Is ½ mυ² the Kinetic Energy or One-Half of the Kinetic Energy?
Xiao En Wang,
Deng Guo Wang,
Yin Bo Wang
In the 1680s, Leibniz experimentally proved that vis viva is the product of the mass and square of
velocity, mυ2. In 1847, Helmholtz studied free fall and found that the work produced or consumed was
(1/2)mυ2 = mgh, and suggested calling the work as vis viva. By the end of the 19th century, people
were still unable to derive (1/2)mυ2 from the vis viva, mυ2, so they proposed to forget the old word 'vis
viva' and create a new word 'kinetic energy', (1/2)mυ2, to replace the old word 'vis viva'. This article
finds that (1/2)mυ2 is not a single valued function and cannot represent the kinetic energy. It can only
represent one-half of the kinetic energy. And it was found that the kinetic energy in free fall motion is
twice the potential energy, and the two cannot be converted into each other, and the correct expression
of mechanical energy conservation was proposed.
