问题 问答题

如图所示,半径为R、圆心为O的大圆环固定在竖直平面内,两个轻质小圆环套在大圆环上.一根轻质长绳穿过两个小圆环,它的两端都系上质量为m的重物,忽略小圆环的大小。

(1)将两个小圆环固定在大圆环竖直对称轴的两侧θ=30°的位置上(如图).在-两个小圆环间绳子的中点C处,挂上一个质量M=m的重物,使两个小圆环间的绳子水平,然后无初速释放重物M.设绳子与大、小圆环间的摩擦均可忽略,求重物M下降的最大距离.

(2)若不挂重物M.小圆环可以在大圆环上自由移动,且绳子与大、小圆环间及大、小圆环之间的摩擦均可以忽略,问两个小圆环分别在哪些位置时,系统可处于平衡状态? 

答案

(1) 重物M下降的最大距离

(2)平衡时,两小圆环在大圆环竖直对称轴两侧角的位置上

(1)重物向下先做加速运动,后做减速运动,当重物速度为零时,下降的距离最大.设下降的最大距离为,由机械能守恒定律得

解得 

(另解h=0舍去)

(2)系统处于平衡状态时,两小环的可能位置为

a.两小环同时位于大圆环的底端.

b.两小环同时位于大圆环的顶端.

c.两小环一个位于大圆环的顶端,另一个位于大圆环的底端.

d.除上述三种情况外,根据对称性可知,系统如能平衡,则两小圆环的位置一定关于大圆环竖直对称轴对称.设平衡时,两小圆环在大圆环竖直对称轴两侧角的位置上(如图所示).

对于重物,受绳子拉力与重力作用,有:

对于小圆环,受到三个力的作用,水平绳子的拉力、竖直绳子的拉力、大圆环的支持力.两绳子的拉力沿大圆环切向的分力大小相等,方向相反

,而,所以

问答题 简答题
单项选择题

American Museum of Natural History is one of the largest natural and historic museums in the world and one of the main natural history research and education centres in the United States, set up in 1869 and located in the west of the Central Park, Manhattan District, New York. It (1) 7 hectares in its total area, (2) classical types of buildings. The (3) of ancient creatures and humanity is (4) the first place of all the museums in the world, (5) the representative samples from South America, Africa, Europe, Asia and Australia were collected, besides those from the (6) country, the United States.

In the museum, there are five kinds of exhibits, including astronomy, mineralogy, human history, and animals in the (7) times and those in modern times. There are thirty-eight exhibition halls with different (8) from 500 to 1,500 square metres. Besides these, there is a Roosevelt Memorial Hall in (9) of President Roosevelt who supported the (10) of the museum, which is also used to have a special exhibition, showing the new important (11) on natural sciences and (12) affairs and social problems, and special topics connected closely with the life of the citizens. Besides this, it is also used for avocation (13) to have all kinds of scientific activities in the laboratories, centres of natural science and centres for citizens. There are more than 10 (14) research departments mainly (15) for collection of samples, research and work of publication.

In the museum, there are (16) and sub-libraries of Aulspond ancient amniote, with about 300 thousand books and magazines (17) natural history, many of (18) are very valuable monographs for the first edition. It has published many expert books and magazines, and a large number of propaganda materials, (19) which are the two magazines, Natural History and Members of Museum that have the biggest (20) of their magazines.

12()

A.present

B.crucial

C.current

D.prevalent