Samuel Hapák comments on An Actually Intuitive Explanation of the Oberth Effect

[Samuel Hapák]

That’s an excellent question!

Change in energy $\Delta E$ must equal work done on the moving body $W$.

Now, work is force over distance $W=F\Delta s$

But we also know that force is mass times acceleration, thus $F=ma$.

If you have a body moving under the influence of constant force $F$ over time $t$, starting from the speed 0, it will have a speed $v=Ft/m$ at the end. It’s easy to see that the average speed it travels will be $v/2$ though and thus the distance travelled will be $\Delta s=vt=\frac{F{t}^2}{2m}$.

Now, the kinetic energy equals work and thus $\Delta E=F\Delta s=\frac{1}{2}m(Ft/m{)}^2=\frac{1}{2}m{v}^2$.

[qvalq]

I’ve learned the maths before.

I think maybe I have no idea what kinetic energy is.

[Samuel Hapák]

Well, the correct question is “What is energy”. And the answer is that energy is some number that we can compute for any physical system and it doesn’t change no matter what as long as the system is reasonably isolated from its surroundings. Kinetic energy is just a portion of this quantity we can compute for something that is moving.

It’s not very intuitive honestly. The best explanation for what energy is I ever read is this one from Feynman:

https://​​www.feynmanlectures.caltech.edu/​​I_04.html