Physics

Skiing Physics Skiing is an extreme sport; sometimes you have to make a move while going 100 mph (161 KPH) on a hill with a 70 degree angle. But even though this may just seem like reflex to an experienced skier, there is actually a lot of physics going on during this. All of these skiing moves even as complicated as doing a whirlybird off an 50ft cliff, can be dissected into small pieces and examined in simple terms. The first thing someone must know is the basics of Newtonian mechanics made by Isaac Newton like force. Force is a push or pull of one thing onto another. Things like for every actions there is an equal or opposite reaction (like when you stretch a rubber-band in your hand the force by one finger is the same as the force by the other. Mass is an intrinsic property of matter that, through Newton's equation of motion, relates the magnitude of the applied force to the acceleration. Skiing also involves rotational, or angular, motion, which may be described using the term angular velocity and angular acceleration. It is the rate of rotation, and is usually measured in radians p/s (per second). There are 2¹ radian in one revolution; angular velocities in terms of revolutions per second are converted to radians per second by multiplying by 2¹. The direction of angular rotation is given by clockwise motion of a right-handed screw as it is rotated. The standard unit of angular acceleration is radians per second. So if w = angular velocity and x= angular acceleration, then x= finishing angular velocity-starting angular velocity) divided by the time elapsed. Torque is the effect that causes rotation of one's body.

If force is put onto the balance point (like in the picture above), the stick moves without rotations. If the same force is put onto another place, the stick rotates in a manner proportional to the distance from the direction of the force and the length of the perpendicular lever arm. Torque is measured in either the "pound foot" or the "Newton Meter." One of the most important forces is Momentum that is very useful for doing fun things such as dusting people. Momentum is the mass of an object, times its volume. Momentum shows what is needed to stop the thing. Momentum P is defined as P=Mv. Because P measures the state of motion of a body, Newton's first law of motion states that if there is not outside force against a body, it will not move. If your have a cup with a playing card on top of the cup and a quarter on top of the card. Then if you pull away the card fast enough the quarter will remain in the same spot. But because it has nothing to hold it up anymore, it will fall into the cup. The concept and application of inertial forces are very important in skiing; it is crucial to understanding ski maneuvers because the skier's momentum changes continuously in magnitude and direction as the skier makes turns and skis down the slope. So it is very important to have a good understanding of Newton's laws of motion. The first one as you probably know is an object at rest will stay at rest and an object in motion will remain in motion unless acted upon by an outside force. The second Law is if a net force act on a body in motion, the body's state of motion must change (Force = mass times acceleration). And the third law is that for every action there is an equal or opposite reaction. The first law let us know that a moving skier (body) will kept moving in a strait line unless a force is acted upon it (life if the person puts more wait on his/her left/right leg). The second law leads to the equations that describe the motion of nay mass body. It says, F=Ma; the change in the momentum of a body is given by Ma, mass multiplied by acceleration, the direction of motion changes or not. The term Ma must be a force because it equals the force F, but it is a force that has the direction opposite to F, so they counteract each other (f+f=0, like 5+-5=0). The third law says the skier standing perfectly hill on a hill has the force of gravity pulling that skier into the snow. If the snow is not strong enough, the person may even fall into the snow into he hits a part that is strong enough to hold him up. Two important factors of forces are Work, Power, and energy. Work is when a force is applied to a body and results in motion in the direction of the force. Work is measured in units of force times the displacement in the direction. If a 150-lb skier is lifted strait up 1000 by a ski lift, he has 150 000 lb. of work done on him. So it requires 3 lb. of force to pull a 150-lb skier overt level ground, moving the skier 1000-ft would need 3000-ft lb. of work. Power is the time rate of doing work If the 150-lb skier was able to climb 1000 ft in 60 min, the average power that he used to move up the body would be 150 * 1000/3600. Since 1 horsepower (hp) is 33000-ft lb./min, than this person worked at the rate of 41.7/550 that when expressed in terms of power yields 0.076 hp. But this power doesn't actually represent the power used to climb the hill, because it does not account for the usually body functions. Then there is Energy. Work and energy are actually the same thing. The work done to lift a skier up a hill that results in change in elevation increases the person's potential energy. A good example of potential and kinetic energy for skiing is easily used. Picture a two hills with a valley in-between. If there was a skier on top of one of these mountains, he has complete potential energy as he is positioned at the top of the mountain ready to go down. As he travels down the mountain he is gaining kinetic energy from his speed and losing potential energy. As the bottom of the valley he was complete kinetic energy. And this Kinetic energy gives the skier the enough power to go up onto the other hill. He would go up to the top of the hill then he could turn around and do the same thing again. If this was a perfect system the skier would go forever, up and down, up and down. But because there of gravity and friction the skiers momentum is slowed done and the skier can't make it to the top of the hill. In skiing the main source of potential energy is gravity. The more gravity there is the more chance that the person can go faster. The equation for that would be potential energy (PE)= Mass (M) * acceleration of gravity (g) * the vertical elevation above some reference elevation (h). But if there is wind blown onto the skier the total energy in the system would increase or decrease depending on which direction the wind and the skier are going. The potential energy can change into kinetic energy but no change in the energy of the system is made unless there is an outside force that affects the energy. Still, this is not completely correct because every human has stored energy inside him or her that can be used at any time to change the energy of the system. Like if a skier uses that energy to flexes his muscles to edge this skis he changes the energy in the system. Dynamics of turn carving: When a skier is going down a hill very fast he/she wants to crave for maximum speed and but also with maximum control. To crave perfectly the skier must remain in a total balanced position. If the skier is perfectly balanced the forces that are affecting the skier are balanced (all together they equal 0). The forces acting upon the skier are gravity, liquid friction (the air) and inertia force parallel but opposite in direction to the skier. But because a skier feels uncomfortable if he has no control, the skier uses the stored energy to change the forces. But the skier can have to skidding or no motion of any part of the ski edge perpendicular to the edge or speed will be lost. If the skier is successful in keeping skidding from happening, the geometry of the skier determine the radius of that turn by when it is deflected to contact the slope. A ski with a sidecut radius of {x} set to an edge angle to the slope of edge angle has a turn radius of Without any changes a ski is perpendicular to a line drawn from the skier's foot to the skier's center of mass (probably the hip). But the skier can change this with their knees or if he rotates his feet changing the position of the ski.