问题 计算题

(12分)如图所示,半径为R的光滑半圆轨道ABC与倾角为=37°的粗糙斜面轨道DC相切于C,圆轨道的直径AC与斜面垂直.质量为m的小球从A点左上方距A高为h的斜面上方P点以某一速度水平抛出,刚好与半圆轨道的A点相切进入半圆轨道内侧,之后经半圆轨道沿斜面刚好滑到与抛出点等高的D处.已知当地的重力加速度为g,取,不计空气阻力.

求:

(1)小球被抛出时的速度v0

(2)小球到达半圆轨道最低点B时,对轨道的压力大小;

(3)小球从C到D过程中摩擦力做的功W.

答案

(1) (2)5.6mg(3)

题目分析:(1)小球到达A点时,速度与水平方向的夹角为,如图所示.则有                                                ①

由几何关系得             ②

                                         ③

(2)A、B间竖直高度                    ④

设小球到达B点时的速度为v,则从抛出点到B过程中有

              ⑤

在B点,有                        ⑥

解得                                  ⑦

由牛顿第三定律知,小球在B点对轨道的压力大小是5.6mg         ⑧

(3)小球沿斜面上滑过程中摩擦力做的功等于小球做平抛运动的初动能,有

       ⑨

评分标准:本题共12分,其中,⑤式2分,⑨式3分,其余每式1分.

点评:本题难度较大,明确从A点切入的速度是求解本题的关键,圆周运动中沿着半径方向的合力提供向心力,恰当应用动能定理是本题的技巧

阅读理解

阅读理解B

Alexander the Great was a mighty(强大的) king and conqueror(征服者). He was one of the greatest military geniuses(军事天才) the world has ever known. He was born in Pella, Macedonia. Alexander grew to be a handsome, brilliant(卓越的) man. Aristotle, the famous philosopher(哲学家), came from Greece to teach him---geography, politics, literature, medicine and science. Alexander’s father, King Philip II of Macedon, taught him to plan and win battles.

The young prince became King when he was 20. He then began the series of marches that continued until he ruled almost all of the then-known world. On his great war horse, Bucephalus, he first took over Greece. He went on to conquer southeastern Europe, Asia Minor, Egypt and India. On his way he crushed(征服) the Persian Empire, and was made King of Egypt and Asia. He and his troops traveled over 11,000 miles(17,700 km). He spread Greek customs and ideas wherever he went.

In India his men refused to go further. They were tired and frightened, and wanted to go home. Worn out, Alexander agreed to turn back. He died of fever in Babylon, at the early age of 33.

小题1:Alexander and his troops traveled and fought probably ________ then.

A.by ship

B.by simple truck

C.on their horses

D.on foot小题2:What’s the main idea of the second paragraph?

A.He spread Greek customs and ideas wherever he went.

B.He began great marches and ruled a lot of countries.

C.How he took over one country after another.

D.In which order he crushed these countries after another?小题3: Which of the following statements is TRUE?

A.He died in his late thirties.

B.Bucephalus was probably a big ship.

C.He conquered all the countries then known in the world.

D.Alexander was very ready to listen to anybody including his officers and soldiers.小题4:What’s the best title of this passage?

A.How Alexander the Great Became King?

B.Great Tragedy

C.Good Education Makes a Great Man

D.Alexander the Great

单项选择题 A1/A2型题