问题 问答题

(17分)

如图所示,在x轴上方有水平向左的匀强电场,电场强度为E1;下方有竖直向上的匀强电场,电场强度为E2,且。在x轴下方的虚线(虚线与茗轴成45°角)右侧有垂直纸面向外的匀强磁场,磁感应强度为B。有一长为L的轻绳一端固定在第一象限内的O′点,且可绕O′点在竖直平面内转动;另一端拴有一质量为m的小球,小球带电量为+qOO′与x轴成45°角,其长度也为L。先将小球放在O′点正上方,从绳恰好绷直处由静止释放,小球刚进人有磁场的区域时将绳子断开。

试求:

(1)绳子第一次刚拉直还没有开始绷紧时小球的速度大小;

(2)小球刚进入有磁场的区域时的速度大小;

(3)小球从进入有磁场的区域到第一次打在x轴上经过的时间。

答案

(1)

(2)

(3)

(1)小球一开始受到的合力为,做匀加速直线运动。设绳子第一次刚拉直还没有开始绷紧时小球的速度大小为v。根据动能定理可得:

…………………………………………①(2分)

解得:………………………②(1分)

(2)设绳子刚绷紧后小球速度大小为v2,则进入有磁场的区域时速度的大小为v3则:

………………………③(2分)

根据动能定理可得:

……………………………………④(2分)

联立②③④式解得:

……………⑤(2分)

(3)带电小球垂直于磁场边界进入有磁场的区域,做匀速圆周运动,设轨道半径为r。由牛顿第二定律可得:

……………………………………………………………………⑥(3分)

带电小球运动半个圆周后,从磁场边界射出有磁场的区域,然后做匀速直线运动,设匀速直线运动的距离为d。则: 

由几何关系得:………………………………………………………⑦(2分)

设小球从进入有磁场的区域到第一次打在戈轴上经过的时间为t。则:

………………………………………………………………⑧(2分)

联立⑥⑦⑧式解得:

……………………………………(1分)

单项选择题 A1/A2型题
阅读理解

阅读理解

     When you are little,  the whole world feels like a big playground.I was living in Conyers,  Georgia the

summer it all happened.I was a second grader,  but my best friend Stephanie was only in the first grade.

Both of our parents were at work and most of the time they let us go our own way.

     It was a hot afternoon and we decided to have an adventure in Stephanie's basement.As I opened the

basement door,  before us lay the biggest room,  full of amazing things like guns,  dolls,  and old clothes.I

ran downstairs,  and spotted a red steel can.It was paint.I looked beyond it and there lay even more paint

in bright colors like purple,  orange,  blue and green.

     "Stephanie,  I just found us a project for the day.Get some paintbrushes.We are fixing to paint."She

screamed with excitement as I told her of my secret plans and immediately we got to work.We gathered

all the brushes we could find and moved all of our materials to my yard.There on the road in front of my

house,  we painted big stripes(条纹)of colors across the pavement(人行道). Stripe by stripe,  our colors

turned into a beautiful rainbow.It was fantastic!

     The sun was starting to sink.I saw a car in the distance and jumped up as I recognized the car.It was

my mother.I couldn't wait to show her my masterpiece.The car pulled slowly into the driveway and from

the look on my mother's face,  I could tell that I was in deep trouble.

     My mother shut the car door and walked towards me.Her eyes glaring,  she shouted,  "What in the

world were you thinking?I understood when you made castles out of leaves,  and climbed the neighbors'

trees,  but this!Come inside right now!"I stood there glaring back at her for a minute,  angry because she

had insulted(侮辱)my art.

     "Now go clean it up!"Mother and I began cleaning the road.Tears ran down my cheeks as I saw my

beautiful rainbow turn into black cement.

     Though years have now passed,  I still wonder where my rainbow has gone.I wonder if,  maybe when

I get older,  I can find my rainbow and never have to brush it away.I guess we all need some sort of

rainbow to brighten our lives from time to time and to keep our hopes and dreams colorful.

1. What did the writer want to do when his mother came home?

A. To introduce Stephanie to her.

B. To prevent her from seeing his painting.

C. To put the materials back in the yard.

D. To show his artwork to her.

2. In his mother's eyes,  the writer________.

A. was a born artist      

B. always caused trouble

C. was a problem solver  

D. worked very hard

3. The underlined word"rainbow"in the last paragraph refers to______.

A. the rainbow in the sky

B. the stripes on the pavement

C. something imaginative and fun

D. important lessons learned in childhood

4. It can be learned from the passage that parents should______.

A. encourage children to paint

B. value friendship among children

C. discover the hidden talent in children

D. protect rather than destroy children's dreams

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