英语练习（A1卷）
I 词汇及语法结构（30分, 30 分钟）本大题共有30小题，每题给出A B C D 四个选择。要求从中
选出最佳答案,并在答题纸上用铅笔将相应字母涂黑。
1. If we _______learn English in the same way, it would not seem so difficult.
A. should
B. could
C. would
D. might
2. And practice needs __________ and takes much time.
A. great force
B. great power
C. great effort
D. great strength
3. If we could learn English in the same way, it would not seem so _________.
A. difficulty
B. difficult.
C. difference
D. different
4. Will you help me when I am________?
A. in trouble
B. out of trouble
C. in difficult
D. have problem
5. He went to his father and _________ some money.
A. ask for
B. asked
C. asked for
D. asked about
6. Good manners really mean to be kind and helpful ________, especially those older or weaker than ourselves.
A. to others
B. for others
C. for the other
D. to the other
7. He cut his hand________.
A. in accident
B. by accident
C. on accident
D. for accident
8. I?ll come ___________ I don?t like to.
A. no matter
B. if only
C. as if
D. even if
9. Just then I noticed that a young porter in a sleeping-car ______at me.
A. was looking
B. look for
C. looking
D. looked
10. I asked the man at the booking office _______ I could have two tickets.
A. that
B. if
C.what
D. which r
11. It was important for me _______ the tickets.
A. having
B. being having
C. to have
D. to having had
12. When people _________for a bus, or in a post office, he takes his turn.
A. are waiting
B. wait
C. waited
D. were waiting
13. Margie _______ her diary almost every day.
A. kept
B. go on
C. keep
D. had
14. She didn?t like her picture book__________, so she threw it away.
A. not more
B. no longer
C. any longer
D. no more
15. Her school was a room _______ her bedroom.
A. next to
B. close upon
C. besides
D. nearby
16. Mark Twain paid the young porter_________ he usually did for a porter for his helping them have two seats in the
sleeping car.
A. twice more as
B. twice as much as
C. twice as many as
D. as twice much as
17. They learned the same things, so they could help _______their homework and talk about it.
A. one another with
B. one other with
C. one another for
D. each other for
18. I?m ashamed of ________I did.
A. which
B. that
C. as
D. what
19. I found a railway official and asked him if I could get a place _______in a sleeping-car.
A. where
B. when
C. somewhere
D. somewhat
20. He kept himself all the time as straight as a young soldier ________.
A. on guard
B. in guard
C. with guard
D. for guard
21. “It will make me _______ tall that people will stop calling me a LITTLE man.”
A. too
B. very
C. so
D. such
22. What was the use _____ such high heels, when people seemed to turn a blind eye to them.
A. to have
B. of having
C. of taking
D. to take
23. It seemed it was going to rain, but it has ______ fine.
A. turned down
B. turned out
C. turned up
D. turned over
24. Edison did not allow his odd moments to _______ while he was earning his living by tapping out messages.
A. slip by
B. slip away
C. slip off
D. slip on
25. Many giants in science or art have made huge success for ________ in the world.
A. himself
B. yourselves
C. themselves
D. yourself
26. How much money _________ when you had bought everything you wanted?
A. was left over
B. left over
C. were left
D. left out
27. Edison succeeded ________a lot of things entirely new to the world.
A. for working on
B. on working out
C. in working on
D. in working out
28. “Do you enjoy ________ beside me?” she asked coldly.
A. sitting
B. seating
C. to sit
D. to seat
29. I?m a little bit ________ this town.
A. dissatisfying with
B. dissatisfied with
C. to dissatisfy to
D. dissatisfy to
30. She is _________better today.
A. a lot of
B. a great deal
C. a great deal of
D. much more
II. 阅读理解（30分，40分钟）
本部分有四篇短文，每篇短文后面有五个阅读理解题，根据短文从A、B、C、D中选出最佳答案，并在
答题纸上用铅笔将相应字母涂黑。
1．The Carter’s Light
An old man was going home late one night with his horse and cart after a hard day?s work. When he was not far from his house, the light on the cart went out. He tried to make the lamp burn again, but he could not.
He was near his home, and so he went along the road without a light. But a policeman saw the cart without a light.
He stopped the old carter.
“Where?s your light?” said the policeman. “No one may take a cart along a road at night without a light. You know that. You?ve broken the law”.
“I had a light,” said the old man, “but it has just gone out.”
“I don?t believe that story,” said the policeman. He took out a book and got ready to write. “What?s your name and where do you live?”
“Please don?t take down my name,” said the man. “My house is just there. You can see it from here. I had a light nearly all the way. I haven?t come far without a light.”
“You came all the way without a light. What?s your name?”
The carter quickly took the policeman?s hand and put it down hard on the top of the lamp. The lamp was still hot, and it burnt the policeman?s hand. He jumped and was very angry.
“Now what do you think?” said the carter. “Did I come all the way without a light?”
“No,” said the policeman, “I believe you now, but I still want to know your name. You?ve broken the law now.
You?ve burnt a policeman?s hand. What?s your name?”
“If I tell you my name, you can?t write it. Your hand?s burnt.”
“You?re right,” said the policeman. “I can?t write now. So you must come with me to the police station. You?ll be there all night.
31.The carter?s light went out ______.
