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bruce2g
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The recent PBS special, Einstein's Big Idea, is well worth watching (it's a history of e = mc^2). One reason is that in the first hour, it traces the historical development of the concepts of mass, energy, electricity and magnetism and electromagnetism in the 1700's and 1800's.
One item of interest to some members of this forum concerns a debate about whether an object's energy should be proportional its velocity, or should be proportional to the square of its velocity. A segment of this program deals with that debate. According to the program, Newton favored the first approach, but Leibnitz the second.
This is similar to the question of whether energy should be Force*Time or Force*Distance, which has arisen in this forum a few times. If you think energy should be Force*Time (i.e., how long you hold down the gas pedal), then you'll favor energy proportional to velocity. If you favor Force*Distance, then you'll get energy proportional to velocity squared.
Mme. Emilie du Châtelet, at French woman who published works on both Newton and Leibnitz around 1740 or so, tackled this problem by asking the following questions: if I drop a weight 1 foot, it achieves a velocity of v. How far do I need to drop it to achieve a velocity of 2v?
The answer is -- 4 feet!
And, how far do I drop it to get a velocity of 3v?
The answer is 9 feet.
They show a reenactment of the experiment on the show about half way through, and you can do it yourself if you want.
So, if you believe that an object dropped 4 feet has 4 times the energy as an object dropped 1 foot, then the energy must be proprtional to the velocity squared, and also proportional to F*X.
Incidentally, the Mme. de Châtelet died after childbirth before all of her results could be published, and the PBS show notes that it was another 100 years or so before there was universal acceptance of energy being proportional to v squared.
Bruce Zweig
The show is covered on the web site: http://www.pbs.org/wgbh/nova/einstein/
(click on Ancestors of E = mc2 for all of the history)
de Châtelet is covered at:
http://www.pbs.org/wgbh/nova/einstein/ance-sq.html
One item of interest to some members of this forum concerns a debate about whether an object's energy should be proportional its velocity, or should be proportional to the square of its velocity. A segment of this program deals with that debate. According to the program, Newton favored the first approach, but Leibnitz the second.
This is similar to the question of whether energy should be Force*Time or Force*Distance, which has arisen in this forum a few times. If you think energy should be Force*Time (i.e., how long you hold down the gas pedal), then you'll favor energy proportional to velocity. If you favor Force*Distance, then you'll get energy proportional to velocity squared.
Mme. Emilie du Châtelet, at French woman who published works on both Newton and Leibnitz around 1740 or so, tackled this problem by asking the following questions: if I drop a weight 1 foot, it achieves a velocity of v. How far do I need to drop it to achieve a velocity of 2v?
The answer is -- 4 feet!
And, how far do I drop it to get a velocity of 3v?
The answer is 9 feet.
They show a reenactment of the experiment on the show about half way through, and you can do it yourself if you want.
So, if you believe that an object dropped 4 feet has 4 times the energy as an object dropped 1 foot, then the energy must be proprtional to the velocity squared, and also proportional to F*X.
Incidentally, the Mme. de Châtelet died after childbirth before all of her results could be published, and the PBS show notes that it was another 100 years or so before there was universal acceptance of energy being proportional to v squared.
Bruce Zweig
The show is covered on the web site: http://www.pbs.org/wgbh/nova/einstein/
(click on Ancestors of E = mc2 for all of the history)
de Châtelet is covered at:
http://www.pbs.org/wgbh/nova/einstein/ance-sq.html
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