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问题 计算题

如图所示，竖直的xOy平面内，在x≤0、y≥0的区域内有电场强度E1=5×102N／C、方向竖直向下的匀强电场，x>0、y<0的区域内有电场强度为E2、方向竖直向上的匀强电场，E2=5El。不带电的小球B在xOy面内绕x轴上的O1点沿顺时针做圆周运动，运动到O点时速度大小vo=20m／s，带正电的小球A在y轴上纵坐标y1=0.4m的P点静止释放，恰好和B在O点发生正碰，并瞬间合成一个整体C，C能够经过最高点02和最低点03做圆周运动。A，B的质量都是m=0.1kg，拴小球B的轻质绝缘细绳长L=0.8m，A的电荷量q=2×10-3C，A、B、C都可以看作质点，g取10m／s2。求：

（1）小球A下落到O点的速度v1是多大？

（2）C运动到03时，绳对C的拉力T是多大？

（3）小球A从y轴上y>0的某些位置开始下落，恰好在O点与B合成为C后，不能够做经过02和03的圆周运动。求这些位置的范围？

答案

解：（1）由动能定理有(qE1＋mg)y1＝

解得v1＝4m/s

（2）设A与B碰后共同速度为v2，以竖直向上为正方向

由动量守恒得mv0－mv1＝2mv2

解得v2＝8m/s

设C运动到O3时速度v3，则

解得T＝7N

（3）C不能做能够经过O2和O3的圆周运动，即C不能达到能够经过O2和O3所需的最小速度。设C能够做经过O2的圆周运动，在O2所需的最小速度为v4，设C能够做经过O3的圆周运动，在O3所需的最小速度为v5，则

 

v4＝m/s，v5＝m/s

C经过O3时速度为v5＝m/s，设经过O2时速度为v6，则

由于＞0

所以v6＞v5＝m/s＞v4＝m/s

即C能够做经过O3就一定能够做经过O2

当C能够做经过O3的速度小于v5＝m/s时，不能做能够经过O2和O3的圆周运动

设C经过O3的速度为v5时，A与B碰后在O点的共同速度为v7，则

v7＝6m/s

C在O点的速度只要大小为v7，不管是向上还是向下，C都能够经过O3

设C的速度向上时，碰前A的速度为v8，在y轴上开始位置的坐标为y2，则

mv0－mv8＝2mv7

(qE1＋mg)y2＝

解得v8＝8m/s，y2＝1.6m

设C的速度向下时，碰前A的速度为v9，在y轴上开始位置的坐标为y3，则

mv0－mv9＝－2mv7

(qE1＋mg)y3＝

解得v9＝32m/s，y3＝25.6m

即1.6m＜y＜25.6m时，C不能做能够经过O2和O3的圆周运动

选择题

在天平两盘上的烧杯中，各放入质量相同的稀硫酸，调节天平至平衡．分别向两边烧杯各加入5g镁和5g铁，镁和铁全部反应而消失后，天平的指针（　　）

A．偏向加铁的一边

B．偏向加镁的一边

C．仍停留在原来的位置

D．无法确定
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阅读理解

A student is learning to speak British English. He wonders(想知道): Can I communicate(交际) with Americans? Can they understand me? Learners of English often ask: What are the differences between British and American English? How important are these differences?

Certainly, there are some differences between British and American English. There are a few differences in grammar. For example, speakers of British English say “in hospital” and “Have you a pen?” Americans say “in the hospital” and “Do you have a pen?”.Pronunciation is sometimes different. Americans usually sound theirs in words like “bird” and “hurt”. Speakers of British English do not sound theirs in these words. There are differences between British and American English in spelling and vocabulary. For example, “colour” and “honour” are British, “color” and “honor” are American.

These differences in grammar, pronunciation, spelling and vocabulary are not important, however. For the most part, British and American English are the same language.

小题1:According to this passage, a student who is learning to speak American English might be afraid that __________.

A．British people cannot understand him

B．American people cannot understand him

C．the grammar is too hard for him

D．the spelling is too hard for him小题2:American English and British English are different in __________.

A．spelling

B．pronunciation

C．grammar

D．all of the above小题3:What is NOT mentioned(提及) in the passage?

A．Whether there are differences between British English and American English.

B．Whether British English and American English are one language or two.

C．How the differences between British English and American English came about.

D．How important the differences are.小题4:Most ______say “Do you have a watch?”

A．British people

B．Americans

C．children

D．teachers小题5:According to this passage, British people and Americans have ______ difficulty in understanding each other.

A．little

B．much

C．some

D．great
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