課程名稱︰普通物理學甲上
課程性質︰系定必修
課程教師︰蘇德潤
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰08-01-18
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. We consider that
PURE Rolling = a translation of center of mass along a straight line + a
rotation.
(a) What can be more than a "pure" and "rolling"?
(b) If a rigid disk of radius "r", angular variable "θ" with corresponding
arc -length "s", and straight displacement "x". What is the relation
between "s", "θ" and "r"?
(c) For rolling without sliding, what is the relation between "x", "θ" and
"r"?
(d) When with sliding of the center of mass with a velocity "V", what are
relations (equalities and inequalities) between "V", "x", "θ" and "r"?
(20%)
2. Figure 14-53 shows a stream of water flowing through a hole at depth h=10cm
in a tank holding water to height H=40cm.
(a) At what distance x does the stream strike the floor?
(b) At what depth should a second hole be made to give the same value of x?
(c) At what depth should a hole be made to maximize x?
(圖片就是一個水缸裡面裝著高H的水,從水面往下h的缸壁有個洞有水噴出來,噴出來初速v,
水落到地面距離缸壁底端x)
(20%)
3. The linear density of a string is 1.6E-4 kg/m. A transverse wave on the
string is described by the equation
y = (0.021 m ) sin[(2.0 1/m)x + (30 1/s)t].
What are (a) the wave speed and (b) the tension in the string?
(20%)
4. For a rubber band stretched dx longer derive the force F appeared for
entropy S change dS at temperature T.
F = -T dS/dx.
Figure 20-33 gives the force magnitude F versus stretch distance X for a
rubber band, with the scale of the F axis set by Fs = 1.50N and the scale of
the X axis set by Xs = 3.50cm. The temperature is 2.00C. When the rubber band
is stretched by x = 1.70cm, at what rate does the entropy of the rubber band
change during a small additional stretch?
(圖片就是一條通過原點斜率為正的直線,橫軸為X(cm)縱軸為F(N),Fs對應到Xs)
(20%)
5. Figure 12-47 shows a 70 kg climber hanging by only the crimp hold of one
hand on the edge of s shallow horizontal ledge in a rock wall. (The fingers
are pressed down to gain purchase.) Her feet touch the rock wall at distance
H = 2.0 m directly below her crimped fingers but do not provide any support.
Her center of mass is distance a = 0.20 m form the wall. Assume that the
force from the ledge supporting her fingers is equally shared by the four
fingers. What are the values of the (a) horizontal component Fh and (b)
vertical component Fv of the force on each fingertip?
(圖片是ㄧ個女的用手扣著一面垂直岩壁的ㄧ個小凸出點,腳尖也碰著岩壁,旁邊有標坐標向
上為y向右為x,手指頭上有向上垂直分力Fv跟向右水平分力Fh,從手指到腳指長H,重心到牆
面的距離a)
大概像這樣
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(第二部分)
When there is no support from the foot like another figure, write the
equations of equilibrium. And discuss the problem under such contitions.
(另一張圖片就是腳尖沒有支撐 是懸空的)
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(20%)
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※ 編輯: dn89022l 來自: 61.230.74.61 (01/18 20:55)