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課程名稱︰普通物理甲
課程性質︰選修
課程教師︰張寶棣
開課學院：電資學院
開課系所︰資工系
考試日期（年月日）︰99.10.22
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.The water in a river flows uniformly at a constant speed of 2.5m/s between
two parallel banks 80.0 m apart.You are to deliver a package directly across
the river,but you can swim only at 1.50 m/s (a)If you choose to minimize the
time you spend in the water,in what direction should you head ?(b)How far
downstream will you be carried ?(c)What if ? If you choose to minimize the
distance downstream that the river carries you,in what direction should you
head ?(d)How far downstream will you be carried ? (20%)
2.A 10.0 Kg block rests on a 5-Kg bracket like the one in Figure 1. The 5-Kg
bracket sits on a frictionless surface.The coefficients of friction between
the 10-Kg block and the bracket on which it rests are μs=0.40 and μk=0.30.
(a)What is the maximum force F that can be applied if the 10-Kg block is not
to slide on the bracket ?(b)What is the corresponding acceleration of the
5-Kg bracket ?(10%)
| F
5Kg← | ____→__
|-◎_____| |
|________|__|__
↓
10Kg
3.A particle of mass 1.18 Kg is attached between two identical springs on a
horizontal frictionless tabletop. The springs have force constant k and each
is initially unstressed.(a)If a particle is pulled a distance x along a
direction perpendicular to the initial configuration of the springs as shown
in Fig. 2,find the potential energy of the system.Assume that L=1.20 m and
k=40.0 N/m.If the particle is pulled 0.500 m to the right and then released,
what is the its speed when it reaches the equilibrium point at x=0 ?(10%)
____ ________
|
L | spring,k
|
O particle
|
L | spring,k
____|________
_____________
.\
. \
L . x\
=> .---O
. /
L . /
___./_______
4.A 5-kg block is held against a spring of force constant 20 N/cm,compressing
in 3 cm.The block is released and the spring extends,pushing the block along a
rough horizontal surface.The coefficient of friction between the surface and
the block is 0.2.(a)Find the work done on the block by the spring as it extends
from its compressed position to its equilibrium position.(b)Find the energy
dissipated by friction while the block moves 3 cm to the equilibrium position
of the spring.(c)What is the speed of the block when the spring is at its
equilibrium position?(d)If the block is not attached to the spring,how far will
it slide along the rough surface before coming to the rest ?(20%)
5.A 100 g ball on a 60-cm-long string is swung in a vertical circle about a
point 200 cm above the floor.The tension in the string when the ball is at the
very bottom of the circle is 5.0 N.A very sharp knife is suddenly inserted to
cut the string directly below the point of support.Where does the ball hit the
floor ?(5%)
6.A ball with mass m is aligned above a ball of mass M (with a separation) and
the two are dropped simultaneously from height h.(Assume the radius of each
ball is negligible compared to h.)(a)If M rebounds elastically from the floor
and then m rebounds elastically from M,what ratio m/M results in M stopping
upon its collisions with m ?(10%)(b)What height does m then reach?(5%)
7.Two curved inclines of two identical wedge-shaped masses M smoothly merge
with a horizontal frictionless surface as indicated in Fig. 3.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 right-hand wedge and ascends it
to some height h'?Please explain.(5%)(c)Please express h' ? in terms of m,M,
and h using the ideas in (a) and (b).(10%)
Ｍ Ｍ
│\▄← m /｜
│﹨ ∕｜
│ \ / ｜
│ Λ Λ ｜
│ ﹨ ∕ ｜
│ ﹨ 兩個物體「相連」 ∕ ｜
│ ˋ 但是沒有「相黏」 ˊ ｜
│ ╲ ╱ ｜
｜ ╲ │ ╱ ｜
｜ ︿ ↓ ︿ ｜
｜ ‵*-,,-*′ ｜
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
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※ 編輯: garychou 來自: 140.112.30.135 (10/22 21:11)