A. on his way to work
B. on his way home
C. in front of his house
D. at the police station
32. The carter was stopped because he __________.
A. had stolen a cart
B. would not give his name
C. had burnt a policeman?s hand
D. was going along the road without a light
33. The carter was stopped by the policeman when he ________.
A. was near his house
B. was still far from his house
C. got to his house
D. left his house
34. The carter put the policeman?s hand down hard on the top of the lamp to prove that _______.
A. he had had a light all the way
B. the light had just gone out
C. he had tried to make the lamp burn again
D. his house was not far away
35. Finally the policeman said the carter had broken the law for __________.
A. coming all the way without a light
B. refusing to give his name
C. burning a policeman?s hand
D. wasting the policeman?s time
2．Christopher Columbus
About five hundred years ago, there lived a boy named Columbus. He loved the ocean, and often went to sea.
He grew up to be a fine sailor.
In the time of Columbus, men did not know much about the earth; most of them thought it was flat. Columbus thought it must be round. He said: “I think I can sail around it, just as a fly can walk around an apple, I will do so.
All I want is a ship and some sailors to go with me.”
But he was a poor man. How could he get ships and some men? He asked many people to help him. Some
made fun of him. Some even thought he was crazy. But he kept on trying for many years.
At last the queen of Spain gave him three ships and some men. With these Columbus sailed west. One week passed, and on he went. Two weeks, and still he sailed on. Three weeks went by, and still he saw the sea, the sea,
only the sea.
The sailors became frightened and wished to turn back, but Columbus would not give up. He said, “Sail on.”
At last the sailors said, “We will not go on any longer.”“Sail on three days longer,” Columbus told them, “only three days. If we do not come to land by then, you may turn back.”
One day went by and no land was seen. Two days, and still no land. The next day passed, and night came.
That night a man on one of the ships called out, “A light! A light!” The other men ran to see it. Yes, there was a
far-off light.
The next morning the sailors saw something dark at the edge of the sky. Was it land? The day grew bright. Land! Land! It was land at last. How glad the men were to see it! Gladdest of all was the brave Columbus.
The sailors got in their boats and went ashore. They shed tears of joy, and even kissed the ground, so happy
were they to be on land again.
This is how the New World was found. It took place in 1492.
36. When Columbus was a boy, he________.
A. became a good sailor
B. began to sail around the earth
C. tried to find a new world
D. was interested in sailing
37. In the time of Columbus, most people________.
A. thought the earth was round
B. didn?t know a lot about the earth
C. knew a lot about the earth
D. supported the idea of sailing around the earth
38. Columbus began sailing west with________.
A. a ship and some men
B. the Queen of Spain
C. three ships and some sailors
D. no help at all
39. After sailing for_______, the sailors got frightened and wanted to turn back.
A. two weeks
B. three weeks
C. a month
D. a month and a half
40. The sailors became frightened because__________.
A. they didn?t think they could reach any land
B. they had nothing to eat
C. the weather turned bad
D. most of them got ill
3．Walt Disney
When Walt Disney was young he loved to draw(画画). But his father had many jobs for him to do. “Stop all
that drawing!” old Disney would say, “There?s work to be done.”
When he was older, Walt decided to make art his career. He worked hard drawing cartoons (漫画). When he
had time, he studied art. He began to make cartoon movies. But he didn?t have much money and he didn?t always have enough to eat.
Sometimes when he worked in his little office, a mouse would run near his desk.
“Would you like to be my pet?” Walt asked the mouse. He caught the mouse and kept him as a pet. He called
him Mortimer.
A few years later, Walt remembered Mortimer and decided to make a cartoon about him.
“I?m making a cartoon about a mouse named Mortimer,” he told his wife.
“Mortimer Mouse? I think Mickey Mouse would be a better name,” she said.
“You?re right! It would.”
Disney made many Mickey Mouse cartoons. People all over the world saw Mickey and loved him. Mickey Mouse made Walt Disney famous. Then came Donald Duck and others.
Walt began to make full-length cartoons. One was Snow White and the Seven Dwarfs (七个小矮人). Then
Walt made movies for TV. Millions of children watched the shows every week.
Walt dreamed of making a beautiful park that every one would like. His dream came true with Disneyland in 1955 in California, real boats, trains, mountains, rivers ―all in one beautiful park.
Years later, Disney World was built. Walt Disney now had another wonderful world of fun in Florida.
Walt Disney died in 1966, but the world will not forget him quickly. Mickey Mouse and all his friends will
help us to remember him.
41. Walt Disney was fond of _______when he was young.
A. music
B. sports
C. drawing
D. Flowers
42. Young Walt couldn?t do what he liked to, because he had to ________.
A. go to school every day
B. help his mother with some housework
C. do a lot of work for his father
D. cook for the family
43. When Walt got older, he decided to _________.
A. become a TV writer
B. make art his career
C. build a beautiful park for children
D. do anything his father liked
44. The first cartoon Walt made was about _________.
A. Donald Duck
B. Mickey Mouse
C. Disneyland
D. Snow White and Seven Dwarfs
45. What made Walt Disney so famous?
A. Disneyland in California
B. Disney World in Florida
C. Mickey Mouse cartoons
D. Donald Duck and other cartoons
4. How to Get Main Ideas
One of the most important tasks of remembering what you read is choosing the right ideas to remember. It?s easy to this, but many readers do not realize that they must learn to choose what is worth remembering.
Just as a traveler in a desert searches for landmarks, you must learn to find …landmarks? to guide you through your reading. These landmarks are the main ideas, the important statements around which the writer builds his article.
To find main ideas easily, you should practice the skill of looking for the most important statement in each paragraph. If this statement were taken away, the paragraph would have no meaning. But if the rest of the paragraph were taken away, statement would still make the writer?s message clear.
By collecting the main ideas of each of the paragraphs you read, you will find you have a series of statements that, put together, make up the main ideas the writer wanted you to discover.
