问题 计算题

如图所示,粗糙斜面AB与竖直平面内的光滑圆弧轨道BCD相切于B点,圆弧轨道的半径为R,C点在圆心O的正下方,D点与圆心O在同一水平线上,∠COB=θ。现有质量为m的物块从D点无初速释放,物块与斜面间的动摩擦因数为μ,重力加速度为g。求:

(1)物块第一次通过C点时对轨道压力的大小;

(2)物块在斜面上运动离B点的最远距离。

答案

解:(1)物块从D到C,根据机械能守恒定律,得

物块经C点,根据牛顿第二定律,得

由以上两式得支持力大小FN=3mg

由牛顿第三定律得,物块对轨道的压力大小为3mg

(2)小物体通过圆弧轨道后,在斜面上运动到最大距离S时速度为0,由动能定理可得

阅读理解

阅读理解。

Dear Amy,

    I couldn't read your two e-mails until today because my computer was broken. I'm sorry to hear

about your problem, but I'm glad you're feeling better and are recovering (康复). I'm surprised that

in China someone's liver(肝脏) matched yours! This is really a moving story- a stranger donated part

of his liver to a girl he doesn't even know!

    You're right. We shouldn't care too much about our weight. I'm happy you stopped taking those

weight-loss pills. From your photo I can see you are now looking very well in the hospital. To keep

slim is important, especially for an actress, but nothing is more important than health. Your doctor's

advice is indeed very good- exercise for at least half an hour every day and eat lots of fruit and

vegetables.

    It's not only in your country. It's the same here with us Chinese- many people are always going on

diets or taking weight-loss pills, which are often dangerous. But in fact, some of them are not overweight

(超重) at all. I hope these people can learn something from your story. Hope you will leave hospital as

soon as possible.

                                                                                                                                      Love 

                                                                                                                                      XXX

1. Who does "a girl" in the letter refer to? [ ]

A. The writer of the letter.

B. Amy.

C. A stranger.

D. An unknown person.

2. Which country is the writer of the letter from? [ ]

A. America.

B. China.

C. Germany.

D. England.

3. Which of the following is NOT right?[ ]

A. Amy has probably just received an operation on liver.

B. Amy is now probably in hospital recovering.

C. A Chinese man donated part of his liver to Amy.

D. Amy is now still going on diets or taking weight-loss pills.

填空题