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Ice Skating and Friction

My brother came home for break, and we had some brother-sister bonding time while ice skating at the Boss Arena at UR.



I decided to time him as he skated from one goal line to the other, requesting that he try to keep as constant a velocity as he could.

Using the stopwatch on my phone, I recorded the time it took him to do my request: 9.1 seconds. After returning home, I looked up the standard measurements of an ice hockey rink to find how far he had skated.



I have decided to use the international measurements of rinks instead of the North American so there are no conversions.

The full length of the rink is 61 meters. From the boards to the goal line is 4 meters, multiplied by 2 is 8, then subtracted from 61 is 53. So my brother skated 53 meters in 9.1 seconds.

Assuming he skated at constant velocity, I can now determine his velocity on the ice using the formula: v =Δx/t

v = 53/9.1
v = 5.82 m/s


I'm curious about the friction of the blades of his skates and the ice. If my brother skates around the center circle at that same velocity, what is the coefficient of friction between his skates and the ice? Some useful information is that the radius of the circle is 4.57 meters, and his velocity is 5.82 m/s.

Free Body Diagram:











Force Equations:

∑Fx = f = mv^2 / r
∑Fy = N = mg


Solving:

∑Fx = f = mv^2 / r → μ*N = mv^2 / r → μ*mg = mv^2 / r
μ*g = v^2 / r
μ = v^2 / rg
μ = 5.82^2 / 4.57*9.8
μ = .756


Comments

  1. Mr GrayJanuary 1, 2018 at 8:26 AM

    In the FBD, what is F? Doesn't seem to belong there.

    ReplyDelete

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