# Physics of Downhill Skiing

Length: 1027 words (2.9 double-spaced pages)

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Skiing is a sport enjoyed by millions of people around the world. The adrenaline rush that skiers get from flying down the slopes is unmatched, but all too often the cause for this rush is overlooked. Physics plays a crucial role in skiing and without it, there would definitely be no skiing. The concept of skiing is simple. You attach a ski to each foot, go to the top of a hill or incline, and slide down, turning side to side. From this basic concept of sliding down an inclined plane, a worldwide sport has evolved. In this paper, I hope you gain a useful knowledge of the vitally important role that physics plays in the sport of downhill skiing.

m = mass of skier
g = gravitational force
a = acceleration
mu = kinetic friction coefficient

· Inertial Forces = (m)(a)
· Frictional Force = (mu)(m)(g)(cos theta)
· Graviational Force = (m)(g)(sin theta)

Gravity is the force that holds the skier to the ground and is also what pulls the skier down the hill. While gravity is acting straight down on the skier, a normal force is exerted on the skier that opposes gravity. As the skier skis down the hill, he or she will encounter an acceleration. This acceleration is due to gravity caused by a change in the skiers velocity. The mass of a skier is different for every person and is easily calculated by multiplying a skiers weight in kilograms by the gravitational force exerted by the earth. These forces and more are explained throughout the rest of this paper.

Gravity is a force that everybody is familiar with and is one of the simplest to understand. We all know that if you were to throw a ball in the air it would fall right back down. This force called gravity exerts a constant acceleration of 9.81 m/sec2 towards the center of the earth. Gravity is what pulls you down the hill. While gravity is being exerted downward, a normal force is being exerted on the skier opposing gravity. This normal force acts perpendicular to the earth's surface, and in this case the mountain on which the skier is skiing. Lets say for instance the skier was on a flat surface, both gravity and the normal force would be acting on the skier but in opposite directions, thereby canceling each other out and resulting in no movement. However when a skier is on the mountain, the combination of gravity and the perpendicular normal force result in the skier being pulled down the mountain at the same angle as the mountain’s slope.

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You would definitely not be able to ski powder or jump cliffs without the force of gravity.

As you ski down a mountain, you will experience both acceleration and deceleration. This can be both fun and dangerous. Acceleration is defined as a change in velocity divided by a given amount of time. A skier accelerates as he gets started going down the mountain and begins to pick up speed. As the skier is coming to a stop, he begins to decelerate. Acceleration is not what kills people, but rather a sudden deceleration. Acceleration is safe as long as the skier is in control, but if the skier were to ever lose control and hit a tree, then Newton’s laws come into effect and the skier could be seriously injured.

Sir Isaac Newton came up with three laws that govern motion. His first law plays a huge role in skiing. It states that “An object in motion will stay in motion, and an object in rest will stay at rest until acted upon by an outside force.” Therefore if there were no friction and you started to ski down the mountain, you could ski indefinitely except for the fact that you would eventually encounter a tree or some other outside force that would bring you to a stop. Newton’s second law states that Force = (mass)x(acceleration) (F=ma). This equation allows you to determine the amount of force you have as you ski down the mountain. It also allows you to see the relationship acceleration plays in your force, and how if you were quickly accelerating and hit a tree, then the force you hit the tree with would be considerably higher than if you were skiing slowly. Newton’s third law says “For every action there is an opposite and equal reaction.” What this simply means is that, with the force that I hit a gate on the slalom course, that gate will exert the exact same amount of force back on me. This law is also what keeps running through my head when skiing through trees, knowing that if I were to hit one, it might be my last run for the day.

Friction is what allows you to stay in control while skiing. Because friction is a force that opposes motion, it is the reason you slow down. In order to stop you use a lot of friction by applying the whole edge of your ski perpendicular to the direction of travel. Skiers apply wax to the bottom of their skis in order to decrease the coefficient of friction. This coefficient is dependent upon snow conditions and varies with temperatures. On a colder day the friction between the snow and the skis will decrease, but when temperatures rise above 30 degrees, the friction increases and the snow becomes sticky.

Downhill skiing presents a great example of the relationship between work and energy. A skier possesses a large amount of potential energy at the top of a mountain. If starting at rest, all of the mechanical energy a skier possesses is in the form of potential energy. As the skier begins to descend down the mountain, his potential energy is depleting and being turned into the form of kinetic energy. At the point the skier reaches the bottom of the mountain, his speed and kinetic energy have reached their maximum. As friction begins to act upon the skier, the quantity of work increases and the mechanical energy of the skier is eventually lost. Finally the skier runs out of energy and comes to a stop. A great animation of this relationship is presented below.