问题 问答题

图所示,质量为m,电荷量为-q,重力不能忽略的带电微粒,以初速度v0从金属板中央平行于金属板方向射入,金属板长为L,间距为d.求:

(1)微粒沿直线运动时的板间电压;

(2)微粒可以在两板间穿过时,两板间电压的范围;

(3)若不计微粒的重力,微粒穿过电场时速度的最大值.

答案

(1)微粒沿直线运动,则受力平衡,即mg=q

U
d

故板间电压U=

mgd
q

(2)微粒可以在两板间穿过,两临界点分别是恰沿上、下极板穿出:水平位移最小为L:

当电场力大于重力时,此时板间电压设为U1,加速度a=

q
U1
d
-mg
m
=
qU1-mgd
md
,微粒恰能沿着上极板穿出,

竖直方向:

d
2
=
1
2
at2
=
1
2
qU1-mgd
md
t2

水平方向:s=v0t=L ②

联立①②得:U1=

m
v20
d2
qL2
+
mgd
q

当重力大于电场力时,此时板间电压设为U2,加速度a=

mgd-qU2
md
,此时微粒恰能沿着下极板穿出

竖直方向:

d
2
=
1
2
at2
=
1
2
mgd-qU2
md
t2

水平方向:s=v0t=L ④

联立③④得:U2=

mgd
q
-
m
v20
d2
qL2

微粒可以在两板间穿过时,两板间电压的范围U2≤U≤U1

即:

mgd
q
-
m
v20
d2
qL2
≤U≤
m
v20
d2
qL2
+
mgd
q

(3)若不计微粒的重力,即微粒只受电场力作用,要求最大速度即微粒刚好穿过两板时的速度

微粒刚好穿过电场时,水平位移s=v0t=L ⑤

竖直位移:y=

d
2
=
1
2
at2

则:a=

v20
d
L2

根据F=ma,可得:F=

m
v20
d
L2

根据动能定理可得:F•

d
2
=
1
2
mv2-
1
2
m
v20

解得:v=v0

1+
d2
L2

答:(1)微粒沿直线运动时的板间电压为

mgd
q

(2)微粒可以在两板间穿过时,两板间电压的范围为

mgd
q
-
m
v20
d2
qL2
≤U≤
m
v20
d2
qL2
+
mgd
q

(3)若不计微粒的重力,微粒穿过电场时速度的最大值为v0

1+
d2
L2

阅读理解

阅读理解。

     A blind boy sat on the steps of a building with a hat by his feet. He held up a sign which said, "I am

blind, please help."

     There were only a few coins in the hat. A man was walking by. He took a few coins from his pocket

and dropped them into the hat. He then took the sign, turned it around, and wrote some words. He put

the sign back so that everyone who walked by would see the new words.

Soon the hat began to fill up. A lot more people were giving money to the blind boy. That afternoon the

man who had changed the sign came to see how things were. The boy heard his footsteps and asked,

"Were you the one who changed my sign this morning? What did you write?"

     The man said, "I only wrote the truth. I said what you said but in a different way."

     What he had written was, " Today is a beautiful day but I cannot see it." Do you think the first sign

and the second sign were saying the same thing?

     Of course, both signs told people the boy was blind. But the first sign simply told people to help by

putting some money in the hat. The second sign told people that they were able to enjoy the beauty of

the day, but the boy could not enjoy it because he was blind.

     The first sign simply said the boy was blind. The second sign told people they were so lucky that they

were not blind.

1. A blind boy sat on the steps of a building in order to______.    

A. wait for some people                    

B. get money from others

C. make the writer help him              

D. hold up a sign

2.The man ______when he saw the blind boy.    

A. took away the blind boy's money              

B. gave the boy a new hat

C. brought the boy a sign                      

D. gave the boy some money and wrote some words on the sign

3. What happened to the blind boy after the man wrote the words on the sign?    

A. The boy was taken away by the police

B. Nobody gave the blind boy money any more

C. More people dropped money into the boy's hat

D. The blind boy could see the beautiful day

4. What do you think of the sign written by the man?

A. It has the different meaning to the first sign

B. It has the same meaning to the first sign and is expressed in another better way.

C. The man's sign tells people it is a beautiful day

D. People know the boy is blind after reading the man's sign

5. What can we learn from this passage?

A. It's helpful of us to help people in need

B. There are many poor people in the world like the blind boy

C. It's a good way to make money by holding a sign

D. We should learn to speak to others in a suitable way

选择题