46. This passage tells us________.
A. how to read
B. how to remember
C. How to find the main ideas to remember
D. the importance of reading
47. If you travel in a desert and don?t want to lose your way, you should follow the ________.
A. footprints
B. main ideas
C. important statements
D. landmarks
48. To find main ideas easily, you should________.
A. take up reading
B. write often
C. practice reading more
D. practice the skill of looking for important statements
49. Without its main idea, a paragraph_________.
A. would be meaningful
B. would be meaningless
C. would still make the writer?s message clear
D. would help the readers to consider
50. The writer wanted you to discover_________.
A. the statement in his article
B. the main ideas
C. the new words
D. the word phrases
III. 完形填空（10分，15分钟）
本部分为一篇短文，中间有10个空，每个空后边有相应的A、B、C、D四个选项，根据短文的意义及结构从后边A、B、C、D中选出最佳答案，并在答题纸上用铅笔将相应字母涂黑。
Language Study
In order to learn a foreign language well, it is necessary to overcome the fear of making 51 . If the primary goal of language use is communication, the mistakes are 52 consideration that
may be dealt 53 gradually as awareness of those mistakes increases. On 54 , students should
not 55 their mistakes. The learner may observe how native speakers express themselves, and
how 56 expressions differ from the way the learner might say them. For example, a Spanish
speaker who 57 “I do it” to express willingness to do something in the immediate future, could,
by interacting (相互作用) 58 native speakers of English, observe that native speakers actually
say “I?ll do it”. The resulting discrepancy(不同) can serve as a basis for the student to modify his
way of using the present tense in English. But a student who is unwilling to interact 59 the first
place would lose this opportunity to learn by 60 and error.
51. A. mistakes B. f laws C. errors D. wrongs
52. A. a dvanced B. secondary C. elementary D. intermediate
53. A. in B. with C. from D. by
54. A. the other hand B. the contrary C. second thought D. condition that
55. A. think about B. neglect C. ignore D. examine
56. A. local B. foreign C. normal D. native
57 A. is saying B. has said C. says D. has been saying
58. A. by B. with C. from D. to
59. A. in B. by C. at D. from
60. A. trying B. try C. trial D. the trial
V. 英译汉（15分，15分钟）
请将下列句子译成中文，用钢笔或圆珠笔写在答题纸上。
61. None of the children ever blamed our parents for the poor living conditions.
62. My father worked his head off from the time I can remember.
63. Professor White helped us with our pronunciation.
64. But I will pour only on this condition: All that falls into the bag shall be gold; but every piece that falls
upon the ground shall become dust.
65. The fish learned in time to go to the circle but not to the square.
V. 汉译英（15分，20分钟）
请将下列句子译成英文，用钢笔或圆珠笔写在答题纸上。
66. 老师告诉我们不要在教室里大声喧哗。
67. 礼貌是非常重要的。如果你懂礼貌，你总是与人为善，乐于助人。
68．医生转过身来，非常有礼貌地同我打招呼。
69. 别把报纸杂志到处乱扔。
70. 我的笔出了毛病。
I 单选：1-5 BCBAC II阅读：31-35 BDABC
6-10 ABDAB 36-40 DBCBA
11-15 CAACA 41-45 CCBBC
16-20 BADCA 46-50 CDDBB
21-25 CBBAC III完形填空：51-55 ABBAC
26-30 ADABB 56-60 DDBAC
