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推 stlispig :謝謝你>< 02/20 14:21
課程名稱︰動力學
課程性質︰必修
課程教師︰陽毅平
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2008/6/17
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A uniform bar of length L mass m is suspended horizontally at its
ends A and B by inextensible strings of equal length b. When one of the
strings is cut, what is the resulting angular acceleration of the bar
and the tension of string? (10%)
2. The two blades of radius R rotate counterclockwise with a constant
angular velocity ω about the shaft at O mounted in the sliding block.
the block is moving to the right with an acceleration of a0.
(a) Determine the acceleration of the tip A of the blade when θ=90 in
terms of inertial coordinates.(5%) (b) If the mass moment of inertia
of each blade is (1/3)mR^2 with respect to its end, what is the mechanical
energy of the system?(5%) (c) Is the mechanical energy conserved? Why?(5%)
3. A metal hoop with a radius r and mass m is projected along the incline
of angle θ with an inertial speed v0 and angular velocity ω0, where
rω0 > v0. The cofficient of kinetic friction is μk, and the mass moment
of inertia about its center is mr^2.
(a) Define the inertial frame and a body-fixed corradinate system on the
hoop.(2%)
(b) Write the displacement, velocity and acceleration vectorsof the conter
of mass.(3%)
(c) Plot the free body diagram with all the forces acting on the hoop before
it rolls without slip.(4%)
(d) Write the equations of motino of the hoop before it rolls with slip.(4%)
(e) How long will it take for the hoop to rotate without slip?(9%)
4. A bowl with a circular cross section of radius R and mass M lies on a
frictionless horizontal surface. initially the system is stationary. A small
block of mass m startsat point A (θ=0) and slides down the inside of the
frictionless bowl.
(a) Define the inertial frame and a body-fixed coordinate system on the small
block m.(4%)
(b) Find the equations of motion of the small mass along the axes of
inertial frame.(6%)
(c) Find the equations of motion of the bowl along the axes of inertial
frame.(6%)
(d) What are unknowns in your eq. of motion obtained in (b) and (c)?(4%)
(e) What is the velocity of the bowl as the small masss reaches the bottom
of the bowl?(10%)
5. A uniform slender bar of mass m is released from rest in the horizontal
position, where x = (2√3) (註：質心 與接觸點的距離). The cofficient of
friction between the bar and edge is μ.
(a) Define the inertial frame and a body-fixed coordinate syster on the bar.
(2%)
(b) Write the general exprassions of position, velocity, and acceleration
of the center of mass before the bar slips.(5%)
(c) Write the general exprassions of position, velocity, and acceleration
of the center of mass after the bar slips.(3%)
(d) What is the inertial angular acceleration of the bar just when it is
released?(extra7%)
(e) Write the eq. of motion of the bar before it slips.(extra6%)
(f) Determine the angle θ at which the cilinder starts to slip.(extra12%)
6. A uniform slender bar of length L and mass m is sliding to the left
on the horizontal surface with velocity v0 when srikes the small step at O.
assume negligible rebond at the step.
(a) What is the angular velocity of the bar immediately after impact?(10%)
(b) What is the percentage energy loss afer impact?(extra5%)
(c) Computethe minimum value of v0 which will permit the bar to pivot freely
about O and just reach the standing position A with no velocity.(5%)
--
██████████████████
▏ ▏O
▏ ▏
▏ ▏
剪 ＠/ ▏ ▏
刀 ＠\ ▏ ▏
▏ ▏
▏ ▏
A ▆▆▆▆▆▆▆▆▆▆▆▆▆ B
Problem 1
--
Y ◢◤ A
▉ ◢◤
▉ ▁▁▁▁ O ◢◤▁▁▁▁
▉▁▁X ▁▁▁▁ ███ ▁▁▁▁▁
◢◤
◢◤
B ◢◤
Problem 2
--
▁ ω0
m / \
▏ G ▏V0 →
\ /
▁▁
▇▇▆▆▅▅▄▄▃▃▂▂▁▁▁ θ
Problem 3
--
A
┌─┐ ┌─┐
│ │
│ B \˙ / │ g↓
│ ▁ │
│ M │
└────────┘
Problem 4
--
｜←──────l──────→︳
O←x→G
▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇
▁▁▁▁▁▁▁◢◣
▉
▉
▉
Problem 5
--
A ．
．
． v0
． ←─ ◢◤
． ◢◤
． ◢◤
． ◢◤
． ◢◤ 60。
█████████▃▃▃▃▃▃▃▃▃
O
Problem 6
ψcccwccc
--
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