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Friction and Skiing


Friction and Skiing


The purpose of this blog is to determine the coefficient of kinetic friction that the ground is imposing on the skis while going down a slope. Over winter break, I went skiing at Jimimy Peak. I determined all of the factors that were necessary to figure out the coefficient of friction for this trail that I was going down which is called Riptide. 

Link to video: https://youtu.be/ZSOnKHrBAM0



The givens are the:
  • Force of gravity - mass * gravity
  • *Initial Velocity - 9.332 m/s
  • *Final Velocity - 13.088 m/s
  • Acceleration - 0.942 m/s^2 
  • Distance travelled - 44.68 m
  • Gravity - 9.8 m/s
  • Mass - kilograms / gravity ---> 49.89 / 9.8 = 5.09 kg (this number cancels out anyways)
  • Angle - 11 degrees
*The initial and final velocity were found with Logger Pro using the video taken. 


This angle is at 11 degrees and was found by extending the lines that the slope makes and using a protractor to figure out the exact angle.

Free Body Diagram:


Force Equations:
∑F(x) = fk - mgsin(Ө) = ma → N * μk - mgcos(Ө) = ma
∑F(y) = N - mgcos(Ө) = 0


 The Math:
N = mgcos(Ө)

mgcos(Ө) * μk - mgcos(Ө) = ma
μk = ( ma +  mgcos(Ө) ) / mgcos(Ө)

M’s cancel out

μk = ( a +  gcos(Ө) ) / gcos(Ө)


Plug in Numbers:
μk = ( 0.942 + 9.8sin(11) ) / 9.619
μk = 0.292

The coefficient of friction in this case is 0.292. In this video, it looks like I am going straight down the mountain as fast as I can, but I am not. During this video, I am going straight but it is still not as fast as I could be going because as you can see, I am still building speed. Technically I was carving with my skis, which is when I move my skis from side to side to reduce the speed so I am not skiing out of control. According to a chart that describes the average coefficient of friction for each situation while skiing, carving while skiing has an average coefficient of friction of between 0.2 and 0.3. A downhill racing turn average coefficient is between 0.3 and 0.45. According to these results, I was going straight down while slightly carving which is exactly what I was doing as I was going down this trail.

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