Algodoo

I find it rather interesting that the equation used to calculate the kinetic energy of a moving body is similar to the equation used to calculate the electrical energy (in joules) of a charged capacitor: E = .5*C*(V^2)

where,

E = energy in Joules or watt-seconds
C = Capacitance in Farads
V = voltage charge on the capacitor

Hey tesla! I think one of your programmers escaped and is posting part of your code to algodo!

Xray,


Yes, I think a capacitor (E = 0.5CV^2) is like a spring (E = 0.5kx^2) and an inductor (E = 0.5Li^2) is like a flywheel (E = Iw^2).


JakubKubo,

I assumed there were cars out there that already had this feature but did not know which ones. Thanks for the info. I also noticed a weakness in my system in that the red car can back up and force the blue car to back up and hit a third car. Maybe you can fix this in your spare time.

The interesting similarity of the formulas is caused by them all having a product as basis:
Spring: F=k*x
Flywheel: L=I*w
Motion: p=m*v
Capacitor: Q=C*V
The Inductor is the only part where I couldn't find a basic formula

In all these cases, a value is calculated from a constant times a variable. If you integrate each of these formulas, you would in each case end up with E=constant*var^2/2, or written differently, E=Const/2*var^2.
The reason why F,L,p and Q all integrate to E is because each describes a physical value that influences the energy in a system . Applying Force(F) increases the energy of a spring , applying momentum(p) to something increases it's kinetic energy, applying angular momentum(L) to a flywheel increases it's rotational energy, applying more charge(Q) to a capacitor increases it's electrical energy. If you were to integrate every variable, what you would get is the SUM of all the energy that you put into the system at each infinitesimal moment of time. Since the system becomes more "resistant to change" as you add more energy, the variable component actually applies squared, as both the variable and the "resistance" increases as you sum up these infinitesimal changes in energy(which is also a natural consequence of the rules of integration, x^n-> x^(n+1)/(n+1)). This can be seen in it taking longer to discharge a capacitor, taking longer to stop a flywheel or a moving object, a spring resisting with more force as you compress it, etc.

Long story short: Most forms of energy are composed of a constant and a changing variable that gets more difficult to change as energy level rise, thus forming the pattern E=const/2*var^2

FRA32,

Good explanation. I never thought about it in those terms. Thanks. I found System equivalence interesting.

Finally some good content.