May The Mass * Acceleration Be With You


[portrait: Newton at 47]

For many years, the concept of Force confused the hell out of me. “Force” in physics means something very specific: Force = mass * acceleration. And that is all it means. Finally realizing this was an “aha!” moment for me in my scientific studies.

I spent most my life believing that when someone spoke of “Force” they meant something like “energy” or “power.” And, indeed, in day to day life, we usually do use the word “force” like this. Also, I realize now that even my science teachers did not understand that they were often using the term “force” when they really meant some other measurement, often “momentum.” Momentum equals mass times velocity — and this is probably closer to what most of us have in mind we talk about the “force” something has.

I’ve even caught several scientists using the term “force” in a technically incorrect manner. For example, when the great Faraday spoke of “force” and “force fields” and “lines of force”– I really don’t think he was thinking “mass times acceleration;” I believe he was thinking of force as a type of energy.

Newton defined Force for us in the 1600s. He was concerned with mass and velocity, and how one object can act to change the velocity of another object (mostly centered on the study collisions and of gravitational effects). Newton reasoned that the heavier something is, the more force will be required to change its velocity. He also reasoned that heavier objects will experience less change in velocity than lighter objects when both are struck by the same force. This gives us a direct relationship between mass and required force, and an inverse relationship between mass and resultant change in velocity.

Change in velocity is the definition of acceleration. Thus we can rewrite the above relationships as the equation:

mass = Force / acceleration

Multiplying both sides of the equation by Acceleration and abbreviating the terms, we get Newton’s famous equation for Force:

f = m * a

But I want to be very clear (which teachers and authors have NOT been with me): this is not “force” as in some vague concept of “energy,” and it is certainly not equivalent to “momentum.” Force in physics is very specifically only mass times acceleration.

Because I so long misinterpreted what Newton’s Force equation tells us, I never trusted Newton. I could not believe that VELOCITY was not included in the concept of Force. For example, I was certain that a baseball moving at a hundred miles per hour (mph) toward me would hurt worse than one coming at me at five mph, even if both were accelerating at one mph. Of course, the Force equation tells you that both baseballs will hit you with the same Force– see my confusion here? Basically, I was confusing force with momentum (I’m still not certain even “momentum” encapsulates all I intuitively mean when I think of the “umph” [and potential bruise] a moving object carries with it).

In some respects my lack of faith in Newton (that force was a lie!) has been a good thing: it’s reinforced my skeptical frame of mind– something very important for scientific thinkers. After all, it takes a certain kind of man to question the laws handed down from Newton, the Moses of the scientific age. And my lack of unquestionable adoration for the laws of Newton probably made it easier for me to doubt the orthodox interpretation of quantum mechanics, which I think is a very appropriate feeling to have toward what I call the “religion of the quantum.”

And one final note on Force: even after correcting myself and aligning my definition of Force with Newton’s definition– there STILL turns out to be a problem with the equation. Electromagnetic theory (for charged bodies) and Relativity theory (for all bodies) both hold that the faster an object goes, the more effective mass it has. Therefore, velocity can affect the “m” in the f = m * a equation… THUS, velocity really can have an effect on Force, which is not obvious from Newton’s equation.

[these thoughts inspired by the wonderful book, Fields Of Force by William Berkson]


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