# Does a ski racer with a larger mass have an advantage?

Does a ski racer with a greater mass have an advantage over a racer with a lesser mass? If mass of one racer is 54 kg and the mass of a more slender racer is 44 kg I know the speed at which they descend should be equal if they were to fall in a vacuum. How does friction force, air resistance and momentum play a part in determining the advantage or disadvantage of larger mass in ski racing?

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## 2 Answers

Viscous drag will tend to favor the heavier person, since surface area scales slower than mass, i.e. $A \propto r^2$, $M \propto r^3$, $F_D / F_G \propto M^{-1/3}$. But I would generally expect this effect to be weak except at very high speeds.

Friction would cancel out if you were skiing on ice, however in soft snow the heavier person would tend to sink deeper in the snow and that extra compaction of the snow is going to take away more energy. Unless the heavier skier has larger skis, i.e. it really would depend on the loading per area of the skis.

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Not exactly. Friction makes no difference, as it is a force proportional to mass ($\mu_k mg\cos\theta$). Since $F=ma$, the $m$ cancels off and we get that the effect of friction on acceleration is constant for different masses. The same goes for gravity. Recall Galileo's famous drop-two-balls-from-the-leaning-tower experiment.

There are only two forces left. Both depend upon the size and shape of the body and not the mass. Since we have to divide by mass to get acceleration, out of two people of the same shape, the heavier one gets the benefit. This can be said to be due to momentum/inertia. The two forces are buoyant force and viscous drag. Buoyant force is directly proportional to volume, and is pretty negligible. Viscous drag depends upon the size and shape and lots of tiny things. Generally, aheavier person will be broader as well, so this one can go either way.

All in all, it really doesn't matter what a skier's mass is, except for overweight people (too much drag I would think). The technique matters much more.

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Buoyancy? That's the same as gravity. –  Bernhard Mar 8 '12 at 19:09
@Bernhard well, kind of (i consider it to be caused by the gravitationally induced pressure difference). Anyways, it has a different direction and behaviour, so i'll keep it seperate. –  Manishearth Mar 9 '12 at 1:13
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