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）︰2013/11/05
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. A ball with 3 layers rolls smoothly from rest down a ramp at angle θ from
height h. The middle part of the ball is an uniform ball with radius R and
1
and mass m . The second layer is a uniform thick shell mass m from radius
1 2
R to R . The last part is a thin shell mass m . (25 pt)
1 2 3
(a) What is the rotational inertia I of the ball? (Using m , R to express
i i
it.)
(b) What is the magnitude of speed v and angular speed ω when the ball
f f
reach the bottom of the ramp. (Using total mass m, inertia I, h, g and
θ to express them.)
(c) What is the magnitude of the frictional force f and the ball's
acceleration a? (Using m, I, h, g and θ to express them.)
2. A ladder of length L and mass m leans against a slick wall (that is, there
1 1
is no friction between the ladder and the wall). The ladder's upper end is
at height h above the pavement on which the lower end is supported (the
pavement is not frictionless). The ladder's center of mass is L from the
c
lower end, along the length of the ladder. Two firefighters of mass m and
2
m climb the ladder until her center of mass is L and L from the lower
3 2 3
end. What then are the magnitudes of the forces on the ladder from the wall
and the pavement? (25 pt)
3. A firecracker (neglect its mass) placed inside a coconut of mass M,
initially at rest on a frictionless floor, blows the coconut into three
pieces that slide across the floor. Mass of piece A is m , mass of piece B
A
is m . Piece C with mass m has final speed v . The angle between v and v
B C C A B
is θ, the angle between v and v is θ. What is the magnitudes of final
1 A C 2
speeds of A and B? (Express them by m , θ and v ) (25 pt)
i i C
4. A spherical hollow inside a lead sphere of radius R; the surface of the
hollow passes through the center of the sphere and "touches" the right side
of the sphere. The mass of the sphere before hollowing was m . (25 pt)
1
(a) With what gravitational force does the hollowed-out lead sphere attract
a small sphere of mass m that lies at a distance d from the center of
2
the lead sphere, on the straight line connecting the centers of the
spheres and of the hollow?
(b) What is the gravitational force if m is on the line perpendicular to
2
the straight line connecting the centers of the spheres and of the
hollow?
├──d──┤
＿ │
╱ ＼
▏．○▏ ●
╲＿╱
//上面這張圖，左邊的圓圈為挖洞，且挖洞應該要碰到大球球心，但是我畫不出來QQ。