波动光学测试题 一.选择题 1. 如图3.1所示，折射率为n2 、厚度为e的透明介质薄膜的上方和下方的透明介质的折射率分别为n1和n3，已知n1 ＜n2 ＞n3，若用波长为(的单色平行光垂直入射到该薄膜上，则从薄膜上、下两表面反射的光束（用①②示意）的光程差是 (A) 2n2e. (B) 2n2e－(/(2 n2 ). (C) 2n2e－(. (D) 2n2e－(/2. 2. 如图 3.2所示，s1、s2是两个相干光源，它们到P点的距离分别为r1和r2，路径s1P垂直穿过一块厚度为t1，折射率为n1的介质板，路径s2P垂直穿过厚度为t2，折射率为n2的另一介质板，其余部分可看作真空，这两条路径的光程差等于 (A) (r2 + n2 t2)－(r1 + n1 t1). (B) [r2 + ( n2－1) t2]－[r1 + (n1－1)t1]. (C) (r2 －n2 t2)－(r1 －n1 t1). (D) n2 t2－n1 t1. 3. 如图3.3所示，平行单色光垂直照射到薄膜上，经上下两表面反射的两束光发生干涉，若薄膜的厚度为e，并且n1＜n2＞n3，(1 为入射光在折射率为n1 的媒质中的波长，则两束反射光在相遇点的位相差为 (A) 2 ( n2 e / (n1 (1 ). (B) 4 ( n1 e / (n2 (1 ) +(. (C) 4 ( n2 e / (n1 (1 ) +(. (D) 4( n2 e / (n1 (1 ). 4. 在如图3.4所示的单缝夫琅和费衍射实验装置中，s为单缝，L为透镜，C为放在L的焦面处的屏幕，当把单缝s沿垂直于透镜光轴的方向稍微向上平移时，屏幕上的衍射图样 (A) 向上平移.(B) 向下平移.(C) 不动.(D) 条纹间距变大. 5. 在光栅光谱中,假如所有偶数级次的主极大都恰好在每缝衍射的暗纹方向上,因而实际上不出现,那么此光栅每个透光缝宽度a和相邻两缝间不透光部分宽度b的关系为 (A) a = b. (B) a = 2b. (C) a = 3b. (D) b = 2a. 二.填空题 1. 光的干涉和衍射现象反映了光的性质, 光的偏振现象说明光波是波. 2. 牛顿环装置中透镜与平板玻璃之间充以某种液体时,观察到第10级暗环的直径由1.42cm 变成1.27cm,由此得该液体的折射率n = . 3. 用白光(4000?～7600?)垂直照射每毫米200条刻痕的光栅,光栅后放一焦距为200cm的凸透镜,则第一级光谱的宽度为. 三.计算题 1. 波长为500nm的单色光垂直照射到由两块光学平玻璃构成的空气劈尖上，在观察反射光的干涉现象中，距劈尖棱边l = 1.56cm的A处是从棱边算起的第四条暗条纹中心. (1) 求此空气劈尖的劈尖角( . (2) 改用600 nm的单色光垂直照射到此劈尖上仍观察反射光的干涉条纹,A处是明条纹，还是暗条纹？ 2. 设光栅平面和透镜都与屏幕平行，在平面透射光栅上每厘米有5000条刻线，用它来观察波长为(=589 nm的钠黄光的光谱线. (1) 当光线垂直入射到光栅上时,能看到的光谱线的最高级数km 是多少? (2) 当光线以30(的入射角(入射线与光栅平面法线的夹角)斜入射到光栅上时，能看到的光谱线的最高级数km 是多少? 3．在杨氏实验中，两缝相距0.2mm，屏与缝相距1m，第3明条纹距中央明条纹7.5mm，求光波波长？
Unit 1 Active reading (1) 5 Match the words in the box with their definitions. 1 achieving good results (productive) 2 the fact of being present at an event, or of going regularly to school, church etc (attendance) 3 the refusal to accept something new, such as a plan, idea, or change (resistance) 4 determined to be successful, rich, famous etc (ambitious) 5 agreement to a plan, offer, or suggestion (acceptance) 6 the written words of a play, film, television programme, speech etc (script) 7 very good, large, or showing great skill (impressive) 6 Complete the paragraph with the correct form of the words in Activity 5. (1) attendance (2) ambitious (3) productive (4) impressive (5) resistance (6) script (7) acceptance 7 Replace the underlined words with the correct form of the words in the box. 1 (mortgage) 2 (deck) 3 (surf) 4 (coastal; defy) 5 (lengthy) 8 Answer the questions about the words and expressions. 1 (b) 2 (a) 3 (b) 4 (b) 5 (b) 6 (a) 7 (b) 8 (b) Active reading (2) 4 Match the words in the box with their definitions. 1 involving three things of the same kind (triple) 2 an area of ground where dead people are buried (cemetery) 3 the part of a place or thing that is at the back (rear)
一、判断题 1. 在自然界中，可以找到实际的质点. ······························································· [×] 2. 同一物体的运动，如果选取的参考系不同，对它的运动描述也不同. ···················· [√] 3. 运动物体在某段时间内的平均速度大小等于该段时间内的平均速率. ···················· [×] 4. 质点作圆周运动时的加速度指向圆心. ···························································· [×] 5. 圆周运动满足条件d 0d r t =，而d 0d r t ≠ . ···························································· [√] 6. 只有切向加速度的运动一定是直线运动. ························································· [√] 7. 只有法向加速度的运动一定是圆周运动. ························································· [×] 8. 曲线运动的物体，其法向加速度一定不等于零. ················································ [×] 9. 质点在两个相对作匀速直线运动的参考系中的加速度是相同的. ·························· [√] 10. 牛顿定律只有在惯性系中才成立. ·································································· [√] 二、选择题 11. 一运动质点在某时刻位于矢径(),r x y 的端点处，其速度大小为：（ C ） A. d d r t B. d d r t C. d d r t D. 12. 一小球沿斜面向上运动，其运动方程为254SI S t t =+-（），则小球运动到最高点的时刻是： （ B ） A. 4s t = B. 2s t = C. 8s t = D. 5s t = 13. 一质点在平面上运动，已知其位置矢量的表达式为22r at i bt j =+ （其中a 、b 为常量）则 该质点作：（ B ） A. 匀速直线运动 B. 变速直线运动 C. 抛物线运动 D. 一般曲线运动 14. 某物体的运动规律为2d d v kv t t =-，式中的k 为大于0的常数。当0t =时，初速为0v ，则速度v 与时间t 的关系是：（ C ） A. 0221v kt v += B. 022 1v kt v +-= C. 021211v kt v += D. 0 21211v kt v +-= 15. 在相对地面静止的坐标系中，A 、B 二船都以2m/s 的速率匀速行驶，A 沿x 轴正方向，B
