Posts Tagged ‘science’

为什么牛顿第一定律不是第二定律的特例

Monday, July 21st, 2008

做物理作业,看到这样一句话,说:牛顿第一定律是独立的一条定律,绝不能简单地看成牛顿第二定律的特例。于是,我就不理解了,再于是, Google 之,找到一些,但是不太清楚, 于是 Wikipedia ,在英文版找到了答案: http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_first_law:_law_of_inertia

Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.[8]

This law is also called the law of inertia.

This is often paraphrased as "zero net force implies zero acceleration", but this is an over-simplification. As formulated by Newton, the first law is more than a special case of the second law. Newton arranged his laws in hierarchical order for good reason (for example, see Gailili & Tseitlin[9], or Woodhouse[10]). The significance of the first law is to establish frames of reference for which the other laws are applicable, such frames being called inertial frames.

To understand why the laws are restricted to inertial frames, consider a ball at rest within an accelerating body: an airplane on a runway will suffice for this example. From the perspective of anyone within the airplane (that is, from the airplane's frame of reference when put in technical terms) the ball will appear to move backwards as the plane accelerates forwards (the same feeling as being pushed back into your seat as the plane accelerates). This motion appears to contradict Newton's second law as, from the point of view of the passengers, there appears to be no force acting on the ball that would cause it to move. The reason why there is in fact no contradiction to the second law is because Newton's second law (without modification) is not applicable in this situation: Newton's first law does not apply because the stationary ball does not remain stationary. Thus, it is important to establish whether the various laws are applicable or not, inasmuch as they are not applicable in all situations.[11] To summarize:[10]

There is a class of frames of reference (called inertial frames) relative to which the motion of a particle not subject to forces is a straight line.

来翻译一下吧,就当是练习英语了,我想我不翻译大家也能看得懂吧:

一切物体总保持匀速直线运动状态或静止状态,直到有外力迫使它改变这种状态为止。

牛顿第一定律也叫做惯性定律。

牛顿第一定律经常解释为“外力为零加速度就为零”,但是这其实被过度简化了。按照牛顿所阐述的,牛顿第一定律不只是牛顿第二定律的特例。牛顿这样分层次安排定律有着很好的理由(比如说,Gailili & Tseitlin[9]和Woodhouse[10])。第一定律的重要性在于它建立了一种其他定律可以应用的参考系,这种参考系叫做惯性系。

想要理解为什么牛顿运动定律只能应用于惯性系,我们考虑一个在加速运动的物体中的静止小球,比如跑道上的飞机。从飞机内的人的视角看(用物理语言说就是把飞机作为参考系),由于飞机正在向前加速,小球似乎要向后运动(就像飞机加速的时候你被向后推的感觉一样)。这种运动好像跟牛第二定律冲突。因为,从地面上人的视角看,好像没有力作用在小球上使它运动。事实上,这并不与牛顿第二定律冲突。其原因是牛顿第二定律(未添加惯性力)在这种情况下不适用。因为原先静止的球现在不保持静止了,所以牛顿第一定律也不适用。由于这些定律并不是总适用,因此有必要确定这些定律是否使用。简单来说:

有这样一种参考系,叫做惯性系。相对于它来观察,不受外力作用的物体的运动为直线运动。

翻译貌似还是不好,唉……英语就这水平了……

谁有什么好的建议,欢迎拍砖。

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除数为什么不能为零

Wednesday, July 5th, 2006

小学老师曾经讲过除数为什么不能为零,好像是说不能把一堆东西分成0份,所以除数不能为零(除数为零没有意义),现在听来,这好像说不过去。我试着用反正法证了一下,老师、同学看看有没有问题。

证明全文:docx格式

已知:实数a、b、c中,a/b=c

求证:b不能等于0

证明:假设b=0

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