问题 填空题

湖边水池高度为h,放满水时池中水总质量为m,设水池下底边与湖面相平,抽放水时忽略湖水水位变化,一台抽水机的出水口刚好在水池的上边缘,而进水管可移动.那么向空水池灌满水至少需做功______,把整池水抽空需做功______.

答案

由于出水口刚好在水池的上边缘,

所以水至少要抽到水池的上边缘,之后水自动流入水池中,任何时刻进水口正好与水面相切时做功最少

由于抽放水时忽略湖水水位变化,所以所有水都要从湖面上升到水池的上边缘,即上升高度为h.

在灌水的过程中水的重力势能增加量为mgh,根据功能关系,向空水池灌满水至少需做功mgh.

由于进水管可移动,整池水的重心在距池底

1
2
h高度,把整池水抽空过程中,整池水上升高度为
1
2
h,

整池水的重力势能增加量为

1
2
mgh.根据功能关系,把整池水抽空需做功为
1
2
mgh.

故答案为:mgh,

1
2
mgh

问答题
问答题

The idea of evolution was known to some of the Greek philosophers. (46) By the time of Aristotle, speculation had suggested that more perfect types had not only followed less perfect ones but actually had developed from them. But all this was guessing; no real evidence was forthcoming. When, in modern times, the idea of evolution was revived, it appeared in the writings of the philosophers—Bacon, Descartes, Leibniz and Kant. Herbert Spencer was preaching a full evolutionary doctrine in the years just before Darwin’s book was published, while most naturalists would have none of it. Nevertheless a few biologists ran counter to the prevailing view, and pointed to such facts as the essential unity of structure in all warm-blooded animals.

(47) The first complete theory was that of Lamarck, who thought that modifications due to environment, if constant and lasting, would be inherited and produce a new type. (48) Though no evidence for such inheritance was available, the theory gave a working hypothesis for naturalists to use, and many of the social and philanthropic efforts of the nineteenth century were framed on the tacit assumption that acquired improvements would be inherited.

But the man whose book gave both Darwin and Wallace the clue was the Reverend Robert Malthus, sometime curate of Albury in Surrey. The English people were increasing rapidly, and Malthus argued that the human race tends to outrun its means of subsistence unless the redundant individuals are eliminated. This may not always be true, but Darwin writes:

(49) In October 1838, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on, from long continued observation of the habits of animals and plants, it at once struck me that, under these circumstances, favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species. Here then I had a theory by which to work.

The hypothesis of natural selection may not be a complete explanation, but it led to a greater thing than itself—an acceptance of the theory of organic evolution, which the years have but confirmed. Yet at first some naturalists joined the opposition. (50) To the many, who were unable to judge the biological evidence, the effect of the theory of evolution seemed incredible as well as devastating, to run counter to common sense and to overwhelm all philosophic and religious landmarks. Even educated man, choosing between the Book of Genesis and the Origin of Species, proclaimed with Disraeli that he was "on the side of the Angels.

(49) In October 1838, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on, from long continued observation of the habits of animals and plants, it at once struck me that, under these circumstances, favourable variations would tend to be preserved, and unfavourable ones to be destroyed.