问题 计算题

在一种新的“子母球”表演中,让同一竖直线上的小球A和小球B,从距水平地面高度为php>1)和h的地方同时由静止释放,如图所示。球A的质量为m,球B的质量为3m。设所有碰撞都是弹性碰撞,重力加速度大小为g,忽略球的直径、空气阻力及碰撞时间。

(1)求球B第一次落地时球A的速度大小;

(2)若球B在第一次上升过程中就能与球A相碰,求p的取值范围;

(3)在(2)情形下,要使球A第一次碰后能到达比其释放点更高的位置,求p应满足的条件。

答案

(1)A球速率 (2)1<p<5   (3)1<p<3

(1)由于两球同时释放,所以球B第一次落地时A球下落的高度为h,设此时A球的速度大小为v0,由可得,

(2)球B第一次落地并与地发生弹性碰撞后做竖直上抛运动。

若球B上升到最大高度h处时刚好与球A发生碰撞,设此时球A自由下落的时间tA,则=h,此时球A自由下落的高度。联立以上两式,可得hA=4h,则ph=hA+h=5h,所以p=5。

若球B在第一次上升过程中就能与球A相碰,则p的取值范围应为1<p<5。

(3)设球B第一次落地并与地发生弹性碰撞后又上升了时间t就与球A相碰,则球A、B在空中碰前的速度大小分别为有,设它们碰后的速度分别为,选竖直向上为正方向,两球发生弹性碰撞,根据动量守恒和能量守恒,

联立解得,

碰撞时,A球自由下落的高度,B球竖直上升的高度

联立解得,即要使球A第一次碰后能到达比其释放点更高的位置

【考点定位】考查自由落体运动、竖直上抛运动、弹性碰撞等考点,意在考查考生的分析综合能力。

多项选择题
单项选择题

Historically, although the children of immigrants may have grown up bilingual and bicultural, many did not pass on much of their parents’ language or culture to their own children. Thus, many grandchildren of immigrants do not speak the language of the old country and are "American" by culture. However, in some parts of the country with established communities that share a common language or culture, bilingualism and biculturalism continue. This is particularly true in communities where new immigrants are still arriving. In general, cultural pluralism (多元化) is more accepted in the United States today than it was in the first half of the 20th century and many of the school systems have developed bilingual programs and multicultural curricula.

At the close of the 20th century, there seemed to be a rise in the consciousness of ethnic groups around the world, and a sense of pride in what makes them unique. This occurs in the United States among many different groups, and in some cases it has resulted in new names to symbolize each group’s identity. In the United States, people have become very sensitive to the language used to describe these groups, and they try to be "politically correct" (P. C. ). For example, many black Americans, particularly young people, prefer the term African-American instead of black, to identify with their African heritage. Some Spanish speakers prefer to be called Latinos (referring to Latin America) instead of Hispanics, while others prefer to be identified by their country of origin (Cuban-American or Cuban, Chicano, Mexican-American or Mexican, and so on).

In spite of some very important differences, however, there is still a tie that binds Americans together. That tie is a sense of national identity—of "being an American" . Incidentally, when citizens of the United States refer to themselves as Americans, they have no intention of excluding people from Latin American countries. There is no word such as United Statesians in the English language, so people call themselves Americans. Thus, what is really a language problem has sometimes caused misunderstandings. Although citizens of Latin American countries may call the people in the United States North Americans, to most people in the United States this makes no sense either, because the term North Americans refer to Canadians and Mexicans as well as citizens of the United States. The word American, then, will be used in this text as the adjective and nationality for the people who live in the United States of America.

Many black Americans prefer to be called "African Americans" instead of "blacks" because ()。

A. they want to be equal to the whites

B. they want to identify with their African heritage

C. they want to be politically correct

D. they want to improve their social status