[試題] 96上 林敏聰 普通物理學甲上

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課程名稱︰普通物理學甲上
課程性質︰系必修
課程教師︰林敏聰
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰96/11/22
考試時限（分鐘）：直到有人趕
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

1.(20%) Please write down the three Newton'slaw of motion in both
  translational and angular forms, including their "equivalent" expressions
  of Newton's second law. What are the assumptions for their application in
  classic mechanics? Are those "equivalent" forms really equivalent? Why?

2.(10%) Please show that the total (internal) torque in an isolated system
  (i.e. without external torque and force) of many particles which act on each
  other with force F   is zero.
                    ij

3.(20%) Two particles, each of mass m and speed v, travel in opposite
  directions along parallel lines separated by a distance d. (a) In term of m,
  v, and d find an expression for the magnitude L of angular momentum of the
  two-particle system around a point midway between the two lines. (b) Dose the
  expression change if we change the point about which L is calculated? (c) Now
  reverse the direction of travel for one of the particles and repeat (a) and
  (b).

4.(15%) Please prove the parallel-axis theorem and calculate the rotational
  inertial of body (a), (b) (see Fig.1).

5.(10%) If one spring does not follow the Hook's law anymore, but behaves as
  F = -kx^3, would its restoring force be conservative? If not, explain why?
  If yes, what would be its potential U(x)?

6.(10%) Consider a damped simple harmonic motion with the total force
  sigma(F) = -kx -bv, where k is force constant of the spring, x the
  displacement, v the velocity, b the damping constant. Please write down and
  solve the (differential) equation of motion from the Newton's Second Law.

7.(10%) One ball, with mass m, radius r, inside a hemispheric bowl, is released
  from the edge, and then rolls down the bowl without sliding. If the bowl,
  with mass M and radius R, is on a frictionless table and therefore moves
  horizontally when the ball rolls down, what will be the force exerted by the
  bowl on the ball when the ball is at the bottom of the bowl?

8.(5%) Prove that a mass point rotates from a centripetal force field should be
  a motion on the plane.

9. Good Luck!!!

圖晚點在補上

http://homepage.ntu.edu.tw/~b96202057/96Physmidtest.pdf

上面是圖檔

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※ 編輯: qazwsxerdfcv    來自: 140.112.242.66       (11/23 11:03)