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问题 计算题

如图所示，竖直固定的半圆弯管与上部的水平管和下部的水平地面均相切，管的半径为R，各表面均光滑。小球A、B由轻弹簧相连，质量均为2m，开始时A球靠在墙边，A、B处于静止状态。小球C的质量为m，现C以某一初速度v0由水平管进入弯管，然后与B正碰，碰后两者速度相同，但不粘连，最后C球恰能返回水平管道。求：

（1）C球的初速度v0；

（2）A球离开墙后弹簧的最大弹性势能（此时B球尚没有进入管）。

答案

解：（1）设小球C到达水平地面时的速度为v1，由机械能守恒定律得：

设C球与B球碰撞后的共同速度为v2，由动量守恒定律得：mv1=3mv2

碰撞后两球一起向左压缩弹簧，当弹簧再次恢复原长时，B、C分离，它们的速度大小仍是v2。已知C球沿弯管恰能返回水平管，则有到达水平管时的速度为零，由机械能守恒定律得：

解得：

解得：

解得：

（2）弹簧恢复原长后，A球离开墙壁，经过一段时间，A、B两球速度达到相同时，弹簧的弹性势能最大。设此时A、B的共同速度为v3，由动量守恒定律得：2mv2=4mv3

解得：

根据能量守恒，弹簧的最大弹性势能为：

单项选择题

对心脏的抑制作用最强的药物是

A．美西律
B．维拉帕米
C．利多卡因
D．卡托普利
E．强心苷
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填空题

World Water Shortage


A new study warns that about thirty percent of the world’s people may not have enough water by the year 2025.
A private American organization called (1) Action International did the new study. It says (2) than three-hundred-thirty-five-million people (3) enough water now. The people live in twenty-eight (4) . Most of the countries are in Africa or the (5) East.
P-A-I researcher Robert Engelman says (6) the year 2025, about three-thousand-million people (7) lack water. At least 18 more countries are (8) to have severe water problems. The demand (9) water keeps increasing. Yet the amount of water on Earth (10) the same.
Mr. Engelman says the population in countries that lack water is (11) faster than in other parts of the world. He says (12) growth in these countries will continue to (13) .
The report says lack of water in the future may (14) in several problems. It may increase health (15) . Lack of water often means drinking (16) not safe. Mr. Engelman says there are problems (17) over the world because of diseases, such as cholera, (18) are carried in water. Lack of water may also result (19) more international conflict. Countries may have to (20) for water in the future. Some countries now get sixty percent of their fresh water from other countries. This is true of Egypt, the Netherlands, Cambodia, Syria, Sudan, and Iraq. And the report says lack of water would affect the ability of developing to improve their economies. This is because new industries often need a large amount of water when they are beginning.
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