Ironic Experiment

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When someone says the Work Energy Theorem is the theorem that describes mechanical energy because momentum cannot, he is both correct and scientifically wrong.  He is correct to the degree momentum cannot describe mechanical energy but, he is wrong to say this is proof for the kinetic energy formula.  This is because momentum's inability to represent mechanical energy does not rise to the standard of proof demanded by the Scientific Method.

Historically, there were only two options considered when the original question was raised.  One was the product of mass and velocity (mv), aka, momentum.  The other was the product of mass and the square of velocity (mv2).  One of these, momentum, is a directional expression and it is that fact that disqualifies it from representing mechanical energy (see the "Explosion Scenario").   However, if we go back a little earlier in time and look at Descartes' first attempt to quantify motion, the product of mass and speed (ms), we actually have a worthy challenger to mv2 or ½mv2.   The product of mass and speed has no direction associated with it and thus it cannot be disqualified in the same way as momentum is. 

Since the scientists of the past saw fit to improve the original winner of the mechanical energy sweepstakes, it is only proper to upgrade its one time and inept challenger by removing its directional component.  Therefore, this website offers a new hypothesis to replace the one Newton offered to challenge how mechanical energy is quantified mathematically.   

Please note; an experiment is done in academia, "The Academic Experiment", that is believed to confirm the Work Energy Theorem.   It is, to say the least, an extremely impressive experiment but, it contains an unseen flaw.  If you do not believe me, check it out by clicking on the link; just don't forget to come back to this page. 

A Provisional New Hypothesis

In formal terms, it is proposed that the product of mass and speed might be a better description of the energy a moving mass has because it is moving.  Mathematically, this new hypothesis is given provisionally as shown here.  It is only offered in this simple manner so as to provide a point from which to challenge the current understanding of the Work Energy Theorem.

ft = Δ ms


f is the applied force that acts in the direction that an object moves; f represents the magnitude of force and is given in newtons

t is the time force acts and is given in seconds

m is the mass of the object given in kilograms

s is the speed of the object and is given in meters per second

Δ is the symbol used to denote "change in"


This New Hypothesis carries with it a prediction which is different from the one given by the Work Energy Theorem.  Specifically, a linear relationship exists between an object's speed and the amount of energy it has due to the fact it is moving.

The s'Gravesande Experiment  

Historically, the only experiment done before scientists elevated Leibniz’s hypothesis to an accepted theory was the s’Gravesande Experiment.  It was performed by Du Châtelet and she failed to account for half the experimental data.  This begs a couple of questions about what occurs when this experiment is examined using ALL the data.  Does this experiment decide the issue?  Does it still support the Work Energy Hypothesis?

An s’Gravesande type experiment is any one in which a moving object slows down at a uniform rate.  Du Châtelet used a soft clay bed and dropped metal spheres from only a few meters into it.  The spheres decelerated so quickly she was unable to see that time was a variable.  Had she used a different version of the s’Gravesande Experiment, she might have noticed time for the variable it is.  Imagine rolling a golf ball onto a perfectly flat putting green at various speeds.  When a relatively fast ball enters, it travels a fairly long distance before stopping and it becomes obvious that time passes.  A ball that begins at a slower speed travels a far shorter distance and noticeably stops more quickly.    

The premise behind the original s’Gravesande Experiment, or any version thereof, is that as an object slows down, it loses the energy associated with motion.  And if energy is removed at a uniform rate, the relationship of mechanical energy with velocity / speed is revealed. 

It is not difficult to analyze what occurs during any s’Gravesande type experiment.  Given how experiments of this type function, only the following variables and formulas are required to derive a table of representative values.  By specifying the rate of deceleration and the object’s initial speed, it is a simple matter to calculate the distance an object travels before stopping and how long that takes in terms of time.   


a  the rate at which deceleration takes place in meters per second per second, a constant in this situation

s — the initial speed of the object in meters per second just before it reaches a uniform rough surface

t — is the time in seconds the object decelerates

d — is the distance in meters the object travels while decelerating

To calculate time and distance, we only need the following two formulas and are of the kind any first year physics student should know.


