问题 计算题

如图所示,质量为3 m的足够长木板C静止在光滑水平面上,质量均为m的两个小物体A、B放在C的左端,A、B间相距s0,现同时对A、B施加水平向右的瞬时冲量而使之分别获得初速度v0和2v0,若A、B与C之间的动摩擦因数分别为μ和2μ,则

(1)最终A、B、C的共同速度为多大?

(2)求运动过程中A的最小速度?

(3)A与B最终相距多远?

(4)整个过程中A、B与木板C因摩擦所产生的热量之比为多大?

答案

(1)0.6v0  (2)vAC=0.5v0  v0=vB

(3)    (4)527

(1)由于A、B、C三个物体构成的系统在水平方向不受外力,所以由动量守恒定律可得

mv0+2mv0=5mv

最终A、B、C的共同速度为

v=0.6v0.

(2)设经t时间A与C恰好相对静止,此时A的速度最小,设为vAC,此时B的速度为vB,由动量守恒和动量定理得

mv0+2mv0=4mvAC+mvB

-μmgt=m(vAC-v0)

(μmg+2μmg)t=3mvAC

解得vAC=0.5v0  vB=v0.

(3)在A与C相对静止前,三个物体的加速度大小分别为aA==μg  aB==2μg  aC==μg

A、B做匀减速运动,C做匀加速运动;在A与C相对静止后,三个物体的加速度大小又分别为

aA′=aC′=μg  aB′=aB=2μg

当A、C相对静止后,A、C做匀加速运动,B做匀减速运动,最终三个物体以共同速度匀速运动.在开始运动到三个物体均相对静止的过程中A、B相对于地面的位移分别为

sA=

sB=

所以,A与B最终相距

Δs=s0+sB-sA=s0+0.425

(4)设整个运动过程中A相对于C滑行距离为s,则B相对于C滑行的距离为s+Δs-s0,由动能定理得

μmgs+2μmg(s+Δs-s0)=

QA=μmgs

QB=2μmg(s

+Δs-s0)

解得

整个过程中A、B与木板C因摩擦所产生的热量之比为

阅读理解

阅读理解

     From the beginning of human history, wild animals provided food, clothing and sometimes medicine

for man. We may not depend as much on wild animals now. But we hear about them every day.

Americans use the names of animals in many ways. Automobile manufacturers and gasoline companies

especially like to use big cats to sell their products. They like lions, tigers and wildcats. When Americans

say wildcat, they usually mean a_lynx, an_ocelot_or_a_bobcat. All these cats attack quickly and fiercely.

So wildcats represent something fast and fierce.  

     An early American use of the word wildcat was quite different. It was used to describe members of

Congress who declared war on Britain in 1812. A magazine of that year said the wildcat congressmen

went home. It said they were unable to face the responsibility of having involved their country in an

unnecessary war.

     Wildcat also has been used as a name for money in the 1800s. At that time, some states permitted

banks to make their own money. One bank in the state of Michigan offered paper money with a picture

of a wildcat on it. Some banks, however, did not have enough gold to support all the paper money they

offered. So the money had little or no value. It was called a wildcat bill or a wildcat banknote. The

banks who offered this money were called wildcat banks. A newspaper of the time said those were the

days of wildcat money. It said a man might be rich in the morning and poor by night.

     Wildcat then was also used for an oil well or gold mine that had almost no oil or gold in it. Dishonest

developers would buy such property. Then they would sell it and leave town with the money. The

buyers were left with worthless holes in the ground.Today, wildcat oil wells are in areas that are not

known to have oil.

1. What is the main idea of the passage?

A. Wildcats and their stories.

B. Wildcats and their characters.

C. Varieties of animal species.

D. Relationship between animals and humans.

2. From the passage we can know that__________.

A. wildcats represent the state of Michigan

B. the use of wildcats was not always the same

C. wildcats are the best friend of human beings

D. honest developers never buy wildcat oil wells

3. The underlined words "a lynx, an ocelot or a bobcat" in Paragraph 1 may refer to "__________".

A. gasoline companies

B. automobile manufacturers

C. names of wildcats

D. brands of automobile

4. Which of the following would people like to have or trust according to the passage?

A. Wildcat congressmen.  

B. Wildcat oil wells.

C. Wildcat banks.  

D. Wildcat cars.

5. It can be inferred that during the days of wildcat money__________.

A. people couldn't buy anything with the money

B. people didn't know how to save money

C. the rich invested too much on oil wells

D. people complained and suffered a lot

单项选择题