課程名稱︰機器動力學
課程性質︰選修
課程教師︰傅增隸
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰97/4/2
考試時限（分鐘）：50~60min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.A baseball player knows that if he hits a ball in just the right spot, the
sensation of achieving a long hit ball with little effort occurs.
The figure below is the top view of the bat with mass m which moves in
constant velocity
(a) Draw the free body diagram of the bat from the d'Alembert's point
of view.(10%)
(b)If the moment of inertia at the rotation center O is Io,determine the
location of the center of percussion (CP) lp by the parameters in the
figure. (10%)
(c)What the difference will you expect for the location of if the aluminum
bat replaces a wooden one with the same dimensions and explain why.
(Note : density of aluminum is 2740kg/m3, density of wood is 438 kg/m3)
(20%)
l<一 h 一>l
+------------============+======+=====
o g cp
l<一 b 一>l<一 lg 一>l
l<一 lp 一>l
ps. b=distance from center of rotation
lg=centroidal distance
lp=center of percussion
2.A solid cylinder in the figure is 4 m in diameter and weights 150 N.
It is acted upon by an upward force F of 100 N applied by a cord
wrapped around it. Note that the cylinder is an ideal rigid body and
continuous contact with ground,its radius of gyration k is 3 m and the
gravity g is 9.81 m/s2
(a) Draw the free body diagram of cylinder and formulate the EOM. (24%)
(b) Find the coefficient of static friction required Us* to
prevent slippage.(15%)
(c) If the coefficients of static and dynamic friction are Us=0.9Us* and
Ud=0.8Us* , respectively, what would be the linear acceleration
“Rg(二次微分)" of the mass center O and the angular acceleration
of the cylinder.(24%)
F .......
l .. ..
l. .
. O .
. + .
. .
.. ..
__________........_________
Ans:
1.(a)略
(b)lp=[Io/m(b+lg)]-b
(c)Moment of inertia for mass center g is Ig = m(k平方), k is the radius of
gyration of the bat, it is effected only by the geometry of the
body and has nothing to do with its material.
lp=lg+(k平方)/(b+lg)
The location of CP for aluminum and wood are the same.
2.(a)fs-(W/g)a=0
F+N-W=0
-Fr+(fs)r+Io(alfa)=0
圖略
(b)0.6154
(c)1.610m/s2 / 1.0956 rad/s2
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