The following table shows the calculations that result when an object decelerates at the uniform rate of 1 m/s2.

Initial Speed in meters per second Time in seconds Distance in meters
2 2 2
4 4 8
6 6 18
8 8 32
10 10 50
12 12 72
14 14 98
16 16 128
18 18 162
20 20 200


From this table, it is quite apparent that both the initial speed and the time in seconds for it to come to rest are linear; the distance travelled is not.  When plotted (Graph A), this fact becomes extremely obvious.

Graph A

Graph A

By only measuring one of the variables and ignoring the other, it is possible to make the case for the status quo or the New Hypothesis.  If we only look at the time an object takes to stop moving, a linear relationship is the result and that supports the New Hypothesis.  If we do as Du Châtelet did and only consider how far the objects travel, we wind up with “conclusive evidence” for the Work Energy Theorem.   What happens if we consider both sets of data?

Using the theoretical data calculated above, we are left with how to combine them (time and distance) mathematically.  Adding them together or subtracting one number from the other makes no sense.  Likewise if we were to divide time by distance.  This leaves us with the logical and usual idea of dividing the distance traveled by how long it occurs (d ÷ t).   This produces the average speed for the object during the entire deceleration process for a given initial speed.  The results are plotted on Graph B.  Interestingly, as the object slows down, its average speed for the rest of the deceleration process reduces and it does so at a linear rate.

Graph B

Graph B

A linear increase in an object’s initial speed produces a linear result when using the entire data set and that does not bode well for the Work Energy Theorem.  Instead, it shows that the New Hypothesis is the proper method to quantify mechanical energy.  Had Du Châtelet seen these results, her conclusion would have been entirely different.  In that case, the scholars of the past, having no respect for or knowledge of her, probably still would have gone with mv2 to represent Vis Viva since by that time they understood why momentum cannot represent mechanical energy.  Evidently, it would seem that Du Châtelet did not understand why momentum was a foolish option despite her conclusion that mv2 was the way to go.

Proponents for the Work Energy Theorem might balk by overthinking the results found in Graph B.  The values produced by dividing distance by time represent the average speed of the object for the entire time it slows down.  Regardless of the significance of average speed, the best way to analyze the experimental results is by thinking of the experiment as a “black box”; data enters and data exits.  In this case, a linear input produces a linear output.

Actual Experiments

Please note that in producing a representative data set, a nice orderly set of integers resulted.  When actually doing such an experiment, the data will not turn out to be so nice.  However, the individual values will be very close in terms of how they fall on a graph with a slight caveat.   Take the case of an automobile traveling at 200 kilometers per hour (kph) and an identical one traveling at 20 kph.  If we apply the brakes exactly equally for both, the faster vehicle will take less time to reduce its speed by 10 kph than the slower one.  This is because the faster automobile encounters far more air.  The more air a vehicle must push out of the way, the greater the counterforce which adds to the counterforce the brakes themselves provide.  This then explains why it is so difficult for those trying to break land speed records; the faster the vehicles go the greater the effect air has in keeping the vehicle from accelerating.  This also tells us that an s’Gravesande type experiment has an issue — counterforce can vary.  And if the effect is significant, it will produce values that land on the graph in a slightly non-linear way for Graph B but only at higher velocities but nowhere near enough to align with the prediction of the Work Energy Theorem.  This issue is relatively minor and can be taken into account when plotting data on a graph.

In the case of automobiles, the effect of air resistance can be demonstrated in another way by using two different vehicles — a corvette and a van.  If both vehicles have the same mass and are fitted with the same drive train, their respective graphs will be different when stopping from high speeds.  The corvette’s graph will be far closer to Graph B than the one the van produces.  If this experiment could be done on a planet or moon with no atmosphere, the graphs for both the corvette and van would be identical and linear looking very much like the theoretical graphs.  In any event and unless a gross error is made, the results of any s’Gravesande type experiment will still confirm the prediction given by the New Hypothesis.

The Bottom Line

Ironically, the only experiment done prior to the general acceptance of the Work Energy Theorem disproves it.  There is of course more to know but, until the physics community recognizes that they have been poorly taught, there is no point in releasing that information. 



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