Snowboarding


 * Title:** Snowboarding


 * Authors:** Alex and Jonathan


 * Abstract:** The goal of this lab was to find how coefficient of friction ( µ) between the board and the snow, a rider's mass, and the angle of the run affect the speed of a rider . We used information on Darren Powell's world record speed run, and a taped hot wheels car and ramp to simulate a snowboard going down a mountain. With logger pro, and a knowledge of physics, we were able to calculate everything needed to achieve this goal.


 * Introduction:** The fastest speed on a snowboard in history was in Les Arcs, France by a man named Darren Powell. The run was on Les Arcs speed track, which is 1700 meters long with a gradient of 70%(35 ° ). Many wonder how Darren was able to achieve such a high speed (202km/hr or 56.1m/s) on such a simple track. In this lab, find out how the coefficient of friction ( µ) between the board and the snow, a rider's mass, and the angle of the run affect the speed of a rider going down its slope. With this information, and neglecting air resistance, we hope to get a general understanding of why Darren beat so many other people to become the fastest man on a snowboard ever.


 * Method: ** First, We found information on Powell's world record run such as his speed of (202km/hr), the length of the track which was 1700 meters, his mass which was 78.5kg(173 lb), and the slope of the track which was 35 degrees. Next we solved for µ and calculated the speed of a theoretical version of his run where friction was negligible. We then set up a hot wheels ramp in order to create our own scaled down version of a snowboard run. We found the car's mass to be 33 grams, made the slope 35 degrees, made a length of 1 meter, attached the tape, and then let the car roll down the slope with the tape attached. We filmed the car and used logger pro to analyze the data and find the speed. We then calculated the speed of a frictionless run of the same specs. Finally, we compared the hot wheels data with Darren Powell's data to see how µ, mass, and angle of slope effect the speed of a snowboarder.

__Darren:__
 * Data:**

56.1m/s with friction

Primary equation used: PE + KE+ W = PE + KE

Using this equation, we can find out the acceleration of F fric which we can then use to find µ. All we need to do is plug our numbers into the equations and solve for the acceleration.

9.8*78.5*1700sin(35)=750128.99J .5*78.5*56.1^2=123527.99J 123527.99-750128.99=-626601J -626601=F*1700*cos(180) F=368.59N 368.59=78.5*a a=4.69m/s/s

Primary Equation used: µ = F fric /F norm

9.8*cos(35)=8.028m/s/s (4.69*78.5)/(8.028*78.5)=.585= µ

Primary equation used: PE = KE

Using this equation, we can find out the theoretical velocity, if there wasn't any friction, and compare it to the actual velocity Darren got.

78.5*9.8*1700sin(35)=750128.99J 750128.99=.5*78.5*v^2 v=138.24m/s without friction

__Hot Wheel Car 1:__

1.87m/s with friction

Primary equation used: PE + KE+ W = PE + KE

.033*.5*1.87^2=.0577J 9.8*.83*.033=.268J .0577-.268=-.211J -.211=F*(.83/sin(35))*cos(180) F=.146N

Primary Equation used: µ = F fric /F norm

9.8*cos(35)*.033=.265J .146/.265=.55= µ

Primary equation used: PE = KE

.033*9.8*.83=.268J .268=.5*.033*v^2 v=4.03m/s without friction

__Hot Wheel Car 2__:

With the same specs other than an increase in the slope from 35 degrees to 65 degrees, the final velocity of the car = 3.52 m/s with friction.

__Hot Wheel Car 3:__ Everything exactly the same to 2 except mass has been increased to .066. Final velocity of the car = 3.535 m/s with friction


 * Results:** Finding ways to decreasing the coefficient of friction and riding down a hill with a bigger angle will increase a snowboarder's velocity. Mass, surprisingly, has no effect on the velocity.


 * Conclusion:** By using our experimental and theoretical situations, we can conclude that the final velocity that a snowboard can reach is dependent on three things other than air resistance. These three things are the mass of the rider, the angle of incline, and the coefficient of friction between the board and the snow. When it comes to the coefficient of friction, it does not change unless the surface changes because both components of the coefficient of friction, F norm and F fric, will always stay in a ratio equalling the µ . If the mass of the rider is increased, the force due to friction will increase and if the angle of the slope is increased, the force due to friction will be smaller because the object pushes on it less. This shows us that one way to increase speed on a snowboard is to wax the rider's board extremely well. Because surface change is one way of decreasing the coefficient of friction, we know that by waxing the board the rider will end up decreasing that coefficient of friction and end up with a higher velocity. Next, we scientifically proved the idea that increasing the angle of the slope will make you go faster. By increasing the angle of the slope, the coefficient of friction decreases because decreasing the force due to friction decreases. This, in turn, increases the final velocity. This increase in velocity due to an increase in slope can be clearly seen in our second Hot wheels 2 trial in which the slope was increase to 65 degrees. By riding down a hill with a higher slope, a snowboarder can increase his velocity. Finally, we considered the effect of the rider's mass on the velocity. Our solution to this part was somewhat surprising. While many believe that a rider's mass would cause some kind of change in the velocity of the rider, our experiments proved otherwise. With just an increase in mass from Hot Wheel's trial 2 to trial 3, an extremely similar (basically the same) velocity was the result. The reason for this is if the numbers are plugged into a kinematic equation, the mass from the initial potential energy and initial friction cancels with the mass from the final Kinetic Energy. In other words, mass has no effect on a snowboarder's velocity. Although one key component of any speed snowboarder's variables, air resistance, is not taken into consideration, many riders may find the information found in this lab beneficial to increasing their speed.