Does crouching in an 'egg position' help a skier?

Classical Mechanics Level 1

In the figure below, the skier crouches in an 'egg position.'

Which of the following options best describes her effort to crouch like that?

She does so to minimize wind resistance She does so to maximize the normal force She does so to increase her density She does so to reduce the friction between her skis and the snow

Shreyansh Mukhopadhyay by Shreyansh Mukhopadhyay , 18, India

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7 solutions

The drag force acting on the skier is given by:

F D = 1 2 C ρ A v 2 \large F_D=\frac{1}{2}C\rho A v^2

where:-

C C is the drag coefficient, which can vary along with the speed of the skier. But typical values range from 0.4 to 1.0

ρ ρ is the density of the air

A A is the projected frontal area of the skier perpendicular to the flow direction (that is, perpendicular to his velocity v) or the cross-sectional area

v v is the velocity of the skier relative to the air

So the skier tries to minimize the drag force acting on her by reducing the cross-sectional area.

Note: The density of the skier does not depend on her position or shape and the drag force doesn't depend on the density of the skier.

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While drag is reduced, if you have ever actually skied you would know that the point of crouching like pictured is to lower the center of gravity, and particularly dig in the skies to maximize the normal force the snow puts on the bottom of the ski. That normal force, combined with the angle of the ski is what causes the skier to turn.

D. Moore - 2 years, 11 months ago

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D. Moore is correct -- in this picture, the skier is clearly taking a turn. Note the angle at which the skies are: if the skies were flat, then the skier is going straight down and the drag argument is completely correct, however, in this case the skier crouches in order to lower the center of mass to take a turn at a higher speed. As such, 'wind resistance' answer definitely does not 'best describes her effort to crouch like that'.

Justas Janonis - 2 years, 11 months ago

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"Take a turn at higher speed" how does lowering of center of mass help in that?

Chaitnya Shrivastava - 2 years, 11 months ago

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@Chaitnya Shrivastava – It increases stability by decreasing the net external torque acting on the skier, so a skier of a fixed skill level can take a turn faster and sharper (due to the lessened torque an increased normal force would provide)

There could also be a benefit to "digging in" beyond simply changing the angle of the normal force, but I don't have anywhere near the physics background to analyze that.

Brian Moehring - 2 years, 11 months ago
Meneghin Mauro
Jun 26, 2018

Wind resistance is one factor, but on the turns having a low centre of mass allows for sharper turns as the low angle of the legs allows for a higher centripetal acceleration

37 Helpful 0 Interesting 0 Brilliant 0 Confused

This would be the actual answer, if this question was framed properly.

S I - 2 years, 11 months ago

Yes, wind resistance is only one to many more factors. The question and solution is framed incorrectly.

Tommy Seo - 2 years, 11 months ago

A skier maximizes his speed by minimizing resistance to motion, both from air resistance and snow resistance. A skier minimizes his air resistance (drag) by reducing his projected frontal area. He does this by going into a crouch position, which (along with improving his ability to hold balance) results in a lower drag force, which acts in a direction opposite his velocity, slowing him down.

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Yuri Barros
Jun 30, 2018

Well, I thought the reason was to lower the center of gravity. But besides lowering drag, all the other alternatives don't make sense, because all of them don't change by crouching.

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Maaz Shah
Jun 29, 2018

As the area is directly proportional to drag force so the object minimize its area to decrease drag force of wind

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David Fairer
Jul 1, 2018

I have ticked the only answer that I could conceive that it could be which is B about wind resistance, but I think that the true answer will be that such a posture makes it easier to keep her balance!?? Regards, David Ps A response either to say that you agree or disagreed would be greatly appreciated!

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Sam Banners
Jun 30, 2018

This shows that the lesser the area, the lesser the friction is. Also, she does so to reduce the drag.

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