Monday, 9 July 2007

Force/mass Confusion

I have just read a news article about the fitness requirements of a Formula-one driver. Due to high accelerations during the races, drivers experience high G-force, which creates stress to their bodies. Below is the article's description of the stress to a driver's neck.
"Head plus helmet weighs 6kg. With added G-forces when cornering, the neck has to support up to 30 kg."
-The Age, 17-03-2007

The article is telling me the cornering G-forces are about 24 kg. Anyone spot the problem? Forces have no mass!! Kilogram -- or more generally, gram -- is a measure of mass, which tells you the amount of "stuff" of an object. A force is not a substance (unless you go into quantum mechanics), so they cannot have any mass. The above sentence implied that G-forces have added additional mass to the head plus helmet system, which is not correct. Rather, the G-forces add to the total downward force exerted on the neck, which originally consisted of just the weight of the head and helmet*.

Since the neck has to support more downward force not more mass it is inappropriate to use a measure of mass, kg. Instead, the sentence should go "...the neck has to support up to 300N.", where "N" refers to Newtons, a measure of force. Note that we arrive at 300N because on Earth, 1kg~10N. However, had the reporter actually written that, no one would understand what he/she meant, so it is better to rephrase it as "...the neck has to support up to an equivalent of 30kg."

* Weight is the gravitational force the Earth (or another large body) exerts on an object and is not equivalent to mass. Strictly speaking, then, it is incorrect to say the head+helmet weighs 6kg, because kg measures mass not force. However, such usage has become mainstream and I shall let it go.

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