the north bank 82 m
upstream from a point directly opposite the clearing on the south bank. (a) In
what direction must the boat be pointed in order to travel in a straight line
and land in the clearing on the north bank? (b) How long will the boat take to
cross the river and land in the clearing? (10%)
2. A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning
disk(Fig. 1) The coefficient of friction between block and disk are 0.750 (
static) and 0.640 (kinetic) while those for the penny and block are 0.520 (
static) and 0.450 (kinetic). What is the maximum rate of rotation in
revolutions per minute that the disk can have, without the block or penny
sliding on the disk? (10%)
3. A 250 g block is dropped onto a relaxed vertical spring that has a spring
constant of k = 2.5 N/m (Fig. 2) The block becomes attached to the spring and
compressess the spring 12 cm before momentarily stopping. While the spring is
being compressed, what work is done on the block by (a) the gravitational force
on it and (b) the spring force? (c) What is the speed of the block just before
it hits the spring (Assume that friction is regligible.) (d) If the speed at
impact is doubled, whate is the maximum compression of the spring? (20%)
4. A 4.0-kg block is stacked on top of a 12.0 kg block, which is accelerating
along a horizontal table at a = 5.2 m/s2 (Fig. 3). Let μk = μs = μ. (a)
What minimum coefficient of friction μ between the two blocks will prevent
the 4.0-kg block from sliding off? (b) If μ is only half of this minimum
value, what is the acceleration of the 4.0-kg block with respect to the table,
and (c) with respect to the 12-kg block? (d) What is the force that must be
applied to the 12.0 kg block in (a) and in (b), assuming that the table is
frictionless? (15%)
5. A small mass m is set on the surface of a sphere (Fig. 4). If the
coefficient of the static friction is μs = 0.60, at what angle ψ would the
mass start sliding? (5%)
6. Two curved inclines of two identical wedge-shaped masses M smoothly merge
with a horizontal frictionless surface as indicated in Fig. 5. The curved
surfaces of the inclines are also frictionless. Another mass m is released at
rest from a height h on one of the inclines. (a) When m reaches the horizontal
plane, is the mechanical energy of m and M conserved? Is the total momentum of
m and M conserved when m reaches the horizontal surface? Why? (5%) (b) After m
reaches the horizontal plane, it encounters the righthand wedge and ascends it
to some height h'. Are both total energy and total momentum conserved when m
reaches height h'? Please explain.(5%) (c) Please express h'? in terms of m, M,
and h using the ideas in (a) and (b). (10%)
7. An atomic nucleus of mass m traveling with speed v collides elastically with
a target particle of mass 2m (initially at rest) and is scattered at 90 degree.
(a) At what angle does the target particle move after the collision? (b) What
are the final speed of the two particles? (c) What fraction of the initial
kinetic energy is transferred to the target particle? (15%)
8. A block of mass m1 = 2.0 Kg slides along a frictionless table with a speed
of 10 m/s. Dirctly in front of it, and moving in the same direction, is a block
of mass m2 = 5.0 Kg moving at 3.0 m/s. A massless spring constant k = 1120 N/m
is attached to the near side of m2, as shown in Fig. 6. When the blocks
collide, what is the maximum compression of the spring? (5%)
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