第十一章真空中的静电场 1．如图所示，真空中一长为L的均匀带电细直杆，电荷为q，试求在直杆延长线上距杆的一端距离为d的P点的电场强度． L P 2.一个点电荷位于一边长为a的立方体高斯面中心，则通过此高斯面的电通量为???，通过立方体一面的电场强度通量是???，如果此电荷移到立方体的一个角上，这时通过（1）包括电荷所在顶角的三个面的每个面电通量是???，（2）另外三个面每个面的电通量是???。 3.在场强为E的均匀静电场中，取一半球面，其半径为R，E的方向和半球的轴平行，可求得通过这个半球面的E通量是（） A．E R2 π B. R2 2π C. E R2 2π D. E R2 2 1 π 4．根据高斯定理的数学表达式?∑ ?= S q S E / dε ? ? 可知下述各种说法中，正确的是（） (A) 闭合面内的电荷代数和为零时，闭合面上各点场强一定为零． (B) 闭合面内的电荷代数和不为零时，闭合面上各点场强一定处处不为零． (C) 闭合面内的电荷代数和为零时，闭合面上各点场强不一定处处为零． (D) 闭合面上各点场强均为零时，闭合面内一定处处无电荷． 5．半径为R的“无限长”均匀带电圆柱体的静电场中各点的电场强度的大小E与距轴线的距离r的关系曲线为( ) E O r (A) E∝1/r 6．如图所示, 电荷-Q均匀分布在半径为R，长为L的圆弧上，圆弧的两端有一小空隙，空隙长为图11-2 图11-3
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大学物理简明教程（上册）习题选解 第1章 质点运动学 1-1 一质点在平面上运动，其坐标由下式给出)m 0.40.3(2 t t x -=，m )0.6(3 2 t t y +-=。求：（1）在s 0.3=t 时质点的位置矢量； （2）从0=t 到s 0.3=t 时质点的位移；（3）前3s 内质点的平均速度；（4）在s 0.3=t 时质点的瞬时速度； （5）前3s 内质点的平均加速度；（6）在s 0.3=t 时质点的瞬时加速度。 解：（1）m )0.6()0.40.3(322j i r t t t t +-+-= 将s 0.3=t 代入，即可得到 )m (273j i r +-= （2）03r r r -=?，代入数据即可。 （3）注意：0 30 3--=r r v =)m/s 99(j i +- （4）dt d r =v =)m/s 921(j i +-。 （5）注意：0 30 3--=v v a =2)m/s 38(j i +- （6）dt d v a ==2)m/s 68(j -i -，代入数据而得。 1-2 某物体的速度为)25125(0j i +=v m/s ，3.0s 以后它的速度为)5100(j 7-i =v m/s 。 在这段时间内它的平均加速度是多少？ 解：0 30 3--= v v a =2)m/s 3.3333.8(j i +- 1-3 质点的运动方程为) 4(2k j i r t t ++=m 。（1）写出其速度作为时间的函数；（2）加速度作为时间的函数； （3）质点的轨道参数方程。 解：（1）dt d r =v =)m/s 8(k j +t （2）dt d v a = =2m/s 8j ； （3）1=x ；2 4z y =。 1-4 质点的运动方程为t x 2=，22t y -=（所有物理量均采用国际单位制）。求：（1）质点的运动轨迹；（2）从0=t 到2=t s 时间间隔内质点的位移r ?及位矢的径向增量。 解：（1）由t x 2=，得2 x t = ，代入22t y -=，得质点的运动轨道方程为 225.00.2x y -=； （2）位移 02r r r -=?=)m (4j i - 位矢的径向增量 02r r r -=?=2.47m 。 （3）删除。 1-6 一质点做平面运动，已知其运动学方程为t πcos 3=x ，t πsin =y 。试求： （1）运动方程的矢量表示式；（2）运动轨道方程；（3）质点的速度与加速度。 解：（1）j i r t t πsin πcos 3+=； （2）19 2 =+y x （3）j i t t πcos πsin 3π+-=v ； )πsin πcos 3(π2j i t t a +-= *1-6 质点A 以恒 定的速率m/s 0.3=v 沿 直线m 0.30=y 朝x +方 向运动。在质点A 通过y 轴的瞬间，质点B 以恒 定的加速度从坐标原点 出发，已知加速度2m/s 400.a =，其初速度为零。试求：欲使这两个质点相遇，a 与y 轴的夹角θ应为多大？ 解：提示：两质点相遇时有，B A x x =，B A y y =。因此只要求出质点A 、B 的运动学方程即可。或根据 222)2 1 (at y =+2(vt)可解得： 60=θ。 1-77 质点做半径为R 的圆周运动，运动方程为 2021 bt t s -=v ，其中，s 为弧长，0v 为初速度，b 为正 的常数。求：（1）任意时刻质点的法向加速度、切向加速度和总加速度；（2）当t 为何值时，质点的总加速度在数值上等于b ？这时质点已沿圆周运行了多少圈？ 题1-6图
1 下列哪一种说法就是正确得( ) (A)运动物体加速度越大,速度越快 (B)作直线运动得物体,加速度越来越小,速度也越来越小 (C)切向加速度为正值时,质点运动加快 (D)法向加速度越大,质点运动得法向速度变化越快 2 一质点在平面上运动,已知质点得位置矢量得表示式为(其中a、b为常量),则该质点作( ) (A)匀速直线运动 (B)变速直线运动 (C)抛物线运动 (D)一般曲线运动 3 一个气球以速度由地面上升,经过30s后从气球上自行脱离一个重物,该物体从脱落到落回地面得所需时间为( ) (A)6s (B) (C)5、 5s (D)8s 4 如图所示湖中有一小船,有人用绳绕过岸上一定高度处得定滑轮拉湖上得船向岸边运动,设该人以匀速率收绳,绳长不变,湖水静止,则小船得运动就是( ) (A)匀加速运动 (B)匀减速运动 (C)变加速运动 (D)变减速运动 5 已知质点得运动方程,则质点在2s末时得速 度与加速度为( ) (A) (B) (C) (D) 6 一质点作竖直上抛运动,下列得图中哪一幅基本上反映了该质点得速度变化情况( )
7 有四个质点A、B、C、D沿轴作互不相关得直线运动,在时,各质点都在处,下列各图分别表示四个质点得图,试从图上判别,当时,离坐标原点最远处得质点( ) 8 一质点在时刻从原点出发,以速度沿轴运动,其加速度与速度得关系为,为正常数,这质点得速度与所经历得路程得关系就是( ) (A) (B) (C) (D)条件不足,无地确定 9 气球正在上升,气球下系有一重物,当气球上升到离地面100m高处,系绳突然断裂,重物下落,这重物下落到地面得运动与另一个物体从100m高处自由落到地面得运动相比,下列哪一个结论就是正确得( )
第一章 质点运动学 1–1 描写质点运动状态的物理量是 。 解：加速度是描写质点状态变化的物理量，速度是描写质点运动状态的物理量，故填“速度”。 1–2 任意时刻a t =0的运动是 运动；任意时刻a n =0的运动是 运动；任意时刻a =0的运动是 运动；任意时刻a t =0，a n =常量的运动是 运动。 解：匀速率；直线；匀速直线；匀速圆周。 1–3 一人骑摩托车跳越一条大沟，他能以与水平成30°角，其值为30m/s 的初速从一边起跳，刚好到达另一边，则可知此沟的宽度为 （)m/s 102=g 。 解：此沟的宽度为 m 345m 10 60sin 302sin 220=??==g R θv 1–4 一质点在xoy 平面运动，运动方程为t x 2=，229t y -=，位移的单位为m ，试写出s t 1=时质点的位置矢量__________；s t 2=时该质点的瞬时速度为__________，此时的瞬时加速度为__________。 解：将s t 1=代入t x 2=，229t y -=得 2=x m ，7=y m s t 1=故时质点的位置矢量为 j i r 72+=（m ） 由质点的运动方程为t x 2=，229t y -=得质点在任意时刻的速度为 m/s 2d d ==t x x v ，m/s 4d d t t x y -==v s t 2=时该质点的瞬时速度为 j i 82-=v （m/s ） 质点在任意时刻的加速度为 0d d ==t a x x v ，2m/s 4d d -==t a y y v s t 2=时该质点的瞬时加速度为j 4-m/s 2 。
