課程名稱：普通物理學甲
課程性質︰必修
課程教師︰陳凱風
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2010/11/11
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
1.Two cars move in the same direction. The position of the first car can be
described by x=3t^2+2t+1(x,t in unit of meters,seconds);the acceleration of
the second car is given by a=-4t(in m/s^2),and at t=0 ,its velocity is 8 m/s.
When the velocities of these two cars match, and what is their velocity?
[10 points]
2.The figure shows two blocks connected by a cord(of negligible mass)that
passes over a frictionless pulley(also of negli gible mass).One block has
mass m1;the other has mass m2. Assuming m2>m1, what is the tension in the
cord?[10 points]
＿＿
╱ ╲
∣滑 輪∣
∣ ＿＿ ∣
﹀ ﹀
∣ ∣
∣ ∣
m1 █ ∣
▊m2
3.Following question 2, if the left block is actually a container, and it is
losing mass(through a leak)at a constant rate R(in the unit of mass over time)
.At what rate is the acceleration magnitude of the containers changing?
i.e. da/dt=?[10 point]
4.A boy is initially seated on the top of a hemispherical ice mound of radius
R. He begins to slide down the ice, with a negligible initial speed.
Approximate the ice as being frictionless.At what height does the boy lose
contact with the ice?[10 points]
5.The figure（一個圓心在(0,0)且半徑為R的圓，挖掉一個邊長為L的正方形，正方形
左下角座標為(0,0)shows a uniform metal plate of radius R, while a square of
length L has been stamped out(removed)in an assambly line.
(a)Using the x-y coordinate system shown,locate the center of mass of the
remaining plate.[5 points]
(b)what's the rotational inertia of the plate,if a rotational axis is assigned
along the z axis and passing through the origin, if mass of the remaining
plate is m?Some of the useful rotational inertias are given in page2.(這張
是HALLIDAY CH10裡列出很多轉動慣量的那張)[10 points]
6.Tap and the bathroom scale:aprecise scale(for measuring your body weight)
is placed 1 meter under a tap.If the water flow of the tap is 300ml per second
,and the speed of water flow is 0.5m/s when the water leaves the tap. What is
the measurement given by the scale,if the water hits the scale and stops
immediateli?Given the free-fall acceleration g is 10m/s^2.[15 points]
7.Pitcher and catcher on boats: a pitcher stands in a boat,throws a baseball of
mass m with speed v(relative to the pitcher)to the catcher on another boat;the
catcher sends the ball back with a slower speed of v/2(relative to the catcher)
to the pitcher.Assume the drag forcrs applying to the boats and the baseball
are negligibly small,and the mass of the picher together with his boat is the
same as the mass of the catcher and his boat(denoted by M).If they start this
playing from rest,what is the speed of the pitcher after he caught the ball
back?9[15points]
8.Two identicaltiny rockets of mass M at rest are binded to a steel thin rod
of length L and mass m. The direction of the two rockets are oppositely
arranged as the following figure.After firing the rockets,3/4 of the rocket
masses are burned and exhaust products leave the rockets with a relative speed
v. Find the final angular speed, treat the rockets as point-like objects.
[15 points]
M m 火
█───────█
火 L M
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