问题 计算题

将一测力传感器连接到计算机上就可以测量快速变化的力,图甲表示小滑块(可视为质点)沿固定的光滑半球形容器内壁在竖直平面的A、之间来回滑动,点与O点连线与竖直方向之间夹角相等且都为很小。图乙表示滑块对器壁的压力F随时间t变化的曲线,且图中t=0为滑块从A点开始运动的时刻,试根据力学规律和题中(包括图中)所给的信息。求:

(1)容器的半径;

(2)小滑块的质量;

(3)滑块运动过程中的守恒量。

答案

解:(1)由图乙得小滑块做简谐振动的周期:

,得 

(2)在最高点A,有

在最低点B,有

从A到B,滑块机械能守恒,有

解得: 

(3)滑块机械能守恒:

单项选择题
单项选择题

"We want Singapore to have the X-factor, that buzz that you get in London, Paris, or New York." That is how Lee Hsien Loong, Singapore’s prime minister, (1) his government’s decision to (2) gambling in the country, (3) two large, Vegas-style casinos. Whether the casinos will indeed help to transform Singapore’s staid image remains to be seen. But the decision bas already (4) an uncharacteristic buzz among the country’s normally (5) citizens.

The government has contemplated, and rejected (6) casinos several times in the past. One reason was (7) Singapore’s economic growth was so rapid that casinos seemed like an unnecessary evil. Buddhism and Islam, two of the country’s main religions, (8) on gambling. The government itself has traditionally had p, and often (9) , ideas about how its citizens should behave. Until recently, for example, it refused to (10) homosexuals to the civil service. It also used to (11) chewing gum, which it considers a public nuisance.

Nowadays, (12) , Singapore’s electronics industry, the mainstay of the economy, is struggling to cope with cheap competition from places like China. In the first quarter of this year, output (13) by 5.8% at an annual rate. So the government wants lo promote tourism and other services to (14) for vanishing jobs in manufacturing.

Merrill Lynch, an investment bank, (15) the two proposed casinos could (16) in as much as $4 billion in the initial investment alone. (17) its estimates, they would have annual revenues of (18) $3.6 billion, and pay at least $600 million in taxes and fees. The government, for its part, thinks the integrated (19) , as it coyly calls the casinos, would (20) as many as 35,000 jobs.

11()

A.ban

B.prevent

C.limit

D.authorize