作者eric01091989 (Mr. luck)
看板NTU-Exam
标题[试题] 96上 蔡丁贵 吕良正合开 应用力学 期末考
时间Tue Jun 17 00:06:49 2008
课程名称︰应用力学
课程性质︰必修
课程教师︰蔡丁贵 吕良正 教授
开课学院:工学院
开课系所︰土木系
考试日期(年月日)︰2008.6.16
考试时限(分钟):110min 10:20~12:10
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
1.As shown in Fig.1, the crate C is being lifted by moving the roller at A
downward with a contant speed v
a=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 x
c and x
a using the problem
geometry, then take the first and second time deravatives.)
(20%)
(fig: Prob.12-189 of p.91)
(淡蓝色皆为下标)
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 μ
s=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/s
2. 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)
(红色为上标)
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
║ ﹨ ∕ │
║ ╲ ╱ │
║ ── ↓
╚════════════════════════════
(无法画圆请见谅 我尽力了...)
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 I
G=[m(a
2+b
2)]/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
请多指教
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