问题 计算题

一轻质细绳一端系一质量为m=0.05kg的小球A,另一端挂在光滑水平轴O上,O到小球的距离为L=0.1m,小球跟水平面接触,但无相互作用,在球的两侧等距离处分别固定一个光滑的斜面和一个挡板,如图所示,水平距离s=2m。现有一滑块B,质量也为m,从斜面上滑下,与小球发生碰撞,每次碰后,滑块与小球速度均交换,已知滑块与挡板碰撞时不损失机械能,水平面与滑块间的动摩擦因数为μ=0.25,若不计空气阻力,并将滑块和小球都视为质点,g取10m/s2,试问:

(1)若滑块B从斜面某一高度h处滑下与小球第一次碰撞后,使小球恰好在竖直平面内做圆周运动,求此高度h;

(2)若滑块B从h'=5m处下滑与小球碰撞后,小球在竖直平面内做圆周运动,求小球做完整圆周运动的次数。

答案

解:(1)小球刚能完成一次完整的圆周运动,它到最高点的速度为v0

在最高点,仅有重力充当向心力,则有

在小球从最低点运动到最高点的过程中,机械能守恒,

并设小球在最低点速度为v,则又有

解①②有m/s

滑块从h高处运动到将与小球碰撞时速度为v2,对滑块由能的转化及守恒定律有 因弹性碰撞后速度交换m/s,解上式有h=0.5m

(2)若滑块从h/=5m处下滑到将要与小球碰撞时速度为u,同理有

解得

滑块与小球碰后的瞬间,同理滑块静止,小球以的速度开始作圆周运动,

滑块和小球最后一次碰撞时速度为至少

滑块最后停在水平面上,它通过的路程为,同理有

小球做完整圆周运动的次数为

解⑤、⑥得,n=10次。

完形填空

阅读下面短文,并按照题目要求用英语问答问题(请注意问题后词数要求)。

〔1〕My mother always told us there is no use crying over spilled milk. That means you should not get angry when something bad happens and cannot be changed. She also told us you have to break some eggs to make an omelet(煎蛋卷). This means you have to do what is necessary to move forward.

〔2〕My mother believed you are what you eat. A good diet is important for good health. She would always give us nutritious food. She liked serving us meat and potatoes for dinner. Meat and potatoes can also mean the most important part of something. It describes someone who likes simple things.

〔3〕My father was also a good and honest person. People said he was the salt of the earth, because he would never pour salt on a wound, or make someone feel worse about something that was already a painful experience. However, sometimes he told us a story that seemed bigger than life. So we had to take it with a grain of salt. That is, we could not believe everything he told us.

〔4〕My manager at work does not always know what is going on in our office. Yet she is right about one thing: there is no such thing as a free lunch. Something may appear to be free, but there may be a hidden cost. When we fail to see problems at work, my manager tells us to wake up and smell the coffee. We need to pay more attention and fix the problem. I once made a big mistake at the office and felt foolish. I had egg on my face.

〔5〕Over the weekend, my friend invited me to watch a football game on television. But I do not like football. It is not my cup of tea.

〔6〕I hope I have given you food for thought, that is, something to think about.

小题1:What is the main idea of the whole passage? ( within 9 words)

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小题2:What would the author’s mother tell them to do when problems came up?

( within 7 words)

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小题3:If someone tells you a story that seems bigger than life , what should you do ?

( within 8 words)

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小题4:What can you say if your face turns red because of a foolish mistake according to the passage? ( within 8 words)

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小题5:Explain the underlined sentence in Paragraph 5. ( within 7 words)

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单项选择题