3 ms·
Not every value is divided by 2. Only the K.E. term is divided by 2. The P.E. term is not. If you ever find where Young worked out the equivalency to P.E. then
by eesmith 5y ago
Not every value is divided by 2. Only the K.E. term is divided by 2. The P.E. term is not.
If you ever find where Young worked out the equivalency to P.E. then you'll find he had m v² = 2 m g h. But I suspect he did not.
The underlying topic is vis viva. As https://en.wikipedia.org/wiki/Vis_viva https://en.wikipedia.org/wiki/Vis_viva points out, Leibniz was the first to point out that m v² was conserved, Bernoulli used 1/2 m v² in 1741, and at about the same time du Châtelet derived the notion of conservation of energy using Newtonian mechanics, Young called the concept "energy" in 1807 (though without the 1/2), and the 1/2 'recalibration' was due to Gaspard-Gustave Coriolis and Jean-Victor Poncelet during 1819–1839.
Quoting https://en.wikipedia.org/wiki/Gaspard-Gustave_de_Coriolis https://en.wikipedia.org/wiki/Gaspard-Gustave_de_Coriolis :
> In 1829, Coriolis published a textbook, Calcul de l'Effet des Machines ("Calculation of the Effect of Machines"), which presented mechanics in a way that could readily be applied by industry. In this period, the correct expression for kinetic energy, ½ mv2, and its relation to mechanical work, became established.
Coriolis gives the specific reason at https://archive.org/details/ducalculdeleffe00corigoog/page/n41/mode/2up?q=vives https://archive.org/details/ducalculdeleffe00corigoog/page/n... :
> .. nous appliquerons cette dénomination à la moitié de ce produit, en sorte que la force vive sera le produit de la masse par la moitié du carré de la vitesse. Cette légère modification à l'usage ancien introduira plus de simplicité dans les énoncés des principes que nous avons à donner.
From Google Translate:
> we will apply this denomination to half of this product, so that the living force will be the product of the mass by half of the square of the speed. This slight modification to the old usage will introduce more simplicity in the statements of the principles that we have to give.
In other words, it's not "a useless convention" as you write, but a convention which simplifies the resulting mathematics.
- SirIsaac 5y agoI understand French. I looked through the document. I could not find any place where Coriolis derived kinetic energy. He was apparently using someone else's derivation. By simple substitution, anyone can easily derive E = mv² from Newtonian equations. One starts with W = Fd = mad, and go from there. There is no need to integrate the difference in initial and final velocities (as is currently being done) because this is already assumed in the definition of acceleration. The 1/2 is a mistake and I stand by it.
- eesmith 5y agoI pointed out you likely need to look to du Châtelet to discover the derivation of what Coriolis refers to as the "old usage". As to the "1/2 is a mistake", one question in physics is, is gravitational mass exactly equivalent to inertial mass? You can omit the 1/2 and continue with the old definition. If you do so, then your system of physics will have an inertial mass which is half the gravitational mass. As such, it's a difference only of philosophy. The main advantage to the 1/2 is the math is cleaner if we assume inertial mass = gravitational mass.
- SirIsaac 5y agoI don't yet see how inertial mass would differ from gravitational mass if the K.E. equation is changed. I'll need to think about it some more. We are currently preparing an experiment to test the prediction of our theory that will leave no doubt. If we are right, textbooks everywhere will have to change, at the very least.
- SirIsaac 5y ago> Not every value is divided by 2. Only the K.E. term is divided by 2. The P.E. term is not. I'm not sure what that means. > If you ever find where Young worked out the equivalency to P.E. then you'll find he had m v² = 2 m g h. I don't get it. mv² is not equal to 2mgh. That makes no sense.
- SirIsaac 5y ago> mv² = 2mgh I think I now know what you mean. You mean that a mass will gain kinetic equal to 1/2 mv² by the time it hits the ground from a height of h. This doesn't prove your claim. Using my own derivation of kinetic energy, I get mgh = mv². Here's why: PE = mgh is the same thing as Newton's Work equation, W = Fd = mad. Why? Because g is acceleration (a) and h is distance (d).
- eesmith 5y agomgh = mv² is experimentally disproven in the ballistics lab experiments I mentioned.
- SirIsaac 5y agoI don't believe it. They're probably measuring mass and velocity and applying the formula afterwards. That doesn't prove anything. Back in Leibniz' days, they would use soft clay and measure the depths of the indentations made by falling weights. This was accurate enough to tell them that the kinetic energy was proportional to mv².
- eesmith 5y agoYour "probably" means you've refused to look at the relevant experimental evidence? "proportional to mv²" also means "proportional to 1/2 mv²" and "proportional to 123.45 mv²". Assuming your gravitational and inertial masses are supposed to be the same, then 1/2 m v² is, by Noether's theorem, a consequence of conservation of energy. https://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy https://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:... .
- deleted 5y ago[deleted]