大碩 102 研究所全真模擬考試試題
科 目：動力學(機械-固力、機械-控制、機械-設計)
共 2 頁之第 1 頁
考試日期：2012/11/24
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1.
A jeep has a weight of 12 kN and an engine output of power of 75 kW with the efficiency
  0.8 which transmits to all the wheels. Assuming the wheels do not slip on the ground.
Determine the angle  of the largest incline the jeep can climb at a constant speed v  10 m/s .
(20%)
2.
The roller-coaster car has a mass of 800 kg, including its passenger. If it is released from rest at
the top of the hill A. Determine the minimum height h of the hill so that the car travels around
both inside loops without leaving the track. Neglect friction, the mass of the wheels, and the
size of the car. What is the normal reaction force on the car when the car is at B and when it is
at C? (20%)
3.
An 8-kg uniform sphere 400 mm in diameter rolls without slipping on a horizontal surface and
strikes a 100 mm-tall step as shown in the figure. The collision with the step is perfectly plastic
(e = 0), and the sphere rotates about the corner of the step after the impact. Determine
(a) The angular velocity  and the velocity of the mass center vG of the
sphere immediately after the collision if the initial speed of the sphere is
v0  2.5 m / s. (6%)
(b) The kinetic energy lost in the collision. (7%)
(c) The minimum initial speed v 0 for which the sphere will rotate all the way
over the upper level. (7%)
大碩 102 研究所全真模擬考試試題
科
目：動力學(機械-固力、機械-控制)
共
2
頁之第
2
頁
4.
A cylinder of radius r and mass M rolls without slipping along a circular path of radius R as
shown in the figure. Find the natural frequency of small oscillation. (20%)
5.
At a given instant the boom AB of the tower crane is rotating about the Z axis with the motion
shown. At this same instant,   60 and the boom is rotating downward such that
  0.4 rad/s and   0.6 rad/s 2 . Determine the velocity and acceleration of the tip of the boom,
A at this instant. The boom has a length of l AB  40 m . (20%)