问题 问答题

两平行金属板间所加电压随时间变化的规律如图所示,大量质量为m、带电量为e的电子由静止开始经电压为U0的电场加速后连续不断地沿两平行金属板间的中线射入,若两板间距恰能使所有子都能通过.且两极长度使每个电子通过两板均历时3t0,电子所受重力不计,试求:

(1)电子通过两板时侧向位移的最大值和最小值;

(2)侧向位移最大和最小的电子通过两板后的动能之比.

答案

(1)电子在t=2 nt0(其中:n=0、1、2、…)时刻进入电场,电子通过两极的侧向位移最大,

在t=(2n+l)t0(其中n=0、l、2、…)时刻进入电场电子通过两板侧向位移最小.

电子侧向位移最大时,进入电场在沿电场线方向上作初速度为零的匀加速运动,

再作匀速运动,后作初速度不为零的匀加速运动,各段运动的时间均为t0

当电子侧向位移最小时,在电场线上只有在第二个t0的时间开始作初速度为零的匀加速运动,

在第三个t0的时间作匀速运动.电子进入偏转电场后,在电场中的加速度均为a=

eU0
md
,电子侧向最大位移为

ymax=

1
2
at02+at02+at02+
1
2
at02=3at02=
3eU0
t20
md
.  

解得:ymax=

d
2

由以上两式解得ymax=t0

6emU0
m

 d=2ymax=2t0

6emU0
m

电子侧向最小位移为ymin=at02/2+at02=

1
2
ymax=
1
2
t0
6emU0
m

解得:ymin=

d
4

(2)电子离开偏转电场时的动能等于加速电场和偏转电场电场力做功之和.

当电子的侧向位移为最大时,电子在电场中加速(只有加速,电场力才做功).

运动的距离为y1=

2
3
 ymax=
d
3
,电子的侧向位移最小时,

电子在电场中加速运动的距离为y2=

1
3
ymin=
d
12

侧向位移最大的电子动能为 Ekmax=eUO+eUO?

y1
d
=
4
3
eUO

侧向位移最小的电子动能为Ekmin=eUO+eUO?

y2
d
=
13
12
eUO

故Ekmax:Ekmin=16:13

答:(1)电子通过两板时侧向位移的最大值

d
2
和最小值
d
4

(2)侧向位移最大和最小的电子通过两板后的动能之比16:13.

阅读理解

There are a number of special days of the year that are celebrated in different countries. The origins of most of the days are unknown. They were certainly not created by individual people. Other days, however, especially those celebrated in western countries, often owe their origins to a particular person. One of the most popular of these, even though it is fairly recent, is Mother’s Day. Mothers have always been highly regarded in all cultures. The ancient Romans had a festival known as Hilaria, during which children took presents to the temple of the “Mother of the Gods”. The Christian Church adopted this idea and called it Mothering Sunday. However, over the years this custom was gradually forgotten and almost disappeared by the end of the 19th century.

Born in 1864 in Virginia, USA, Anna Jarvis was a school teacher and believed children should show gratitude to their mothers for all their love and care. Encouraged by a friend, she wrote to thousands of important people—politicians, churchmen, doctors, city officials—and asked them to support her idea: a special day of the year for thanking mothers.

In 1910 the Governor of West Virginia introduced Mother’s Day into the state. The date chosen was May 10—the second Sunday in May, which is still observed in America today. This date was chosen because May 10 was the date on which in 1908 Anna Jarvis’s mother had died. In 1914 President Woodrow Wilson made May 10 the official date for Mother’s Day throughout the United States.

Soon there was a Mother’s Day International Association and the custom began to be adopted in many countries of the world.

Anna Jarvis, a sad and disillusioned(失望的) woman, died in 1948. The custom she had worked so hard to establish and which had become almost universal had lost its original purpose. It had been taken over by business. Like Christmas, the giving of presents and the sending of cards had become a multi-million-dollar industry.

小题1:The story is about     .

A.Mothering Sunday for Christmas

B.the origin of a special day for mothers

C.President Wilson and Anna Jarvis

D.how people celebrate Mothers Day小题2:Anna Jarvis wanted to       .

A.thank her mother for her care

B.introduce a celebration for mothers

C.meet thousands of important people

D.make her pupils celebrate her on Mother’s Day小题3:May 10 became the date for Mother’s Day because       .

A.May is in the American spring

B.it was the second Sunday in May in 1910

C.President Wilson liked the date

D.this was the date on which Anna Jarvis’s mother died小题4:Unfortunately, Anna Jarvis was not happy with Mother’s Day when she died because     .

A.her mother was not there to see it

B.she had never been a mother herself

C.people were too interested in making it a business

D.no one gave any presents or cards to their mothers

单项选择题