问题 计算题

(15分)如图所示,质量为m的砝码A放置在质量为M的滑块B上,B与弹簧相连,它们一起在光滑的水平面上作简谐运动,弹簧的劲度系数为k,砝码与滑块之间的动摩擦因数为,要使砝码与滑块在振动过程中不发生相对运动,问最大振幅等于多少?(设最大静摩擦力等于滑动摩擦力)

答案

μ(m + M)g / k

题目分析:振幅是偏离平衡位置的最大距离,在最右端,两物体间的作用力为最大静摩擦力,A的加速度为μg,再以整体为研究对象,加速度与A的加速度相同,由弹簧弹力提供,则弹簧弹力为μ(m + M)g,则弹簧伸长量为μ(m + M)g / k,即为振幅

点评:难度较小,注意本题中两物体不发生相对运动的前提条件,在最大位移处整体加速度最大,由牛顿定律求解

阅读理解

When I lived in Spain, some Spanish friends of mine decided to visit England by car. Before they left, they asked me for advice about how to find accommodation (住所). I suggested that they should stay at “bed and breakfast” houses, because this kind of accommodation gives a foreign visitor a good chance to speak English with the family. My friends listened to my advice, but they came back with some funny stories.

“We didn’t stay at bed and breakfast houses,” they said, “because we found that most families were away on holiday.”

I thought this was strange. Finally I understood what had happened. My friends spoke little English, and they thought “VACANCIES” meant “holidays”, because the Spanish word for “holidays” is “vacaciones”. So they did not go to house where the sign outside said ‘VACANCLES’, which in English means there are free rooms. Then my friends went to house where the sign said ‘NO VACANCLES’, because they thought this meant the people who owned the house were not away on holiday. But they found that these houses were all full. As a result, they stayed at hotels!

We laughed about this and about mistakes my friends made in reading other signs. In Spanish, the word “DIVERSION” means fun. In English, it means that workmen are repairing the road, and that you must take a different road. When my friends saw the word “DIVERSION” on a road sign, they thought they were going to have fun. Instead, the road ended in a large hold.

English people have problems too when they learn foreign languages. Once in Paris. when someone offered me some more coffee, I said ‘Thank you’ in French. I meant that I would like some more, However , to my surprise the coffee pot was taken away! Later I found out that ‘Thank you’ in French means ‘No, thank you.’

1. My Spanish friends wanted advice about ______.

A. learning English                     B. finding places to stay in England

C. driving their car on English roads        D. going to England by car

2. I suggested that they stay at bed and breakfast houses because ______.

A. they would be able to practise their English

B. it would be much cheaper than staying in hotels

C. it would be convenient for them to have dinner

D. there would be no problem about finding accommodation there

3. “NO VACANCIES” in English means ______.

A. no free rooms        B. free rooms      C. not away on holiday    D. holidays

4. If you see a road sign that says ‘Diversion’, you will ______.

A. fall into a hole

B. have a lot of fun and enjoy yourself

C. find that the road is blocked by crowds of people

D. have to take a different road

5. When someone offered me more coffee and I said “Thank you” in French, I ______.

A didn’t really want any more coffee      B. wanted them to take the coffee pot away

C. really wanted some more coffee        D. wanted to express my politeness

单项选择题