課程名稱︰普通物理學甲上
課程性質︰數學系大一必帶
課程教師︰黃暉理
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2013/10/01
考試時限（分鐘）：60
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. An airplane B is flying with the constant velocity v = (v , 0). At t = 0, a
B 1
cannon fires the ball at origin with initial speed v and launch angle θ,
2
and the plane just flying cross the point (0, h). And the ball hit the plane
at time t . (Suppose when the ball hit the plane and the plane will crash.)
1
Consider the gravity g, and neglect the air resistance. (25 pt.)
(a) If we know the value of v , v . Show the launch angle θ and the hitting
1 2
time t by v , v , h and g. (10 pt.)
1 1 2
(b) If we know the value of v . What is the minimum value of v if the ball
1 2
can hit the plane? (15 pt.)
.
. y
. ↑
↗θ ┼→x
￣￣￣￣￣
A
Fig. 1
2. Fig. 2 shows a section of a cable-car system. The mass of each car is m. The
cars, riding on a support cable, are pull by a second cable attached to the
support tower on each car. Assume that the cables are taut and inclined at
angle θ. What is the difference in tension between adjacent section of pull
cable if the cars are being accelerated up the incline at acceleration a.
(25 pt.)
Support cable
╱ Pull cable
╱╱
╱╱θ
╱╱|￣￣
╱╱ □
╱|
□
Fig. 2
3. The two blocks in Fig. 3 are not attached to each other. The coefficient of
static friction between two blocks is μ. And the surface beneath the larger
block is frictionless. What is the minimum magnitude of the horizontal force
F require to keep the smaller block from slipping down the larger block?
(25 pt.)
┌──┐
┌─┤ │
F→│m │ M │
└─┤ │ frictionless
│ │↙
────┴──┴─
Fig. 3
4. A ball mass m slide to the ground along a frictionless slope with angle θ
2
from height h to the ground. m = 1 kg, g = 9.8 m/s and h = 1 m. (25 pt.)
(a) What is the work done by the gravity if θ = 30°?
(b) What is the work done by the gravity if θ = 45°?
(c) What is the work done by the gravity if θ = 60°?
(d) What is the work done by the gravity if the ball free fall from height
h?
(e) What is the work done by the normal froce on the slope if θ = 45°?
o
╱▏
╱ ▏
╱ h▏
╱θ ▏
￣￣￣￣
Fig. 4
//考驗我的畫工= =