自测题9 一、选择题(共33分) 1. 在真空中波长为λ的单色光，在折射率为n 的透明介质中从A 沿某路径传播到B ，若A ，B 两点位相差为3π，则此路径AB 的光程为( A ) (A)1.5λ． (B)1.5nλ． (C)3λ． (D)1.5λ/n ． 2. 单色平行光垂直照射在薄膜上，经上下两表面反射的两束光发生干涉，如题9-1-1图所示，若薄膜的厚度为e ，且n 1
第1章质点的运动与牛顿定律 一、选择题 易１、对于匀速圆周运动下面说法不正确的是（） （A）速率不变；（B）速度不变；（C）角速度不变；（D）周期不变。易：２、对一质点施以恒力，则；（） （A）质点沿着力的方向运动；（ B）质点的速率变得越来越大； （C）质点一定做匀变速直线运动；（D）质点速度变化的方向与力的方向相同。易：３、对于一个运动的质点，下面哪种情形是不可能的（） (A)具有恒定速率，但有变化的速度；(B)加速度为零，而速度不为零；(C)加速度不为零，而速度为零。(D) 加速度恒定(不为零)而速度不变。中：４、试指出当曲率半径≠0时，下列说法中哪一种是正确的（） (A) 在圆周运动中，加速度的方向一定指向圆心； (B) 匀速率圆周运动的速度和加速度都恒定不变； (C)物体作曲线运动时，速度方向一定在运动轨道的切线方向，法线分速度 恒等于零，因此法问加速度也一定等于零； (D) 物体作曲线运动时，一定有加速度，加速度的法向分量一定不等于零。 难：５、质点沿x方向运动，其加速度随位置的变化关系为:．如在x = 0处，速度，那么x=3m处的速度大小为
(A) ； (B) ； (C) ； (D) 。 易：６、一作直线运动的物体的运动规律是，从时刻到间的平 均速度是 (A) ； (B) ； (C) ； (D) 。 中7、一质量为m 的物体沿X 轴运动，其运动方程为t x x ωsin 0=，式中0x 、ω均 为正的常量，t 为时间变量，则该物体所受到的合力为：（ ） （A ）、x f 2ω=； （B ）、mx f 2ω=； （C ）、mx f ω-=； （D ）、mx f 2ω-=。 中：８、质点由静止开始以匀角加速度 沿半径为R 的圆周运动．如果在某一时 刻此质点的总加速度与切向加速度成角，则此时刻质点已转过的角度为 (A) ； (B) ； (C) ； (D) 。 难９、一质量为本10kg 的物体在力f=（120t+40）i （SI ）作用下沿一直线运动， 在t=0时，其速度v 0=6i 1-?s m ，则t=3s 时，它的速度为： （A ）10i 1-?s m ； （B ）66i 1-?s m ； （C ）72i 1-?s m ； （D ）4i 1-?s m 。 难：1０、一个在XY 平面内运动的质点的速度为 ，已知t = 0时，它通过(3，-7) 位置处，这质点任意时刻的位矢为 (A) ； (B) ；
静电场部分练习题 一、选择题 ： 1．根据高斯定理的数学表达式?∑=?0 εq s d E ，可知下述各种说法中正确的是（ ） A 闭合面的电荷代数和为零时，闭合面上各点场强一定为零。 B 闭合面的电荷代数和不为零时，闭合面上各点场强一定处处不为零。 C 闭合面的电荷代数和为零时，闭合面上各点场强不一定处处为零。 D 闭合面上各点场强均为零时，闭合面一定处处无电荷。 2．在静电场中电场线为平行直线的区域（ ） A 电场强度相同，电势不同； B 电场强度不同，电势相同； C 电场强度、电势都相同； D 电场强度、电势都不相同； 3．当一个带电导体达到静电平衡时，（ ） A 表面上电荷密度较大处电势较高。 B 表面曲率较大处电势较高。 C 导体部的电势比导体表面的电势高； D 导体任一点与其表面上任意点的电势差等于零。 4．有四个等量点电荷在OXY 平面上的四种不同组态，所有点电荷均与原点等距，设无穷远处电势为零。则原点O 处电场强度和电势均为零的组态是（ ） A 图 B 图 C 图 D 图 5．关于高斯定理，下列说法中哪一个是正确的？（ ） A 高斯面不包围自由电荷，则面上各点电位移矢量D 为零。 B 高斯面上处处D 为零，则面必不存在自由电荷。 C 高斯面上D 通量仅与面自由电荷有关。 D 以上说法都不对。 6．A 和B 为两个均匀带电球体，A 带电量+q ，B 带电量-q ，作一个与A 同心的球面S 为高斯面，如图所示，则（ ） S A B
A 通过S 面的电通量为零，S 面上各点的场强为零。 B 通过S 面的电通量为 εq ，S 面上各点的场强大小为2 04r q E πε= 。 C 通过S 面的电通量为- εq ，S 面上各点的场强大小为2 04r q E πε- =。 D 通过S 面的电通量为 εq ，但S 面上场强不能直接由高斯定理求出。 7．三块互相平行的导体板，相互之间的距离1d 和2d ，与板面积相比线度小得多，外面二板用导线连接，中间板上带电，设左、右两面上电荷面密度分别为1σ，2σ。如图所示，则比值1σ/2σ为（ ） A 1d /2d ; B 1 C 2d /1d ; D (2d /1d )2 8．一平板电容器充电后切断电源，若改变两极板间的距离，则下述物理量中哪个保持不变？（ ） A 电容器的电容量 B 两极板间的场强 C 两极板间的电势差 D 电容器储存的能量 9．一空心导体球壳，其外半径分别为1R 和2R ，带电量q ，当球壳中心处再放一电量为q 的点电荷时，则导体球壳的电势（设无穷远处为电势零点）为（ ）。 A 1 04R q πε B 2 04R q πε C 1 02R q πε D 2 02R q πε 10．以下说确的是（ ）。 A 场强为零的地方，电势一定为零；电势为零的地方，均强也一定为零； B 场强大小相等的地方，电势也相等，等势面上各点场强大小相等； C 带正电的物体，也势一定是正的，不带电的物体，电势一定等于零。 D 沿着均场强的方向，电势一定降低。 11．两个点电荷相距一定的距离，若在这两个点电荷联线的中垂线上电势为零，那么这两个点电荷为（ ）。
Online HomeWork_U1B3 I. Reading Comprehension Section A Fast Reading Back in a tiny village near Nuremberg, lived a family with eighteen children. Just to keep food on the table for the family members, the father worked almost eighteen hours a day. Two of Albrecht Durer the Elder’s children, Albrecht and Albert, wanted to pursue talent for art, but they knew that their father would never be financially able to send either of them to Nuremberg to study at the academy. After many discussions, the two boys decided to toss a coin. The loser would go down into the nearby mines and, with his earnings, support his brother while he attended the academy. Then, when that brother