问题 计算题

(16分)如图所示,固定在水平地面上的横截面为“”形的光滑长直导轨槽,槽口向上(图为俯视图,图中两组平行双直线表示“”形槽的两侧壁).槽内放置一个滑块,滑块的左半部是半径为R的半圆柱形光滑凹槽,滑块的宽度为2R,恰与“”形槽的两内侧壁的间距相等,滑块可在槽内沿槽壁自由滑动.现有一金属小球(可视为质点)以水平初速度v0沿槽的一侧壁冲向滑块,从滑块的半圆形槽口边缘进入滑块凹槽.已知金属小球的质量为m,滑块的质量为3m,整个运动过程中无机械能损失.求:

(1)当金属小球滑离滑块时,金属小球和滑块的速度各是多大;

(2)当金属小球经过滑块上的半圆柱形槽的最右端A点时,金属小球的对地速率.

答案

(1)当金属小球滑离木质滑块时,金属小球和木质滑块的速度分别是

(2)当金属小球经过木质滑块上的半圆柱形槽的最右端A点时,金属小球的对地速度为

题目分析:(1)设滑离时小球和滑块的速度分别为

由动量守恒,             (2分)

又整个运动过程中无机械能损失:

               (2分)

得:             (3分)

(2)小球过A点时沿轨道方向两者有共同速度v,设小球对地速度为v′,则

由轨道方向动量守恒得

             (3分)

             (4分)

得:             (2分)

阅读理解

阅读理解。

     This is a song millions of Americans will hear this New Year’s Eve. It is called Auld Lang Syne (友谊地久天长). It is the traditional music played during the New Year’s celebration. Auld Lang Syne is an

old Scottish poem. It tells about the need to remember old friends.

      The words "auld lang syne" mean "old long since".No one knows who wrote the poem first. However, a version by Scottish poet Robert Bums was published in 1796. The words and music we know today

first appeared in a song book three years later.

      The song is played in the United States mainly on New Year’s Eve. The version you are hearing today is by the Washington Saxophone Quartet. As we end our program with Auld Lang Syne. I would like to

wish all our radio friends a very Happy New Year! This is Buddy Thomas.

1. This passage is from ______.

A. a newspaper        

B. a magazine        

C. a radio program      

D. a book    

2. ______ is introducing Auld Lang Syne to us.

A. Robert Bums                

B. the Washington Saxophone Quartet.      

C. Buddy Thomas                

D. Scottish poet

3. From the passage, we know that the song Auld Lang Syne is mainly played in the USA ______.

A. on New Year’s Eve              

B. on Christmas Eve    

C. on weekends                  

D. on Thanksgiving Eve

4. The words and music of Auld Lang Syne we know today first appeared ______.

A. in 1796                  

B. in 1793            

C. in 1799    

D. in 1790

5. The song Auld Lang Syne is about ______.

A. the history of Scotland                  

B. an old Scottish poet    

C. the need to remember old friends          

D. Buddy Thomas

单项选择题