问题 问答题

已知真空中电量为Q的点电荷电场中,若取无穷远为零电势点,则离电荷距离为r的某点的电势表达式为φ=

kQ
r
(k为静电力常数).如图所示,带正电的甲球固定在足够大的光滑绝缘水平面上的A点,其带电量为Q;质量为m、带正电的乙球在水平面上的B点由静止释放,其带电量为q;A、B两点间的距离为l0.释放后的乙球除受到甲球的静电力作用外,还受到一个大小为F=
kQq
4l02
、方向指向甲球的恒力作用,两球均可视为点电荷.求:

(1)乙球在释放瞬间的加速度大小;

(2)乙球的速度最大时两个电荷间的距离;

(3)乙球运动的最大速度vm为多少?

(4)乙球运动过程中,离开甲球的最大距离和最小距离是多少?

答案

(1)乙球受到电场力和F的作用,根据牛顿第二定律得

   K

qQ
l20
=ma

解得,a=

3kqQ
4m
l20

(2)乙球的合外力先向左,所以乙球向左做加速度减小的加速运动,当合力为零时,速度最大,则有

  K

qQ
r2
-K
qQ
4
l20
=0

解得 r=2l0   

(3)乙球的电势能:ε=qϕ=

kqQ
r
,电场力做正功,等于电势能的减少:

  WE=-△ε=-(K

qQ
2l0
-K
qQ
l 0
)=k
qQ
2l0

外力做负功:WF=-K

qQ
4
l20
l0=-K
Qq
4l0

由动能定理:WE+WF=

1
2
m
V2m
-0

得:

V m
=
kqQ
2ml0

(4)乙球达到速度最大后,再向左做加速度增大的减速运动,当速度等于零时,离甲球最远.V=0此时离开甲球距离为rm,然后又向右运动,根据对称性可知,当r=l0时速度又等于零.所以离开A球最近的距离为l0

 根据动能定理得  WE+WF=0

kqQ
rm
-
KqQ
l0
=-k
qQ
4
l20
(rm-l0)

解得,rm=4l0      

答:

(1)乙球在释放瞬间的加速度大小是

3kqQ
4m
l20

(2)乙球的速度最大时两个电荷间的距离是2l0

(3)乙球运动的最大速度vm

kqQ
2ml0

(4)乙球运动过程中,离开甲球的最大距离4l0,最小距离是l0

阅读理解

William Shakespeare is the greatest English writer 0f all time. Also Shakespeare was an actor and famous poet. The Sonnesls(十四行诗)and Romeo and Juliet are almost known in every comer of the world.

Shakespeare was born in Stratford-upon-Avon, a small town in England, in 1564. In his youth, he moved to London and began a career as a playwright(~ij作家). By 1594, he had become a key playwright of popular acting company in the city.

Shakespeare's work also has a big influence on the English language. Shakespeare was said to have had a huge vocabulary. His works included more than 30,000 different words. And he is master of words. He created about l,700 English, including everyday ones like "lonely", "hurry" and "critical".

There are over 400 films and TV dramas adapted(改编) from Shakespeare's work. He wrote 400 years ago and his English was very different from that of today, but it doesn't affect his popularity. His plays have been translated into every major language and are performed more often than any other playwright.  Shakespeare is not of an age, but for all time.

Enjoy some of Shakespeare's works.

Romeo and Juliet

Romeo and Juliet fall in love with each other when they meet at a ball. But unfortunately, their families are long-standing enemies and try to prevent the young lovers form being together. In order to stay with Romeo, Juliet takes medicine and pretends to be dead. But Romeo doesn't know and thinks Juliet has truly died. He kills himself. When Juliet wakes up, it is too late.

Hamlet

Hamlet, the Prince of Denmark, is so sad when his father died. A month later, his mothermarries his uncle.

At this moment ,Hamlet knows that this uncle killed his father .All of this makes  Hamlet angry and hopeless .The only thing he wants is revenge(复仇) .Although he finally kills his uncle ,he is trapped(陷害) by bad guys and loses his life .

The Merchant of Venice

Antonio,aVenetian merchant, borrows money from the moneylender Shylock. Shylock said that ifAntonio cannot pay back the money, he will get a pound of flesh(肉)from Antonio. Antonio loses all his business and must pay this terrible price. In order to help Antonio, his girlfriend Portia dresses up as a lawyer. Her wisdom not only saves Antonio but also punishes Shylock.

小题1:根据短文内容完成句子填空(每空限填一个单词)。

According to the passage, we know that Shakespeare wrote many________called The Sonnets as afamous poet and wrote lots of____   as the greatest writer.

小题2:根据短文内容完成句子填空(每空限填一个单词)。

At the age of_______,Shakespeare became a key playwright. All his works effected English language greatly and some new words have been _______by Shakespeare.

小题3:根据短文内容回答问题。

According to the passage, why did the author say Shakespeare is not of an age, but for all time?

_______________________________________________________________________________

小题4:把短文中画底线的句子译成汉语。

_____________________________________________________________________________

小题5:根据短文内容用一个完整的英文句子(限10个词以内)回答问题。

What's the main idea of the passage?

_____________________________________________________________________________

单项选择题