问题 计算题

如图,半径为的四分之一光滑圆弧轨道固定在竖直面内,最低点与长的水平轨道相切于点。离地面高点与一倾角为的光滑斜面连接。质量的小滑块从圆弧顶点由静止释放,滑块与BC间的动摩擦因数。取。求:(1)小滑块刚到达圆弧的点时对圆弧的压力;(2)小滑块到达点时的速度大小;(3)小滑块从点运动到水平面所需的时间。

答案

(1),向下    (2)    (3)

解答:解:(1)设小滑块运动到B点的速度为vB,由机械能守恒定律有:mgR=mvB2      

由牛顿第二定律有,F-mg=m,联立 上式解得:F=30N ,压力方向向下             

(2)设小滑块运动到C点的速度为vC,由动能定理有:mgR-µmgL=mvC2     

解得小滑块在C点的速度,vC=4 m/s                             

(3)小滑块平抛到地面的水平距离,s=vCt=vC=1.2m , 

斜面底宽d=hcotθ=0.45m , 因为S>d,所以小滑块离开C点将落在水平地面上,小滑块在空中的飞行时间即为小滑块平抛运动所用时间t==0.3s     

答:(1)小滑块刚到达圆弧的点时对圆弧的压力大小为30N,方向向下;

(2)小滑块到达点时的速度大小为4 m/s

(3)小滑块从点运动到水平面所需的时间0.3s.

点评:本题关键是分析清楚物体的运动情况,然后根据动能定理、平抛运动知识、牛顿第二定律、向心力公式列式求解.

阅读理解

阅读理解。

    That little "a" with a circle around it is most commonly used as the "at" symbol. The symbol is usually

found in e-mail addresses. Surprisingly though, there is no official (官方的) name for this symbol, there

are lots of strange ways to describe the @ symbol. Before the @ symbol became the popular symbol for e-mail, it was used to show the cost of something. For example, if you bought 6 apples, you might write

6 apples @$1.10 each.

    As e-mail is becoming more and more popular, the@symbol or the"at sign is used between a person's

online user name and his mail server address, for example, joe@126.com. The symbol's use on the

Internet made it necessary for people to put this symbol on keyboards in the countries that had never seen or used the symbol before.      

    The actual origin (起源) of the @ symbol remains a mystery. According to an ancient western legend, during the Middle Ages before the invention of the printing press (印刷机), every letter of a word had

to be written by hand for each copy of a book. The monks (僧侣) looked for ways to make the letters

of common words less. Although the word "at" was quite short, it was quite a common word in texts and

documents. As a result, they circled around "a" and created @.

根据短文内容,选择最佳选项。

1. What did someone mean by writing 5 pears @$2.0 each in the past?

A. He bought 5 pears for free.  

B. He paid $7.0.

C. 5 pears cost $2.0.  

D. Each pear was $2.0.

2. Why did the monks in the old times create @ most probably?

A. Because @ could be printed very easily and clearly.        

B. Because they were ordered to invent some symbols.

C. Because they didn’t want to write the word "at" again and again. 

D. Because they wanted to make their texts or documents look special.

3. Which of the following is NOT true?

A. @ is often seen in e-mail addresses today.

B. The @ symbol has always meant the same in history.

C. The Internet makes @ become more popular.

D. The actual origin of @ is still difficult to explain.

4. What do we know from the passage?

A. @ was used before the Middle Ages.

B. @ is still always used to show prices of goods now.

C. No one had seen @ before it was put on the keyboard.

D. There was no @ on keyboards in some countries before.

5. Which is the BEST title for the passage?

A. What is @              

B. The secret of @

C. How to use @          

D. The actual origin of @  

单项选择题