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）︰2013/10/22
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 :
題目圖片：http://i.imgur.com/vKq88zo.jpg
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.