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如图所示，质量分别为M和m的两个小球A、B套在光滑水平直杆P上，整个直杆被固定于竖直转轴上，并保持水平，两球间用劲度系数为K，自然长度为L的轻质弹簧连接在一起，左边小球被轻质细绳拴在竖直转轴上，细绳长度也为L，现欲使横杆P随竖直转轴一起在水平面内匀速转动，其角速度为ω，求当弹簧长度稳定后，细绳的拉力和弹簧的总长度各为多少？

答案

设直杆匀速转动时，弹簧伸长量为x，

对A球有：FT-F=Mω2L

对B球有：F=mω2（2L+x）

F=Kx

解以上方程组可得：FT=Mω2L+

2mω2KL
K-mω2

x=

2mω2L
K-mω2

则弹簧的总长为：L′=L+

2mω2L
K-mω2
=
K+mω2
K-mω2
L

答：当弹簧长度稳定后，细绳的拉力为FT=Mω2L+

2mω2KL
K-mω2
，弹簧的总长度为
K+mω2
K-mω2
L．

阅读理解

Are two holidays not enough? Do you dream of three, or even four? (61)这不再是梦想! Last month, the State Council(国务院) encouraged primary and high schools to give students a spring or autumn break without changing the total number of student vacation days.

Students in China currently only have long holidays in two seasons —summer and winter. These holidays are usually 10 to 12 weeks in total.“If we had spring and autumn breaks, (62)I would have time to taste all four seasons instead of burying (埋) myself in my studies,”Gao Yiran, a 15-year-old boy told China Daily. Seasonal holidays during autumn and spring may be something new in China, but not in other countries.

In the US, students usually have three holidays. Summer holiday is the longest one, and runs from mid-June until early September. Summer camp is one of kids’ favorite places to go to, where they can make new friends and try some new activities. Winter holiday starts from mid-December and ends in early January. Most kids and their parents go to spend time together over the Christmas period. Spring break comes in mid- March and (63) it is usually a 10-day holiday.

Schools in Japan start in April, as most people think that spring is the perfect time for new things. For school children ,summer holiday lasts from July 20 to August 31. Most kids are busy with club activities including sports and dancing. Spring break starts at the end of March and continues till early April. It is a good chance for a short family trip around the city.

阅读短文，按要求完成下面的任务。

任务一　将61处的中文翻译成英文。

任务二　将62处斜体部分的英文翻译成中文。

任务三　写出63处“it”指代的内容。

任务四　64.What do Japanese kids usually do in their spring break?

任务五　65.为该文段拟写一个标题。
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单项选择题

下述风湿性病变中，哪一项对机体危害最大()

A．反复发作的环形红斑

B．反复发作的风湿性心内膜炎

C．反复发作的风湿性关节炎

D．风湿性动脉炎

E．风湿性皮下结节
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