问题 计算题

如图所示,水平桌面上有一轻弹簧,左端固定在A点,自然状态时其右端位于B点。D点位于水桌面最右端,水平桌面右侧有一竖直放置的光滑轨道MNP,其形状为半径R=0.8m的圆环剪去左上角135°的圆弧,MN为其竖直直径,P点到桌面的竖直距离为R,P点到桌面右侧边缘的水平距离为2R。用质量m1=0.4kg的物块将弹簧缓慢压缩到C点,释放后弹簧恢复原长时物块恰停止在B点。用同种材料、质量为m2=0.2kg的物块将弹簧缓慢压缩到C点释放,物块过B点后其位移与时间的关系为,物块从D点飞离桌面后恰好由P点沿切线落入圆轨道。g=10m/s2,求:

(1)BD间的水平距离;

(2)判断m2能否沿圆轨道到达M点;

(3)m2释放后在桌面上运动的过程中克服摩擦力做的功。

答案

解:(1)设物块由D点以初速度做平抛,落到P点时其竖直速度为 

     

      得m/s

      或设平抛用时为t,则

      在竖直方向上:

      在水平方向上:

      可得

      在桌面上过B点后初速m/s,加速度a=-4m/s2

      BD间位移为m

(2)若物块能沿轨道到达M点,其速度为,由机械能守恒定律得: 

     

      轨道对物块的压力为FN,则

      解得

      即物块不能到达M点

(3)设弹簧长为AC时的弹性势能为Ep,物块与桌面间的动摩擦因数为μ

      释放m1时:

      释放m2时:

      且m1=2m2

      解得J

      m2释放后在桌面上运动过程中克服摩擦力做功为Wf,则由能量转化及守恒定律得:

     

      解得Wf=5.6J

阅读理解

Jay, an American, wanted to write a book about famous churches (教堂)around the world. Firstly, Jay bought a plane ticket and took a trip to Columbus, Ohio, USA, thinking that he would start by working his way across the USA from East to West. 

On his first day he was inside a church taking photos when he noticed a golden telephone on the wall with a sign that read "$10,000 per call".

Jay was intrigued so he asked a priest (牧师) what the telephone was used for.

The priest told him that it was a direct (直接的) line to heaven(天堂) and that for $10,000 you could talk to God. Jay thanked the priest and went along his way.

Next stop was in Des Moines, and there at a very large church, he saw the same looking golden telephone with the same sign under it. A nearby nun(修女)told him that it was a direct line to heaven and that for $10,000 he could talk to God.

Jay decided to travel to Australia to see if they had a similar phone. He arrived at Western Australia, and again, in the church he entered, there was the same looking golden telephone, but this time the sign under it read "40 cents per call."

Somewhat surprised, Jay asked the priest about the sign. 'Father Brian, I travelled all over the world and I saw this same golden telephone in many churches. I know it is a direct line to Heaven, but in all of them price was $10,000 per call. Why is it so cheap here?'

Father(神父)Brian smiled and answered, 'My son, you're in Australia now - this is Heaven, so it's only a local call.'

小题1:How many churches did Jay go to in the passage?

A.Three

B.Four

C.Five

D.Six小题2:The underlined word ‘intrigued’ in Paragraph 3 may mean ‘       ’.

A.恐惧的

B.欣喜的

C.犹豫的

D.好奇的小题3:Which is TURE according to the passage?

A.Jay was a singer.

B.In all of churches, the price was $10,000 per call

C.All the telephones look the same.

D.Jay travelled in America by car.小题4:We can infer (推断) from the Father Brian’s words in the last Paragraph?

A.Jay was from Australia.

B.Jay would spend less money in Australia because everything was cheaper there.

C.Australia is as beautiful as Heaven.

D.Father Brian found his real son at last.

选择题