The creation (discovery?) of kinetic energy was a major step toward the creation of energy itself. It’s a pretty straight-forward concept:

K.E. = ½ mv²

But how kinetic energy arrived wasn’t so straight-forward.

The lever: weight x change in vertical height

In their study of the lever, the Ancient Greeks identified the importance of the quantity weight times changes in vertical height, later to become known as “work.” Light people have to move further out on the teeter-totter to balance heavy people. The further out the weight, the greater the change in vertical height during the up-and-down teeter-totter motion. A light weight with large change in vertical height balances a heavy weight with a small change in vertical height. In today’s mechanical energy terminology, balance or equilibrium occurs because the changes in (gravitational) potential energies at each end cancel each other.

Free fall: change in vertical height 𝜶 v²

Galileo’s free fall, as I wrote about here, showed us that the change in vertical height is proportional to the change in the square of velocity. Weight (or mass) does not play a role in free fall; recall those experiments at the Leaning Tower of Pisa? Newton would later explain why this is so; mass cancels in his famous F = ma equation since gravitational force (F) itself is proportional to mass (m).

[Note: the lever and free fall are connected to each other by the same change in vertical height, i.e., the same change in gravitational potential energy. In other words, the lever has to do with changes in potential energy (PE), free fall with the transformation of potential energy into kinetic energy (KE), and the two together with the conservation of mechanical energy (PE + KE = constant) that was defined by 1750. But I’m getting ahead of myself.]

Huygens used collision theory to connect mass with free fall

The lever (Statics) and free fall (Dynamics) traveled different historical paths that finally met when Christiaan Huygens (1629-1695) used both during his study of collision theory involving systems of moving bodies. In an early statement on the impossibility of perpetual motion, a very hot topic back then, Huygens reasoned that the centers of gravity of such systems cannot rise on their own. And because the center of gravity is based on the weights of the moving bodies, Huygen’s mathematics connected weight with Galileo’s v² to deliver a new variable to the world of physics: mv². To Huygens, this was a stand-alone, untethered insight. But not so to another important figure in this story, Gottfried Wilhelm Leibniz.

Leibniz put a spotlight on the new quantity: mv² (vis viva)

“In regard to the quantity mv², what was a mere number to Huygens was invested by Leibniz with cosmic significance” – Richard Westfall [1]

While Leibniz did not reason his way to mv², he was the one who brought attention to it. In his own studies of motion involving the lever, free fall, and collisions, Leibniz realized, in an earlier attempt at a conservation law, that a cause-effect equality must exist in nature based on the quantity mv², which he called vis viva. Newton’s mechanics added the ½, and in the mid-1800s the complete ½mv² term became known as kinetic energy, a critical cornerstone of the theory of energy and its conservation.

Thank You!

Thank you for reading! The progression of thought leading from the lever and free fall to kinetic energy is a fascinating, and at times complicated, journey. Explore this journey in Chapter 10 of my book, Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

References

[1] Westfall, Richard. 1971. Force in Newton’s Physics: The Science of Dynamics in the Seventeenth Century. American Elsevier, New York. p. 284.

END