问题 问答题

粗糙水平地面与光滑半圆形轨道连接,两个小球A、B可视为质点,最初A、B两球静止在半圆形轨道圆心O的正下方,如图所示。若A、B球之间夹有一小块炸药,炸药爆炸后,小球A恰能经过半圆形轨道的最高点,B球到达的最远位置恰好是A球在水平地面上的落点;已知粗糙水平地面与B球之间的摩擦因数为0.2,求A、B两球的质量之比。

答案

设A、B球的质量分别为mAmB,炸药爆炸后的速度分别为vAvB, A球到达半圆形轨道最高点时的速度为vC,半圆形轨道半经为R。A球离开C点做平抛运动的时间为t,B球在水平面上移动的距离为S。则:

炸药爆炸过程由动量守恒定律得:

  ①

A球由最低点上升到C的过程,由机械能守恒定律得:

 ②

A球在最高点C,由圆周运动向心力公式得:

  ③

A球做平抛运动,由平抛运动规律得:

      ④

B球在水平方向的运动,由动能定理得:

  ⑤

联立①②③④⑤并代入数据解得: 

阅读理解

阅读短文,根据其内容回答问题。

English writer teaches us a lot about life

Charles Dickens is a great British writer in the 19th century. Most of his books are still popular even today.

In 1812, Charles Dickens was born in Portsmouth, England. Dickens didn't like playing with other boys when he was a little child, but he loved reading books. Childhood was not easy for Dickens. He began to work at a factory at the age of 12. Every day, he spent 10 hours washing bottles and cleaning shoes.

When Dickens was 16, he became a reporter for a newspaper. During that time, Dickens wrote his first book, The Pickwick Papers. The book came out in 1836-37 and made Dickens rich and famous. His hard times were at an end.

Most of Dickens' books are about the difficulties of living in Victorian England. The characters(人物)in his books are often children. They usually live a hard life in a boarding(寄宿)school, or have to work in a factory at a young age.

However, Dickens' works are all about hope. He wrote sad and dark stories, but they are always filled with humor(幽默). And most of his stories have happy endings, as with A Christmas Carol. It is about a selfish man. He finds love and friendship after looking back on his life one Christmas Eve.

小题1:Where was Dickens from?

小题2:Was life difficult for Dickens when he was a child?

小题3:What made Dickens rich and famous?

小题4:What do the children in his books usually do?

小题5:Why does the writer say "Dickens' works are all about hope."?

单项选择题