[試題] 普物甲 梁啟德 2004.11.13

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課程名稱︰普通物理甲
課程性質︰大一必修
課程教師︰梁啟德
開課系所︰
考試時間︰2004.11.13

試題 :                              →      →      →     →→       →
1.Three vectors (向量) are given by a = 3.0 i + 3.0 j -2.0 k , b = -1.0 i
        →      →     →      →      →      →
  - 4.0 j + 2.0 k ,and c = 2.0 i + 2.0 j + 1.0 k .Please find
      →     →  →
  (a) a ˙ ( b ×c ) (5分)
      →     →  →
  (b) a ˙ ( b + c ) (5分)
      →     →  →
  (c) a × ( b + c ) (5分)

2.If a particle travels along a circle or circular are with radius(半徑)
  γ at constant speed ν,it is in uniform circular motion(等速率圓周運動)
  Prove that the particle has an acceleration a of magnitude a=ν^2/γ.
  (10分)

3.Please prove the parallel axis theorem(平行軸定理)Ι=Ιcm + Μh^2 where
  Ι is the rational inertia(轉動慣量)of a body about any axis,Ιcm is the
  rational inertia of the body about an axis that passes through its center
  of mass(質心),h is the perpendicular distance between the two axes ,and
  Μ is the mass of the body.(10分)

4.The position of a particle is given by x(t)=4+ln(t)sin(2t) where t is the
  time in units of second.Please find the velocity v(t)(5分)and the
  acceleration a(t)(5分)

5.A 55kg woman runs up a flight of stairs with a height of 4.5m in 3.5s.
  What average power(平均功率)is required of her?(10分)

6.Two particles of equal masses have an elastic collision,the target particle
  being initially at rest.Show that(unless the collision is head-on),the two
  particles will always move off perpendicular to each other after the
  collision(碰撞後兩者運動方向互相垂直)(10分)

7.The two blocks(with m = 16kg and M = 88kg)shown in Fig.1 are not attached.
  The coefficient of static friction between the blocks is μs=0.38 but the
  surface beneath the larger block is frictionless.     →
  What is the minimun magnitude of the horizontal force F required to keep
  the smaller block from slipping down the larger block?(10分)
                  m
              ┌───┬──────┐
              │  →  │            │
              │  F   │            │
              └───┤     M      │frictionless
                      │            │    ↓
              ────┴──────┴───
                       Fig.1

8.A 2.0kg block is dropped from a height of 0.40m onto a spring constant
  k=1960N/m(Fig.2).Find the maximun distance the spring is compressed(10分).

              ┌───┐
              │ 2.0kg│
              └───┘┬  ─
                        │  ↑
                        │ 40cm
                        │  ↓
                ───  ┴  ─
                  ╲
                  ／
                  ╲
                  ／   k=1960N/m
                  ╲
                  ╱
                ───
                 Fig.2

9.In your own words,please explain what a conservative force(保守力)is?(10分)
  Can you name one conservative force?請舉例說明一保守力(5分)

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