who won the coin toss completed his studies, he would support the other brother at the academy, either with the sales of his artwork or, if necessary, also by laboring in the mines. They tossed a coin after coming back from church on a Sunday morning. Albrecht Durer won the toss and went off to Nuremberg. Albert went down into the dangerous mines and financed his brother, whose work at the academy was an almost immediate sensation. Albrecht’s etchings (版画), woodcuts (木刻画) and oils were far better than those of most of his professors, and by the time he graduated, he was beginning to earn considerable fees for his commissioned works. When Albrecht Durer returned to his village, the family held a big dinner to celebrate Albrecht’s homecoming. After the meal, Albrecht rose to drink a toast to his beloved brother for the sacrifice that had enabled Albrecht to fulfill his ambition. He said, “Albert, now it is your turn to go to Nuremberg to pursue your dream, and I will take care of you.” Albert rose and glanced down the long table at the faces he loved, and said softly, “No, brother. Look what four years in the mines have done to my hands! The bones in every finger have been smashed at least once, and lately I have been suffering from arthritis (关节炎) so badly in my right hand that I cannot even hold a glass to return your toast, much less make delicate lines on canvas (画布) with a brush.” By now, Albrecht Durer’s hundreds of masterful portraits, sketches and woodcuts hang in every great museum in the world, but most people are familiar with only one of Albrecht Durer’s works. More than merely being familiar with it, you very well may have a reproduction hanging in your home or office. To pay homage to Albert, Albrecht Durer drew his brother’s hands with palms together and thin fingers stretched skyward. He called his drawing “Hands,” but the entire world immediately opened their hearts to his great masterpiece and named it “The Praying Hands.” Statements based on the passage: T 1. The father of Durer family could not afford any child’s study at the academy. F 2. Albrecht and Albert had to toss a coin to decide who should go to the academy, because one of them had to stay at home and help their father. F 3. Before deciding to toss a coin, Albrecht and Albert had many discussions with their father. T 4. Albrecht achieved great success at the academy, and his works were even better than most of his professors’. F 5. Albrecht decided to support Albert’s study at the academy with the sales of his artwork and by laboring in the mines. F 6. Albert said it was too late for him to go to the academy because he was no longer interested in art after working in the mines for many years. F 7. Although Albrecht had many masterful portraits, only one of them has received popular recognition. T 8. Among Albrecht’s works, “Hands” is the one which is reproduced most. T 9. Albrecht created “Hands” in order to show respect and honor for his brother Albert. F 10. People renamed Albrecht’s drawing “The Praying Hands” because they just wanted to pay homage to his great achievement. Section B Passage Reading Passage 1 Valentine’s Day probably has its origin in the ancient Roman celebration called Lupercalia(牧神节). It was celebrated on February 15. In the Roman calendar February was in the spring. The celebration honored the gods Lupercus and Faunus as well as the twin brothers Romulus and Remus, the legendary founders