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Physics of Alpine Skiing
Skiing is enjoyed by millions of people every year. Skiers enjoy moving fast down
steep slopes but seldom stop to think about what is making them move. Skiing is
an example of an everyday activity affected by elements of physics. Many
aspects of skiing depend fully on physics and surely without physics, there would
be no skiing.
The basic concept of skiing is simple. Attached to each foot is a long narrow
board with tips in front of you that flip up. The bottom of the ski is smooth so you
slide so one can slide over the slippery, cold snow with greater ease. With your
skies you go to the top of an incline and slide down, turning left and right
because, as any skier knows, for some reason you go faster and faster and too
fast if you were to go straight down the slope. As you go down, you wear goggles
because the air flies past you so fast it begins to blind you. From this basic
concept of sliding down an incline many types of skiing have developed. One
type is ski jumping, where you fly off a jump and try to suspend yourself in mid-air
as long as possible. Another is ski racing where you fly down a course of poles
as fast as you possible can. Or cross-country skiing, where instead of going
down an incline you use your own human force to push yourself along the snow,
still wearing skies. There are many types of skiing, different ways to ski,
conditions which suite different people, and different types of ski equipment but in
general many different variables but everything comes down do to one sure
thing: without physics, non of this would be possible.
Out of all the things that effect the skier’s movement as they go down a hill,
gravity is perhaps the simplest to understand. Gravity is the force that holds "us"
down, the force that keeps everything from flying away, keeps objects grounded.
Gravity is the force that earth exerts on an object, pulling the object toward
earth’s center. If you through something in the air, it comes back down to the
ground because of gravitational pull. Acceleration due to gravity equal 9.81 m/s,
this number can often be useful when used in equations to find values for a
skier’s speed (velocity) or mass. In the case of skiing, gravity pulls the skier down
the hill. The gravity tries to pull the skier straight toward the center of the earth
and meanwhile a normal force is being exerted on the skier, which acts as the
opposing force to gravity. The normal force acts perpendicular the surface the
object is on, in this case perpendicular to the mountain the skier is on. If the skier
was on level ground she would not move because the force of gravity would be
pointing down and normal force would point straight up and they would cancel
each other out and there would be no change in velocity, however this is not the
case on the mountain. The combination the perpendicular normal force and the
gravity will result in the skier being pulled down the mountain at the same angle
the mountain’s slope is at.
As the skier skies down the mountain, she goes threw an acceleration.2 That is,
her speed changes as her velocity increases. Acceleration is defined as a
change in velocity and that is what happens to the skier. She accelerates
because gravity is pulling her down. There is a positive acceleration as she gets
started down the mountain and picks up speed. As she comes to a stop she goes
threw a negative acceleration. People get hurt skiing not because of their
acceleration or speed but because they decelerate to quickly. For instance, if a
skier were skiing at a ridiculously fast speed of 50mph they would be very safe
until they hit an object such as a tree. Then momentum must be conserved and
the tree won’t move as the skier flies into it.
Friction often affects a skier. As the skier moves down the mountain, the snow
can resist the motion of the skier, slowing her down and providing friction. A
frictionless surface is one that does not have such resistance to an object moving
across it, snow however does have friction. As the skier skies down the
mountain, friction is the force that keeps her from flying down with an
acceleration of 9.81m/s; it pulls her in the opposite direction. The friction acting
on the skier is acting in directed opposition to the displacement of the skier. The
largest amount of friction is used when stopping. You great a huge amount of
friction by digging the edge of the ski facing down the mountain into the snow,
facing sideways to the slope. This creates so much friction that you are
immediately stopped. The coefficient of friction in the case of skiing depends on
conditions. If it is a colder day (below about 25F degrees) than the snow is dryer
and therefore slicker meaning the ski will slide over it with greater ease making
the coefficient of friction in this case smaller. On a warmer day (about freezing,
32F degrees) the snow is wetter and will clump making the surface not a smooth,
here the coefficient of friction is higher.
Reducing friction is the object of ski racers. The more the skier is able to reduce
friction against their skies, the faster they will go. Wax is applied to the bottom of
skies in order to reduce the amount of friction between the ski and the snow.
