问题 计算题

如图所示,长l的细绳一端系质量m的小球,另一端固定于O点,细绳所能承受拉力的最大值是7mg.现将小球拉至水平并由静止释放,又知图中O′点有一小钉,为使小球可绕O′点做竖直面内的圆周运动.试求OO′的长度d与θ角应满足的关系(设绳与小钉O′相互作用中无能量损失).

答案

本题考查圆周运动、动能定理、机械能守恒的应用,在临界状态的受力和特点是本题的难点,

设小球能绕O′点完成圆周运动,如图所示.其最高点为D,最低点为C.对于D点,依向心力公式有

    (1)(2分)

其中vD为D点速度,vD可由机械能守恒定律求知,取O点为重力势能的零势能位置,则

(2)(2分)

将(1)式与(2)式联立,解之可得(1分)

另依题意细绳上能承受的最大拉力不能超过7mg,由于在最低点C,绳所受拉力最大,故应以C点为研究对象,并有

(3)    (1分)   其中vC是C点速度,

可由机械能守恒定律求知(4) (2分)

将(3)式与(4)式联立,解之可得(1分)

(1分)

阅读理解

阅读理解。

     Thomas Edison was a famous American scientist. He was born in 1847. When he was a child, he liked

  to find out how things worked. He was in school for only three months. He asked his teacher a lot of

  strange questions, Most of them had nothing to do with his lessons. The teacher thought the boy was

 not bright and was not worth (值) teaching. When he told this to Edison's mother, she took her son out of

  school. As she had been a teacher, she taught him herself. The boy read a lot. Soon he became very

  interested in science. At the age of ten, Edison had already built a chemistry lab (实验室) for himself.

 Ever since then, he never stopped searching (探索) for new and better ways to do things.

1. Edison was born in the _____  century ( 世纪).

    A. eighteenth    

    B. nineteenth  

    C. nineteen      

    D. eighteen      

2. While he was in school, Edison _____  .

    A. studied his lesson very hard  

    B. was often late for school

    C. liked to ask questions      

    D. was not bright and enough to study

3. Edison learned more from _____  .

    A. his mother    

    B. his teacher  

    C. other boys    

    D. his father

4. Young Edison was interested in _____  .

    A. sports    

    B. playing games  

    C. making trouble  

    D. science

5. He was always searching for new and better ways to do things after he _____  .

    A. read books                    

    B. finished school  

    C. built a lab                    

    D. was taken out of school

单项选择题