Experiments cannot determine the correct definition of energy, because elastic force cannot be separated from inelastic force in experimental results. So pure mathematics is needed. Here, a rocket is used as a substitute for gravity. In rocket analysis, the inelastic force is constant for constant powered rockets eliminating the problem.

Explanation of the Concept

Energy is defined as "that which is conserved during transformations." Conserved means totals stay the same when components are re-arranged. So the test for the definition of kinetic energy is to re-arrange the components and see which total stays the same.

Leibniz used this test in 1686, but he predetermined a false outcome by starting with the claim that force times distance should be a conserved quantity (F x s = ½mv²). He did no more than show that force times distance equals mass times velocity squared, which is no longer a question but does not show it is kinetic energy.

A correct test compares the two alternatives including force times time, which equals mass times velocity unsquared (F x t = mv). It shows that Leibniz was wrong, because he never compared to force times time to get mv, momentum.

The Test

The definition of energy was argued for 200 years but the wrong alternative was chosen. Now, rocket math can be applied to the original test, and it shows the error. The value of a rocket is that there are no complexities to mask the result.

This model, involving falling objects, was the original basis for the definition of kinetic energy.

Rockets are used to calculate force, which is independent of the definition of energy.

Part 1: Kinetic energy is not ½mv².

A 4kg object dropped 1m (meter) has the same amount of ½mv² as a 1kg object dropped 4m, because force times distance equals ½mv² for an accelerating mass. But a rocket accelerating the masses to those velocities requires twice as much energy as fuel for the large mass as for the small one.

Rocket burn time:
large mass: 1.77177876722800 seconds   mv=17.7
small mass: 0.88588938361400 seconds   mv=8.86

Therefore, both masses do not have the same energy; the rocket does not transform energy in proportion to ½mv²; ½mv² is not kinetic energy; and a gallon of fuel does not produce a consistent amount of ½mv².

Part 2: Kinetic energy is mv.

A 4kg object dropped for 1s (second) has the same amount of mv (momentum) as a 1kg object dropped for 4s, because force times time equals mv for an accelerating mass. A rocket accelerating the masses to those velocities uses the same amount of energy as fuel for both masses.

Rocket burn time:
large mass: 3.92400000000000 seconds   mv=39.2
small mass: 3.92400000000000 seconds   mv=39.2

Therefore, both masses have the same amount of energy; the rocket transforms energy in proportion to mv; mv is kinetic energy; and a gallon of fuel produces a consistent amount of mv.

All logic and evidence of energy point to the same conclusion. The logic created the need to derive the mathematical proof.

About ninety percent of physics is corrupted by the error.

Key Point:

With rocket math, the analysis is referenced to the combustion chamber, where equal and opposite forces determine the result. The reference point is where the force acts. Everywhere else, energy is defined relative to the starting point or some similar, external reference frame.

When the reference is the point where the force acts, you get the correct definition of energy, which is momentum. When the reference point is anyplace else, you get the incorrect definition of energy, which is ½mv².

This is because the incorrect definition of energy is equal to force times distance for an accelerating mass. Distance references to something other than the point were the force acts.

Concise Math

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