Applying wax to skies helps to prevent them from drying out, when the ski is dry
the bottom is not as smooth thus making a greater coefficient of friction between
the ski and the snow.
As there is friction working against the skier, work is also done. The amount of
work is found by using the equation:
Force x displacement x cosine 180 = Work
Work can only be done unto an object if there is a force working against it, this is
another way we know that the skier is accelerating and working against a force.
We know there is friction working against the skier, therefore work is done in
order for her to act against the friction. Work is only done if there is a force to act
against, and there is no force if the object, in this case the skier, is not
accelerating.
Friction is not the only thing that slows skiers down. When skiing down a
mountain standing straight up your body is almost acting as a parachute to air
causing air resistance. In order to reduce air resistance, ski racers where very
tight suits called gs suits which fit snug against their bodies and provide the skier
with the least amount of area for air to get trapped in. Ski racers also ski in what
is known as the "tuck" position making them very aerodynamic. In the tuck, the
skier makes herself as small as possible by crouching down with her arms
stretched out in front of her giving her body a pointy shape as it goes down the
mountain. When ski racers do larger courses such as a downhill or super G
course they are in the tuck position more because the gates are more spread out
and they don’t have to turn as quickly, therefore they are in the tuck position
more. These skiers sometimes have special curved poles that fit around their
bodies while they are in the tuck position; the curved poles allow the skier to be
as small as possible.
The conservation of energy is one of the most important concepts in
understanding the physics of skiing. Potential energy is energy associated with a
falling object, an object that has an initial elevation and with a position such that
relative a certain frame of reference it could fall. The formula for finding potential
energy is
Mass x gravity x height = Potential energy
A skier gains potential energy as she goes up the lift. This is because she is
gaining height. Potential energy is always gained when an object is working
against the force of gravity because the farther the object goes up the higher it is
and therefore will have a greater potential energy. When the skier is at the
bottom of the mountain, height is equal to zero and therefore potential energy is
equal to zero.
As the skier heads down the mountain, kinetic energy is gained. Kinetic energy
equals:
1/2mass x velocity2
So the kinetic energy of the skier will depend on how much she weighs and how
fast she is going. As she accelerates down the hill, kinetic energy is gained. This
is also in relation to potential energy, the skier gains kinetic energy as she goes
down the mountain but looses potential energy at the same time. Therefore,
potential energy lost equals kinetic energy gained. Right before the skier hits
height equals zero, the kinetic energy is at its maximum and as the skier hits
height equals zero she will continue to move on the flat surface because she still
has energy. As the energy runs out, she will decelerate and slow down,
eventually stopping all together. The total energy is found by adding potential
energy to mechanical energy.
Mechanical energy is another form of energy that affects the skier. The
mechanical energy of a skier is directly related to work and friction. The more
friction affects the skier over a longer distance, the greater the amount of work
done will be and the more friction and work increase, the more mechanical
energy decreases. Therefore:
Amount of work done = loss of ME
The formula for mechanical energy is:
Mechanical energy = Kinetic energy + potential energy
Or
Mechanical energy = ½ mass x velocity 2 + mass x gravity x height
If the forces of friction and work were insignificant, than the mechanical energy
and therefore the energy of the skier would be conserved. This would mean that
the forces of gravity and normal force and the only two forces acting on the skier.
That is, her energy when she first began to ski would be the same as when she
was at her maximum speed. At the top of the mountain, mechanical energy
equals the potential energy because there is a large height but no velocity and
therefore no kinetic energy. And likewise, as the bottom of the mountain
mechanical energy equals kinetic energy because there is no longer any height
and so potential energy must equal zero. So if kinetic energy at the bottom
equals potential energy at the top, energy is conserved.
As one can see, there are many aspects of physics that go into alpine skiing.
From the seemingly simple concept of sliding down a mountain with each foot
attached to a long smooth board you find that many things attribute to what most
skiers never take notice of. Without gravity, you would not fly down the mountain
but without friction you would go to fast and never be able to stop, making skiing
to dangerous. This what makes physics fun; the different concepts apply in so
many days to our everyday life, not just in the heart of winter on top of a
mountain