问题 问答题

如图5-7-4所示,在水平固定的光滑平板上,有一质量为m的质点P与穿过中央小孔O的轻绳一端相连着,平板与小孔都是光滑的,用手拉着绳子下端,使质点做半径为A、角速度为ω0的匀速圆周运动.若绳子突然放松至某一长度B而立即被拉紧,质点就能在半径为B的圆周上做匀速圆周运动.求质点由半径A到半径B所需的时间及质点在半径为B的圆周上运动的角速度.

图5-7-4

答案

.

本题考查利用圆周运动、离心运动以及运动的合成和分解等知识综合分析、处理问题的能力.要注意分析质点的运动过程,要明确绳松开后,向心力突然消失,质点沿切线方向飞出,沿光滑平板做匀速直线运动,这是该题的易错点.

质点在半径为A的圆周上以角速度ω0做匀速圆周运动,其线速度为:va=ω0a

图5-7-5

突然松绳后,向心力消失,质点沿切线方向飞出,以va的速度做匀速直线运动,直到质点mO点的距离为B时,绳子将被拉直.如图5-7-5所示,作出质点这一过程的俯视图,则质点在匀速直线运动中的位移:

因此质点m由半径AB所需的时间为:.

当线刚被拉直时,质点的速度为:vA=ω0A

把这一速度分解为垂直于绳的速度vb和沿绳的速度vb′,在绳绷紧的过程中vb′减为零,质点就以vb沿着半径为B的圆周做匀速圆周运动.设其角速度为ω,根据相似三角形得:,即,则质点沿半径为B的圆周做匀速圆周运动的角速度为:.

问答题

In my children’s lifetimes, I believe gorillas, chimpanzees and orangutans will all become extinct in the wild. So the question we have to ask ourselves is this: do we want our children to see only in zoos what used to exist in the real world (46) It is the great apes that will disappear first, because there are so few of them left, and because they’re so vulnerable to changes in their habitats.

Many of the threats to these animals result from a global economy not local pressures. The threat to the orangutan in Indonesia, for example, is largely a result of deforestation and the risks to primates in Africa result from the timber-trade and the demand for bush-meat. (47) The two work together: logging opens up the forest, which means that the bush-meat can be got out fast, to Kinshasa or to London.

(48) If we want to avoid the disaster scenario, people in developed countries will have to take a global perspective and accept responsibility for the damage export crops such as timber, coffee, cut flowers or even green beans, do to the environment. The challenge is to avoid simply imposing western attitudes on local peoples.

Already there are no truly wild places left in the world. (49) Looking at wildlife has become the preserve of the middle classes over the last twenty-odd years, and as wild animals become even rarer, so more tourists want to see them. But tour ism alone plainly cannot conserve the world’s animals; economic development is the priority.

For the future, I suspect that ff you really want to do something about wild life conservation, you would be better off putting your money into women’s education rather than just into the protection of flagship species. (50) Women often bear the direct costs of wildlife conflict; their knowledge of how to deal with conflict and how to control their own reproductive destinies may yet determine the survival of many threatened species.

If we want to avoid the disaster scenario, people in developed countries will have to take a global perspective and accept responsibility for the damage export crops such as timber, coffee, cut flowers or even green beans, do to the environment.

多项选择题