# I Reverse engineering potential and kinetic energy

1. Jan 4, 2017

### q-ball

The equation for momentum (potential energy) is PE=M*V.

The equation for kinetic energy is KE=(1/2)*(M*V^2).

You will notice that PE is the derivative of KE. and then you might add that M, simply Mass, is the derivative of PE.

However, because M is simply a scalar quantity, and the other functions are expressions of energy added TO mass, I might suspect the correct approach is to say that you start with mass and take the *antiderivative* with regard to velocity.

and there is more, but first some observations.

PE and KE are two seperate expressions of energy. upon inspection we find that they have completely different effects, when an object, let's say a solid ball, encounters a medium:

1A) PE: the solid ball encounters another solid ball. there is an elastic conservation of momentum as the second ball goes off on a particular trajectory, the angle and velocity of which are accounted for by Potential Energy.

1B) PE: the solid ball encounters a wall of oatmeal. exactly how far the ball continues before coming to rest is a function of its momentum (PE), notwithstanding fluid dynamics.

2) KE: the solid ball encounters a thin, hard barrier such as a sheet of glass. if the KE is sufficient, the solid ball will overcome the barrier.

As we can see those are two completely different phenomena. Of course, otherwise they would have the same name, being the same thing. But they don't and they aren't. They are seperate phenomena.

Now for the questions.

We can easily deduce a third antiderivative. ??=(1/6)*(M*V^3) so, what sort of energy does that represent? what
physical phenomenon does it describe? as in 1A), 1B), and 2), and ...?

that is what I am most interested in.

but we can also ask, what prevents nature from making use of an infinite array of further antiderivatives in an infinite series of discrete expressions of energy? who says we must stop at the second antiderivative (KE)? Shouldn't there be a name for this set of equations, this class of expression, which goes from the 0th to the nth antiderivative of Mass with regard to Velocity?

2. Jan 4, 2017

### Staff: Mentor

Momentum is not potential energy. Momentum is not energy. So the rest of your post doesn't really make sense.

3. Jan 4, 2017

### Staff: Mentor

No, momentum is not PE.

No, the closest that you could come to this is that the generalized momentum is the derivative of the Lagrangian with respect to the generalized velocities.

The laws of nature that we have observed thus far are second order differential equations with respect to the coordinates. There is nothing mathematically preventing you from constructing higher order differential equations, but they don't seem to represent natural laws so most people don't bother.

4. Jan 4, 2017

### q-ball

I suppose that answers the question then.