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Snow Angel Physics

The (Simple) Mechanics Behind a Snow Angel

After a cold morning of running during practice over break, I decided to relax for a minute and make a snow angel outside of La Salle's Athletic Center. The footage can be found below in both regular speed and slow motion. 










The snow was loosely packed and relatively dry. Observing the video one can see that as I made my snow angel, my arms glided over the surface of the snow and displaced some of the loose top layer. Although some snow was moved, a thin bottom layer remained. Knowing this information, I decided to attempt to find the coefficient of kinetic friction between my arms and the snow while moving my arms up and down. However to do this I needed to find some extra information:
  • Mass of one arm: 2.81 kg
  • Length of one arm: 0.62 m
  • Weight of one arm: 27.579 Newtons (6.2 lbs converted)
  • Velocity of arm through snow: 1.62 m/s (found by dividing distance traveled by arm by time):
    • 2𝜋r/4=distance traveled by arm in one swing
    • 2𝜋(.62)/4=0.973894
    • 0.973894/0.6=1.62

  • Acceleration of arm through snow: 2.7 m/s/s (found by dividing velocity by time)

After establishing the background information, finding the coefficient of friction is a simple matter of drawing a free-body diagram and plugging information into a sum of forces equation.
FBD: 




















Sum of Forces Equation: ∑F=F-f=mv2/r
ma-𝜇N=mv2/r
7.587-𝜇(27.579)=2.81(1.622)/0.62
𝜇=0.156186
𝜇=0.16

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