问题 计算题

如图所示,一对杂技演员(都视为质点)乘秋千(秋千绳处于水平位置)从A点由静止出发绕O点下摆,当摆到最低点B时,女演员在极短时间内将男演员沿水平方向推出,然后自己刚好能回到高处A。求男演员落地点C与O点的水平距离x。已知男演员质量m1和女演员质量m2之比,秋千的质量不计,秋千的摆长为R,C点比O点低5R。

答案

解:设分离前男女演员在秋千最低点B的速度为v0,由机械能守恒定律有

 

设刚分离时男演员速度的大小为v1,方向与v0相同;女演员速度的大小为v2,方向与v0相反,由动量守恒定律有

(m1+m2)v0=m1v1-m2v2

分离后,男演员做平抛运动,设男演员从被推出到落在C点所需的时间为t,根据题给条件,由运动学规律得4R=

根据题给条件,女演员刚好回到以A点,由机械能守恒定律得

已知m1=2m2,由以上各式可得x=8R

单项选择题

It’s easy to get the sense these days that you’ve stumbled into a party with some powerful drug that dramatically alters identity. The faces are familiar, but the words coming out of them aren’t. Something has happened to a lot of people you used to think you knew. They’ve changed into something like their own opposite.

There’s Bill Gates, who these days is spending less time earning money than giving it away--and pulling other billionaires into the deep end of global philanthropy(慈善事业) with him. There’s historian Francis Fukuyama, leading a whole gang of disaffected fellow travelers away from neoconservatism. To flip-flopis human. It can still sometimes be a political liability, evidence of a flaky disposition or rank opportunism. But there are circumstances in which not to reverse course seems almost pathological(病态的). He’s a model of consistency, Stephen Colbert said last year of George W. Bush:" He believes the same thing Wednesday that he believed on Monday -- no matter what happened on Tuesday."

Over the past three years, I found people who had pulled a big U-turn in their lives. Often the insight came in a forehead-smiting moment in the middle of the night: I’ve got it all wrong.

It looked at first like a sprinkling of outliers beyond the curve of normal human experience. But when you stepped back, a pattern emerged. What these personal turns had in common was the apprehension that we’re all connected. Everything leans on something, is both dependent and depended on.

"The difference between you and me," a visiting Chinese student told University of Michigan psychologist Richard Nisbett not long ago," is that I think the world is a circle, and you think it’s a line." The remark prompted the professor to write a book, The Geography of Thought, about the differences between the Western and the Asian mind.

To Western thinking, the world is linear; you can chop it up and analyze it, and we can all work on our little part of the project independently until it’s solved. The classically Eastern mind, according to Nisbett, sees things differently: the world isn’t a length of rope but a vast, closed chain, incomprehensibly complex and ever changing. When you look at life from this second perspective, some unlikely connections reveal themselves.

I realized this was what almost all the U-turns had in common: people had swung around to face East. They had stopped thinking in a line and started thinking in a circle. Morality was looking less like a set of rules and more like a story, one in which they were part of an ensemble cast, no longer the star.

Which of the following is the best title for this text()

A. The Age of U-Turns

B. Western and Eastern Cultural Differences

C. A Circle World

D. The Importance of Change

多项选择题