问题 问答题

如图所示,ABC为一细圆管构成的

3
4
圆轨道,将其固定在竖直平面内,轨道半径为R(比细圆管的半径大得多),OA水平,OC竖直,最低点为B,最高点为C,细圆管内壁光滑.在A点正上方某位置有一质量为m的小球(可视为质点)由静止开始下落,刚好进入细圆管内运动.已知细圆管的内径稍大于小球的直径,不计空气阻力.

(1)若小球经过C点时恰与管壁没有相互作用,求小球经过C点时的速度大小;

(2)若小球刚好能到达轨道的最高点C,求小球经过最低点B时的速度大小和轨道对小球的作用力大小;

(3)若小球从C点水平飞出后恰好能落回到A点,求小球刚开始下落时距离A点的高度.

答案

(1)设通过C点时小球速度为vc

小球与管壁没有相互作用,则重力充当向心力,即:mg=

m
v2c
R

解得:vc=

gR

(2)小球恰好通过C点,故小球通过C点的速度为零,

对小球由B到C的过程根据动能定理,有:0-

1
2
m
v2B
=mg2R ①

又由小球经过B点时,由牛顿第二定律:FN-mg=

m
v2B
R

①②联立可得:vB=2

Rg
,FN=5mg

(3)小球从C点飞出后做平抛运动,

竖直方向:R=

1
2
gt2

水平方向:R=vc′t

解得:vc′=

gR
2

由初末机械能守恒可得:mg(h-R)=

1
2
m
v′2c

解得:h=

5
4
R

答:(1)若小球经过C点时恰与管壁没有相互作用,小球经过C点时的速度大小为

gR

(2)若小球刚好能到达轨道的最高点C,小球经过最低点B时的速度大小为2

Rg
,轨道对小球的作用力大小为5mg;

(3)若小球从C点水平飞出后恰好能落回到A点,小球刚开始下落时距离A点的高度为

5
4
R.

阅读理解

(B)

People can be addicted to different things — e.g. alcohol, drug, certain foods, or even television. People who have such an addiction are compulsive: they have a very powerful psychological need that they feel they must satisfy. According to psychologists, many people are compulsive spenders. They feel that they must spend money. This compulsion, like most others, is impossible to explain reasonably. For compulsive spenders who buy on credit, charge accounts are even more exciting than money. In other words, compulsive spenders feel that with credit, they can do anything. Their pleasure in spending large amounts is actually greater than the pleasure that they get from the things they buy.

There is even a special psychology of bargain hunting. To save money, of course, most people look for sales, low prices, and discounts. Compulsive bargain hunters, however, often buy things that they don’t need just because they are cheap. They want to believe that they are helping their budgets, but they are really playing an exciting game. When they can buy something for less than other people, they feel that they are winning. Most people, experts claim, have two reasons for their behavior: a good reason for the things that they do and the real reason.

It is not only scientists, of course, who understand the psychology of spending habits, but also business people. Stores, companies, and advertisers use psychology to increase business. They consider people’s needs for love, power, or influence, their basic values, their beliefs and opinions, and so on in their advertising and sales methods.

Psychologists often use a method called “behavior therapy(疗法)” to help individuals solve their personality problems. In the same way, they can help people who feel that they have problems with money.

60.According to the psychologists, a compulsive spender is one who spends large amounts of

money _____.

A. and takes great pleasure from what he or she buys

B. in order to satisfy his or her basic needs in life

C. just to meet his or her strong psychological need

D. and feels he or she is cheated

61. Which of the following statements is TRUE according to the text?

A. People spend money for exactly the same reason that they need to buy things.

B. Business people and advertisers can use the psychology of people’s spending habits to

increase sales.

C. Business people understand the psychology of compulsive buying better than scientists do.

D. Compulsive bargain hunters do not have problems with money.

62. What is the text mainly about?

A. The psychology of money-spending habits. 

B. The habits of compulsive spenders.

C. A special psychology of bargain hunting.

D. The use of the psychology of spending habits in business.

63.From the text we may safely conclude that compulsive spenders or compulsive bargain hunters

_______________.

A. are really unreasonable         B. need special treatment

C. are really beyond drugs        D. can never get any help to solve their problems with money

单项选择题