问题 计算题

如图所示,匀强电场方向沿x轴的正方向,场强为E。在点有一个静止的中性微粒,由于内部作用,某一时刻突然分裂成两个质量均为m的带电微粒,其中电荷量为q的微粒1沿y轴负方向运动,经过一段时间到达点。不计重力和分裂后两微粒间的作用。试求

(1)分裂时两个微粒各自的速度;

(2)当微粒1到达(点时,电场力对微粒1做功的瞬间功率;

(3)当微粒1到达(点时,两微粒间的距离。

答案

解:(1)微粒1在y方向不受力,做匀速直线运动;在x方向由于受恒定的电场力,做匀加速直线运动。所以微粒1做的是类平抛运动。设微粒1分裂时的速度为v1,微粒2的速度为v2,则有:

在y方向上有:-

在x方向上有:,-

,根号外的负号表示沿y轴的负方向

中性微粒分裂成两微粒时,遵守动量守恒定律,有

,方向沿y正方向

(2)设微粒1到达(0,-d)点时的速度为v,则电场力做功的瞬时功率为

其中由运动学公式

所以

(3)两微粒的运动具有对称性,如图所示,当微粒1到达(0,-d)点时发生的位移

则当当微粒1到达(0,-d)点时,两微粒间的距离为

单项选择题
阅读理解

Are you worried by the rising crime rate? If you are, you probably know that your house, possessions(财产) and person are increasingly in danger of suffering from great rise in the cases of burglary(夜盗;抢劫) and attack.

Figures show an ever-increasing crime rate, but it is only too easy to imagine "It will never happen to me". Unfortunately, statistics show that it really can happen to you and, if you live in a large city, you run twice the risk of being a victim.

Fortunately, there is something definite which you can do. Protect Alarms can help to protect your house with a burglar alarm system(报警系统) which is effective, simple to operate and easily affordable.

You must remember that owning a burglar alarm is no indication(暗示) that your house is packed with valuable possessions. It quite simply indicates to unwelcome visitors that yours is one house they will not break into easily, so they carry on to an unprotected house where their job is made a lot easier.

Send now for our free leaflet(宣传册) telling you how we can Protect Alarm your house quickly, easily and cheaply. Complete and tear off the slip below and post it to us. Postage is free. Also, telephone us on 327 6721 where we have a round-the-clock answering service. It costs nothing to find out about Protect Alarm.

小题1:Anyone who takes an interest in the crime rate will, according to the text, be aware that ___________.

A.more burglars are being caught than ever before

B.people have more possessions to worry about nowadays

C.burglars are more at risk than they used to be

D.homes are more likely to be broken into nowadays小题2:It seems that people who live in cities are ____________

A.more often victims than those living in other areas

B.of the opinion that statistics are wrong

C.twice as well as people living in other areas

D.of the opinion that burglars only rob unprotected homes小题3:The article suggests that possessing an alarm system will _________.

A.show burglars that you have something worth stealing

B.persuade burglars not to break into your house

C.make the burglars' job less complicated

D.persuade burglars to try again another time小题4:In order to find out more information about this alarm system one can _______.

A.buy a leaflet

B.write enclosing a stamped, addressed envelope

C.sign a contract

D.phone at any time of day or night小题5:The underlined word "Figures" in the second paragraph can be replaced by"      "

A.Pictures

B.Fingers

C.Numbers

D.Mathematics