of Rome. As part of the ceremony the priests paired up young men and women. The girls’ names were placed in a box and each boy drew a girl’s name. The couple was paired then until the next Lupercalia. In 260 AD the emperor Claudius II, called Claudius the Cruel, decided that young soldiers would only be distracted by marriage and so ordered that young men may not marry. Valentinus (Valentine), a Christian priest, defied the emperor and got married in secret. He was caught and executed on February 14, the eve of Lupercalia. His name became associated with young love forever after. In 496, Pope Gelasius set aside February 14 to honor him as Saint Valentine and it has been St. Valentine’s Day ever since. In the Middle Ages some of the customs of the Lupercalia still persisted in spite of the attempts of the Church to put an end to these non-Christian customs and Christianize the holiday. Both men and women drew names from a bowl to see who their valentines would be. They would wear the names on their sleeves for a week. Today we still sometimes “wear our hearts on our sleeves” when we cannot conceal our feelings. In the 1600s, it became common to give flowers, particularly the rose, as a sign of love as the “language of flowers”. This came to Europe from Turkey. The color and placement of the rose held a special significance--a red rose, for example, meant beauty. Flowers have been part of Valentine’s Day ever since. D 11. What does the passage mainly tell us? A. The custom of Valentine’s Day. B. A story about how Valentinus defied the emperor. C. The relationship between marriage and religion. D. The origin of Valentine’s Day. B 12. Young soldiers were not allowed to marry because the emperor was afraid that ______. A. they would associate with St. Valentine B. they wouldn’t concentrate on their job C. they would defy the emperor’s order D. they were too young to marry
第一章 质点运动学 1．1 一质点沿直线运动，运动方程为x (t ) = 6t 2 - 2t 3．试求： （1）第2s 内的位移和平均速度； （2）1s 末及2s 末的瞬时速度，第2s 内的路程； （3）1s 末的瞬时加速度和第2s 内的平均加速度． [解答]（1）质点在第1s 末的位置为：x (1) = 6×12 - 2×13 = 4(m)． 在第2s 末的位置为：x (2) = 6×22 - 2×23 = 8(m)． 在第2s 内的位移大小为：Δx = x (2) – x (1) = 4(m)， 经过的时间为Δt = 1s ，所以平均速度大小为：=Δx /Δt = 4(m·s -1)． （2）质点的瞬时速度大小为：v (t ) = d x /d t = 12t - 6t 2， 因此v (1) = 12×1 - 6×12 = 6(m·s -1)， v (2) = 12×2 - 6×22 = 0 质点在第2s 内的路程等于其位移的大小，即Δs = Δx = 4m ． （3）质点的瞬时加速度大小为：a (t ) = d v /d t = 12 - 12t ， 因此1s 末的瞬时加速度为：a (1) = 12 - 12×1 = 0， 第2s 内的平均加速度为：= [v (2) - v (1)]/Δt = [0 – 6]/1 = -6(m·s -2)． [注意] 第几秒内的平均速度和平均加速度的时间间隔都是1秒． 1．2 一质点作匀加速直线运动，在t = 10s 内走过路程s = 30m ，而其速度增为n = 5倍．试证加速度为，并由上述数据求出量值． [证明]依题意得v t = nv o ，根据速度公式v t = v o + at ，得 a = (n – 1)v o /t ， (1) 根据速度与位移的关系式v t 2 = v o 2 + 2as ，得 a = (n 2 – 1)v o 2/2s ，(2) （1）平方之后除以（2）式证得：． 计算得加速度为：= 0.4(m·s -2)． 1．3 一人乘摩托车跳越一个大矿坑，他以与水平成22.5°的夹角的初速度65m·s -1从西边起跳，准确地落在坑的东边．已知东边比西边低70m ，忽略空气阻力，且取g = 10m·s -2．问： （1）矿坑有多宽？他飞越的时间多长？ （2）他在东边落地时的速度？速度与水平面的夹角？ [解答]方法一：分步法． （1）夹角用θ表示，人和车（人）在竖直方向首先做竖直上抛运动，初速度的大小为 v y 0 = v 0sin θ = 24.87(m·s -1)． 取向上的方向为正，根据匀变速直线运动的速度公式 v t - v 0 = at ， 这里的v 0就是v y 0，a = -g ；当人达到最高点时，v t = 0，所以上升到最高点的时间为 t 1 = v y 0/g = 2.49(s)． 再根据匀变速直线运动的速度和位移的关系式：v t 2 - v 02 = 2a s ， 可得上升的最大高度为：h 1 = v y 02/2g = 30.94(m)． 人从最高点开始再做自由落体运动，下落的高度为;h 2 = h 1 + h = 100.94(m)． 根据自由落体运动公式s = gt 2/2，得下落的时间为:= 4.49(s)． 因此人飞越的时间为：t = t 1 + t 2 = 6.98(s)． 人飞越的水平速度为;v x 0 = v 0cos θ = 60.05(m·s -1)， v a 2 2(1)(1)n s a n t -= +2 2(1)(1)n s a n t -= +2 2(51)30 (51)10 a -= +2 22h t g =70m 22.5o 图1.3