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两平行板间有水平匀强电场，一根长为L，不可伸长的不导电细绳的一端连着一个质量为 m、带电量为q的小球，另一端固定于O点．把小球拉起直至细线与电场线平行，然后无初速度释放．已知小球摆到最低点的另一侧，线与竖直方向的最大夹角为θ=30°求：

（1）匀强电场的场强

（2）小球到最低点的速度

（3）经过最低点时，细线对小球的拉力

（4）小球运动过程中线的最大张力．

答案

（1）根据动能定理研究小球从释放到最低点到最低点的另一侧的过程列出等式

小球无初速度释放摆到最低点的另一侧的过程：

mgLcosθ-qEL（1+sinθ）=0-0=0     θ=30°

解得：E=

mgcosθ
q(1+sinθ)
=
3
mg
3q
  ①

（2）根据动能定理研究小球从释放到最低点的过程得：

mgL-qEL=

1
2
mv2   ②

由①②得：v=

2gL(3-
3
)
3
③

（3）小球最低点时由重力和细线的拉力的合力提供小球的向心力，

根据牛顿第二定律得

     F-mg=m

v2
L
  ④

由③④得：F=

mg(3+3sinθ-2cosθ)
1+sinθ
=3mg-
2
3
mg
3

（4）将电场力与重力合成F合=

2
3
mg
3
，由图可知，合力方向与竖直方向成30度角斜向右下，O′为对应的“等效最低点”．

在O'点产生最大加速度，对应最大拉力．  由几何关系得 α=60°．

根据动能定理研究O点到O'点，得：

mg•

3
2
L-Eq•
L
2
=
1
2
m
v2O′
-0  ④

由①④得：

v2O′
=
2
3
gL
3

小球在O'点时由重力、电场力和细线的拉力的合力提供小球的向心力，

根据牛顿第二定律得

     Fmax-F合=m

v2O′
L

Fmax=

4
3
mg
3

答：（1）匀强电场的场强是

3
mg
3q

（2）小球到最低点的速度是

2gL(3-
3
)
3

（3）经过最低点时，细线对小球的拉力是3mg-

2
3
mg
3

（4）小球运动过程中线的最大张力是

4
3
mg
3
．

单项选择题

线性电阻的大小与（）无关。

A、电流

B、材料

C、长度

D、横截面
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阅读理解

阅读理解。

     In many parts of the world, people live to healthy old ages. What is the secret of their long lives?

     Three  things  are  very  important: fresh air, fresh  food  and a  simple  way of life. People  living in

Himalayas (喜马拉雅山) are famous for their long and healthy lives. They work near their homes in the

clean mountains. They do not have buses, cars or trains. They do not sit all day in busy offices. They take

more exercise and eat less food than people in the cities. They eat vegetables grown by themselves. They

drink milk taken from their own cows. For years, the Hunzas of the Himalayas do not need doctors, for

there is not much illness. They are happy and healthy people.

1. Which is NOT the life of the people living in Himalayas?

A. They work near their homes in the clean mountains.

B. They take more exercise and eat more food than people in the cities.

C. They eat vegetables grown by themselves.

D. They drink milk taken from their own cows.

2. Which one is NOT true about the people living in  Himalayas?

A. They live in a simple life in the mountains.

B. They grow vegetables and milk cows themselves.

C. When they're ill, they do not go to see the doctors.

D. They do not sit all day in busy offices.

3. Which is NOT the secret of long life?

A. Fresh air.    

B. Fresh food.    

C. A simple way of life.  

D. A simple way of eating.

4. What are the Hunzas famous for?

A. Vegetables.    

B. Milk.    

C. Food.      

D. Their long and healthy lives.

5. They do not need doctors, for        .

A. the doctors are not good                

B. there is not much illness

C. there is no illness                      

D. they are happy
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