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）︰2013.6.18
考試時限（分鐘）：3小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
註：範圍：Tongue Dynamics Ch6-Ch7 (Total:115 points)
圖形：http://ppt.cc/JW0Y
1. A cylinder is released from rest from point A. As it rolls past B it
moves from a constant slope of angle α(radian) and onto a circular
path. The distance from A to B is d (meter), the radius of the cylinder
is r1 (meter) and the radius of the circular path is r2 (meter)， and
the mass of the cylinder is m. Assume no-slip conditions.
(a) Define your inertial frame, body-fixed coordinates and its
angular velocity of the cylinder for the motion from A to B.
(5%)
(b) What is the pure rolling condition for the motion from A to B?
(5%)
(c) Write equations of motion of the cylinder from A to B, check
unknowns and add additional equations if necessary. (4%)
(d) On the circular path， what is the pure rolling condition in
terms of the velocity of mass center and the angular velocity
of the cylinder? (6%)
2. A uniform disk with mass m (kg) and radius r (meter) has a bungie
cord of unstretched length L (meter) attached to its center, where the
other end of the cord is fixed to a post at the top of a rough incline
angled at θ=30°to the horizontal. The height of point P is the same
as the radius of the disk. Suppose the disk is rolling down the incline
from P so that its mass center's initial speed is v0 (m/s). The cylinder
rolls without slip, and it comes to a stop when the bungie cord is
stretched δ＝L meter. What is the gungie cord's stiffness k? (15%)
3. A hoop of mass m and radius r rolls without slip with a constant
speed v0 on level ground. Find the hoop's angular velocity immediately
after it strikes an incline angled at β with respect to the horizontal.
The rotational inertia for the hoop about its mass center G is given by
2
I ＝ m r , and assume zero rebound. (15%)
G
→ → → →
(Hint: You may want to use H ＝ H + r x m v , where A is the point of
A G AG G
strike on the incline.)
4. A uniform rod of mass m and length L is initially held in the depicted
configuration, where θ=60°with respect to the horizontal. The rod is
supported by a rough horizontal surface at its end A. The coefficient
between the rod and surface is μ. Suppose the rod is released from rest
and allowed to fall.
(a) Define the inertial frame and body-fixed coordinate, and
write the position, velocity and acceleration of the mass
center. (5%)
(b) Write the equations of motion of the system, both for slip and
no-slip motion. (10%)
(c) What is the minimum friction μ so that the rod falls without
slip initially at θ＝60°?(5%)
5. The rotating arm OA is connected to the fixed guide by means of a
pin P that rides within both the slot in the arm and the channel in the
fixed guide. The channel in the fixed guide is circular, with radius b.
Remind that the constraints from geometry are Φ=2θ and r=2bcosθ.
(a) Define your inertial frame, the body-fixed coordinates on OA and
along CP. (3%)
(b) Write the position and velocity of P in terms of the body-fixed
coordinates defined on OA.(3%)
(c) Write the position and velocity of P in terms of the body-fixed
coordinates defined along CP.(3%)
‧
(d) Show that if θ is a constant, the acceleration of the pin is
constant in magnitude.(6%)
6. At the configuration shown (η=30°), the link AB has an angular
‧ →
velocity of θ k (rad/s) and an angular acceleration of zero. Point C
slides freely on the horzontal surface.
(a) Define your inertial frame, the body-fixed coordinates on link AB
as well as on link BC.(5%) ‧
(b) What is the angular velocity of link BC in terms of θ at the
configuration of η=30°.(5%) ‧
(c) What is the angular acceleration of link BC in terms of θ at the
configuration of η=30°.(5%)
7. A uniform arrow flies with angle β to a rigid, smooth surface with
→ →
velocity v = v j before it strikes on the surface. The mass of arrow
is M, and its length is L. The arrow strikes the surface without rebound.
What is the angular velocity immediately after the arrow strikes the
surface?(15%)
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◆ From: 114.36.14.28
※ 編輯: ndpe1220 來自: 114.36.14.28 (06/24 21:36)
※ 編輯: ndpe1220 來自: 114.36.14.28 (06/24 21:52)