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）︰2013/10/22
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 :
题目图片：

1. A ball mass m with initial velocity equals to 0 slide from a slope composed
1
by 4 parts. AB(/BC) is the quarter of circle with radius R (/R .) CD(/DE) is
1 2
a slope with length S (/S ) and angle θ(/θ) (θ = π/4 ). AB and CD are
1 2 1 2 1
frictionless, BC's(/DE's) coefficient of kinetic friction is μ (/μ ). All
1 2
the collisions between the ball and the slope are completely inelastic
collisions. (50 pt.)
Note:
R < 3R
2 1
S > 6R
1 1
θ > θ
1 2
Magnitude of velocity v at B
1
First collision at time t, height h, velocity at the moment before the first
collision v , after the collision v and the energy waste W.
2b 2
Magnitude of velocity v at D
3
Magnitude of velocity v at E
4
Magnitude of velocity v , v after the last collision of m , m
5 6 1 2
(a) What is the magnitude of velocity v as the ball reach B? (Show it by g,
1
R )
1
(b) After the ball reach B, the ball will fly then hit the slope (Considered
as completely inelastic collision). What is the hitting time t, hitting
height h, the magnitudes of velocities at the moment before and after
the collision (v and v ) and the energy waste W in the collision?
2b 2
(Show h by v , S , S , θ, g, R and μ , show the others by m , v , S ,
1 1 2 2 2 1 1 1 1
g, R and μ )
2 1
(c) What is the magnitude of velocity v as the ball reach D? (Show it by v
3 1
, S , g, R and μ )
1 2 1
(d) What is the magnitude of velocity v as the ball reach E? (Show it by v
4 3
, S , θ, μ and g)
2 2 2
(e) After m reach the ground, it does a completely elastic collision with
1
m with initial velocity = 0. What are the velocities of m and m after
2 1 2
the collision (v and v )? (Show them by m , m and v )
5 6 1 2 4
2. Calculate the rotational inertia of
(a) The spherical thin shell with mass m radius R.
(b) Uniform solid block with mass m.