课程名称︰普通物理学甲上
课程性质︰数学系大一必带
课程教师︰黄晖理
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2013/10/01
考试时限（分钟）：60
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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
//考验我的画工= =