→ shrek0665 :第一次畫圖... 04/17 16:18
課程名稱︰動力學
課程性質︰系必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2010-04-13
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
1.
The pin follows the path described by the equation r = a + bcosθ.
At the instant θ =30 度(我不會打那個上標的小圓) ,the angular velocity θ'
and angular acceleration θ"are 0.7 rad/s and 0.5 rad/s^2. Determine the
magnitudes of the pin's velocity and acceleration at this instant.
Given a=0.2 m and b=0.15 m. (15%)
2.
A single wire ACB of length 2m passes through a ring at C that is attached
to a sphere which revolves at a constant speed v in the
A ﹨ horizontal circle shown (以O為圓心，OC為半徑之圓). Knowing
﹨ that∠OBC =60度 and ∠ABC =30度 and the tension is the same
﹨ in both portions of the wire,determine the speed v. (15%)
﹨
B ﹨
╲ ﹨
╲ ﹨
╲ ﹨
╲﹨
O‧ ● C
3.
The boy of mass 40kg is sliding down the spiral slide at a constant speed such
that his position, measured from the top of the chute, has components r=1.5m
θ=0.7t and z= -0.5t. Determine the components of force Fr,Fθand Fz which the
slide exerts on him at the instant t=2sec. Neglect the size of the boy.
(螺旋狀的滑梯，半徑固定，螺距固定) (15%)
4.
| |-------5m-----------| A basketball player shoots when she is 5m
→| |←d from the backboard. Knowing that the ball
_|____ has an initial velocity v0 at an angle of
| | ﹨ 30度 with the horizontal, determine the
| 30度↖ value of v0 when d is equal to 430mm.
| 3.048m _____●
| ﹨
| 2m
| _∕_________________∕_ (10%)
5.
Plane A is flying along a straight-line path,
while plane B is flying along a circular path
↑ 700 km/hr ↑600 km/hr having a radius of curvature of r=400km.
Determine the velocity and acceleration of B
▲ A ▲ B as measured by the pilot of A.
(飛機B作圓周運動，圖我畫不出來)
↑50 km/hr^2 ↓100 km/hr^2
| |
| |
|------4km-------|
| | (15%)
| |
6.
The small object is placed on the inner surface of
the conical dish at the radius shown. If the
A | 0.2m | ／ coefficient of static friction between the object
| ／ and the conical surface is 0.30, for what range of
| m◇／ angular velocities ω about the vertical axis AB will
| ／ the block remain on the dish without slipping?
| ／ Assume that speed changes are made slowly so that any
| ／ angular acceleration may be neglected.
B |∠ 30 度 (15%)
7.
A A 1-kg collar C slides without friction along the rod OA
╱ and is attached to rod BC by a frictionless pin. The rods
╱ rotate in the horizontal plane(ABCO皆在一水平面上). At
C ╱ the instant shown BC is rotating counterclockwise and the
◆ speed of C is 1m/s, increasing at a rate of 1.3m/s.
╱∕ Determine at this instant the tension in rod BC.
╱ ∕ Given sin 23.8度 = 0.40 and cos 23.8度 =0.92.
O╱ ∕ 附註：
∕ OB=0.3m, BC=0.6m
∕ 角OBC=30度
∕
B∕
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