課程名稱︰應用力學
課程性質︰必修
課程教師︰蔡丁貴 呂良正 教授
開課學院：工學院
開課系所︰土木系
考試日期（年月日）︰2008.6.16
考試時限（分鐘）：110min 10:20~12:10
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.As shown in Fig.1, the crate C is being lifted by moving the roller at A
downward with a contant speed va=2 m/s along the guide. Determine the
velocity and acceleration of the crate at the instant s=1 m. When the roller
is at B, the crate rests on the ground. Neglect the size of the pulley in
the calculation. (Hint:Relate the coordinates xc and xa using the problem
geometry, then take the first and second time deravatives.)
(20%)
(fig: Prob.12-189 of p.91)
(淡藍色皆為下標)
2.As shown in Fig.2, the 750-N(about 75-kg) man lies against the cusion for
which the coefficient of static friction is μs=0.5. If he rotates about the
the z-axis with a constant speed v=10 m/s, determine the smallest angle θ
of the cusion at which he will begin to slip off.
(20%)
(fig: Prob.13-66 of p.135)
3.As shown in Fig.3, the collar has mass of 2 kg and travels along the smooth
horizontal rod defined by the equiangular spiral r=exp(θ) m, where θ is in
radians. Determine the tangental force F and the normal force N acting on
the collar when θ=π/2, if the force F maintains a constant angular motion
θ'=2 rad/s.
(20%)
(fig: Prob.13-103 of p.147)
4.As shown in Fig.4, the slider block B is moivg to the right with an
acceleration of 2 m/s2. At the instant shown, its velocity is 6 m/s.
Determine the angular acceleration of link AB and the acceleration of point
A at this instant.
(20%)
(fig: Prob.16-128 of p.365)
(紅色為上標)
5.As shown in Fig.5, a wheel with the mass of 500 kg rotating at a speed of
20 rad/s breaks away from the steam engine that drives it and falls on the
floor. It is known that the radius of gyration of the flywheel is 1 m and
its diameter is 2.2 m. Assume the coefficient of dynamic friction between
the floor and the flywheel surface is 0.4.
(a)At what speed will the flywheel axis(center of mass) move after 2 sec?
(10%)
(b)At what speed of the center of mass will the flywheel hit the wall A?
(10%)
║←─────30m──────────→
║
║ ── ─
║ ╱ ╲ ↖ ω ↑
║ ∕ ﹨ │ │
A║ │ │ │
║ ｜ ｜ 2.2m
║ ﹨ ∕ │
║ ╲ ╱ │
║ ── ↓
╚════════════════════════════
(無法畫圓請見諒 我盡力了...)
6.A thin plate with the mass of 10 kg is supported as shown in Fig.6.
Determine the reactions at support B at the instant when support A is
removed? Note that the mass moment os inertia of a plate with respect to its
center of mass is IG=[m(a2+b2)]/12, where m = the mass = 10 kg, a=4 m and
b=5 m are the dimensions of the plate.
(20%)
│←──4m──→│B ∥
─ ╔═══════╗＜∥
↑ ║ ║ ∥
│ ║ ║
│ ║ ║
│ ║ ║
5m ║ ║
│ ║ ║
│ ║ ║
↓ ║ ║
─ ╚═══════╝
A △
════
all pictures are from
R.C. Hibbeler, Engineering Mechanics DYNAMICS, 11e in SI units
請多指教
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◆ From: 218.160.69.193
※ 編輯: eric01091989 來自: 218.160.69.193 (06/17 00:14)
※ 編輯: eric01091989 來自: 140.112.4.234 (06/17 12:22)