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Archive for the ‘Magical Physics’ Category

初等数学证明开普勒第二定律

Posted in Magical Physics  by Eagle Fantasy on February 8th, 2007

开普勒第二定律是这么说的:在相等的时间内,行星与恒星的连线扫过的面积相等。当我第一眼看到这条定律的时候,觉得非常神奇,而当我看到了这个定律的证明时,不禁更觉神奇了!下面我把从《物理定律的本性》上看到的关于这个定理的证明简要写下来供大家欣赏。

如图,O为恒星,直线AC为行星不受引力时的轨迹。设行星从A到B、从B到C所用的时间间隔Δt相等,A处的时刻为t1,B为t2,C为t3。现在假设行星不受O的引力作用,那么这时扫过的面积SΔABO和SΔBCO相等(等底同高)。现在行星受到引力作用了,因为引力的方向时刻指向恒星,所以在从t1到t3这段时间里,行星所受的引力的方向的总效果应该沿着BO方向(这需要一点向量的知识)。因此,t3时刻行星的位置C’应该由两个向量相加而得到:向量AC+向量CC’(作CC’平行于BO,因此沿BO方向的向量等价于CC’)。这样,SΔBCO=SΔBC’O(同底等高)。因此,SΔBC’O=SΔABO。因为Δt是任取的,所以在相等的时间内,行星与恒星的连线扫过的面积相等。

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A Funny Mistake

Posted in Magical Physics  by Eagle Fantasy on January 14th, 2007

At noon that day, we found a strange phenomenon. She Fei’s bottle, which was half filled with boiled water, had many bubbles going up from the bottom to the top, with the sound of ‘zizizizi’. It’s so interesting that Zhang Cheng , Wang Wenkai and I came to explain it. I observed the bottom of the bottle, and found that there was a scratch on the bottom. I remembered a TV show, which said a scratch may cause water boil if the water has a high enough temperature and a too smooth pot cannot boil the water. So I guessed that phenomenon might be cause by the scratch, the scratch made the water boil. Wang said the scratch might cause the pressure decrease, so the lower decrease cause the water reach its boil temperature. Then he thought of a method to prove his assume. He asked Zhang to open the cap of the bottle to see whether he was correct. Zhang opened it carefully, and he was surprised that his left hand beneath the bottle felt very hot at the moment the cap was opened and the bubble stopped to travel! He was puzzled. I observed the bottle again, and I found that there was some water on my hand beneath the bottle! Ahhhh, I made the final correct conclusion: the bottle leaked!!!

According to this funny mistake, I know that we shouldn’t make a conclusion too quickly without thinking deeply, and we shouldn’t believe an assumption without experiment. We should observe a phenomenon carefully, think about it deeply, and have a small experiment to prove the assumption. Maybe a reason of a strange thing is very easy, and we should remember it forever!

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找棒状物重心的简单办法

Posted in Magical Physics  by Eagle Fantasy on January 14th, 2007

分别用两手的食指支持住棒的两端,之后两手同时用力渐渐向中间并拢。这时,你会惊奇的发现,在任意时刻,只有一根手指头相对于棒在滑动,而另一只手指则会相对静止,尽管两只手都在用力。最终,两手靠在一起,这个地方一定就是棒的重心。其道理,主要是静摩擦力以及转轴平衡的知识。

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纸的承受能力竟然是如此之大

Posted in Magical Physics  by Eagle Fantasy on January 7th, 2007

前几天,强人王鸿飞和我们讨论了一个奇特的现象。
大家都认为,纸是很脆弱的,但事实上纸的承受能力惊人的大,不信你可以做个实验看看。
拿一张没有褶皱没有裂缝的纸,双手握住纸的两边(注意是握住,而不是用指头捏住或掐住,目的是尽量减小纸在手处的扭曲形变),使劲用力拉纸,无论你用多大的力气你也不可能把纸从中间拉断。纸就算断了,也一定是从你的手那里断的,那里发生了扭曲形变。
神奇吧!分子力就是这么神奇,物理就是这么神奇!

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一根钉子上搭上六根钉子

Posted in Magical Physics  by Eagle Fantasy on January 3rd, 2007

现在给你一个固定好的尖朝下竖直的钉子,如何才能在它上面搭上六根钉子呢?不准用任何辅助工具,例如磁铁、胶水、绳子等等。也不准用手扶着让他不倒。

这不是脑筋急转弯,要的不是小聪明式的耍花招的回答,而是完全根据物理知识,在实际生活中能够做到的答案!

很多人看到我做成功了之后,都大惊:原来可以这样!如果绞尽脑汁也想不到的话,可以看一看下面的答案,是我搭上六根钉子后拍下来的两张照片。你一定会恍然大悟的!不过,这个也是有一定技术含量的,即使知道应该怎么打也不一定能打出来,还得练技术!

答案: Read the rest of this entry »

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