[試題] 102上 黃暉理 普通物理學甲上 期中考

[xavier13540 (柊 四千)]

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。

--
第01話 似乎在課堂上聽過的樣子          第02話 那真是太令人絕望了
第03話 已經沒什麼好期望了              第04話 被當、21都是存在的
第05話 怎麼可能會all pass              第06話 這考卷絕對有問題啊
第07話 你能面對真正的分數嗎            第08話 我，真是個笨蛋
第09話 這樣成績，教授絕不會讓我過的    第10話 再也不依靠考古題
第11話 最後留下的補考                  第12話 我最愛的學分

--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.112.196.111
※ 文章網址: http://www.ptt.cc/bbs/NTU-Exam/M.1403535089.A.624.html