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如图所示，一条长为L的细线上端固定在O点，下端系一个质量为m的小球，将它置于一个很大的方向水平向右的匀强电场中，已知小球在B点时平衡，细线与竖直线的夹角为45°，求：

（1）现将小球提至某一位置悬线伸直，试通过计算说明此时悬线与竖直方向夹角应为多大，才能使小球由静止释放后运动至最低点时，小球速度恰好为零？

（2）当细线与竖直方向成45°角时，至少要给小球一个多大的速度，才能使小球做完整的圆周运动？（结果可保留根号）

答案

（1）小球静止在B点时，根据平衡条件得

    mgsin45°=Fcos45°

得到，电场力F=mg

从释放点到最低点过程，根据动能定理得

   mgL（1-cosα）-FLsinα=0

 得到，sinα+cosα=1

解得，α=90°

（2）设当小球运动到关于B对称的A点时，临界速度为vA．根据牛顿第二定律得

 Fsin45°+mgsin45°=m

v2A
L

解得，vA=

2gL

由A到B过程，根据动能定理得

mg2Lcos45°+F2Lsin45°=

1
2
m
v2B
-
1
2
m
v2A

解得，vB=

5
2gL

答：

（1）悬线与竖直方向夹角应为90°，才能使小球由静止释放后运动至最低点时，小球速度恰好为零．

（2）当细线与竖直方向成45°角时，至少要给小球一个

5
2gL
的速度，才能使小球做完整的圆周运动．

单项选择题

500kV变压器、电抗器施加电压前变压器油电气强度不小于（）。

A.40kV/2.5mm

B.50kV/2.5mm

C.60kV/2.5mm

D.70kV/2.5mm
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·Read the following passage and choose the best word for each space.
Do you want to send an e-mail message to the White House
Good luck.
In the past, (26) President Bush — or at least those assigned to read his mail — what was (27) your mind it was necessary only to sit down at a personal computer connected to the lnternet and (28) a note to president@ whitehouse.gov.
But this week, Tom Matzzie, an online organizer with the A.F.L.-C.I.O., discovered that (29) with the White House had become a bit more (30) . When Mr. Matzzie sent an e-mail protesting (31) a Bush administration policy, the message was bounced back With an automated reply, saying he had to send it again in a new way.
Under a system (32) on the White House Website (33) the first time last week, those who want to send a message to President Bush must now (34) as many as nine Web pages and (35) a detailed form that starts by asking whether the message sender supports White House policy (36) differs with it.
The white House says the new e-mail system is an effort to be more responsive (37) the public and offer the administration "real time" access (38) citizen comments.
Completing a message to the president also requires (39) a subject from the provided list, then entering a full name, organization, address and e-mail address. (40) the message is sent, the writer must wait for an automated response (41) his message, (42) whether the addressee intended to send the message. The message is delivered to the White House only after the person using that e-mail address (43) it.
"Over (44) , it’s a very cumbersome process," said Jakob Nielsen, an authority on Web design. "It’s probably designed deliberately to (45) on their e-mail.\

A. cut off B. see off C. dash off D. give off
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