问题 问答题

所谓“水流星”表演时,就是用绳系着装有水的小桶,在竖直平面内做圆周运动,而水不洒落.如果在表演“水流星”节目时,栓杯子的绳长为L,其最大承受力是杯子和杯内水的重量的8倍,要使绳子不断裂,节目表演成功,杯子通过最高点时速度的取值范围为多少?

答案

杯子在最低点时,进行受力分析如图

设杯子在最低点时的瞬时速度为v2,杯子和杯内的水的总质量为m

T-mg=

mv2
L
 

T=mg+

mv2
L

又0≤T≤8mg     ②

∴由①②式可以解得

1
2
mv2
7
2
mgL     ③

在杯子的整个运动过程中,只有重力做功(绳子的拉力的方向始终与运动的方向垂直,所以不做功,空气阻力忽略不计),机械能守恒.

设杯子在最高点时的瞬时速度为u

1
2
mu2+2mgL=
1
2
mv2    ④

由③④式可以解得u≤

3gL

又要使杯子和杯内的水能在竖直平面内做完整的圆周运动,在最高点时,必须满足至少杯子和杯内的水的重力全部用来提供向心力.

mg≤

mu2
L

u≥

gL
综上所述
gL
≤u≤
3gL

答:杯子通过最高点时速度的取值范围为

gL
≤u≤
3gL

阅读理解

Asking for information or help is a very common and necessary activity, especially when we visit a foreign country. So knowing how to ask for information politely is important. In English, "Where are the restrooms?" and "Could you please tell me where the restrooms are?" are similar requests—both are correct English, but the first could sound rude. It’s important to use correct language, but sometimes this alone is not enough—we need to learn how to be polite when we make requests.

In English, just like in Chinese, we change the way we speak when talking with different people. The expressions you use might depend on whom you are speaking to or how well you know them. If you say to your teacher, "Where is my book?" this will sound rude. But if you say, "Excuse me, Mr West. Do you know where my book is?" your question will sound much more polite. On the other hand, it might be alright to say "Where is my book?" in some situations, perhaps with people you know well.

And you would not usually say, "Peter, lend me your pen. " A very direct order like this can sound rude in English. Usually in English polite questions are longer and include extra language, such as "Could you please...?" or "Can I ask...?" It sounds more polite to say, "Peter, could you please lend me your pen?" Sometimes we might even need to spend some time leading in to a question or request. For example, if you stop a stranger in the street, we might first say, "Excuse me. I wonder if you can help me. " or "I’m sorry to trouble you but," before asking them for help.

It might seem that speaking politely is more difficult than being direct, and in a way this may be true. However, in order not to offend people, learning about the language etiquette is just as important as learning grammar or vocabulary. And doing this will also help you become better at English, or any other language you wish to speak.

小题1: It’s important to know how to_     _in English when we visit a foreign country.

小题2: When you talk with different people, you need to__       _.

小题3: Extra words are used to help__      ___.

小题4:._      _is as important as learning language structure.

小题5: How do you say " Don’t smoke here. " politely? "_         __*

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