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Friction During a Track Race

In the opening week of my Christmas Break I competed in a track race at the Providence Career and Technical Academy. The race took place on an indoor track that features straightaways of 45 meters and curves of 55 meters. The race that I competed in was the 3000 meter run.

Below is footage that was taken approximately halfway through my race, with about six laps to run. I am the runner in first with the maroon kit. Note that the turn begins at the white pole to the right of me(picture below). Also note that I am wearing green racing spikes.


The turn ends when I am at the painted green line(picture below).

Video:


It took me approximately 10.40 seconds to round the curve which makes my average velocity 5.28 meters/second. From this we can obtain my centripetal acceleration using the equation Ac=v^2/r. Note the curves radius is 17.5 meters. 

Equation for Centripetal Acceleration: 

Ac=5.28^2/17.5
Ac=5.28 m/s^2

Unlike many of the better indoor tracks, PCTA's track is flat and not banked. Because of this, times are generally slower on the PCTA, because runner's have to battle to not overpower the force of friction. I was curious to see exactly what the coefficient of friction was on the track and to find out the maximum speed at which one could go without overcoming friction. 

Free Body Diagram: 

Force Equations: 

Fx= f = mv^2/r
Fy= N = mg

Solution: 

Fx=f=mv^2/r 
Fx=μN=mv^2/r
Fx=μmg=mv^2/r
Fx=ug=v^2/r
Fx=μ=v^2/rg
μ=5.28^2/17.5*9.8
μ=0.03 

Maximum Speed FBD: 

The FBD for this situation will be the same as the one above, however friction will be positive rather than negative. 

Force Equations: 

Fx= f = mv^2/r
Fy= N=mg

Solution: 
Fx=ug=v^2/r
μgr=v^2
sqrt(μgr)=v
sqrt(0.03*9.8*17.5)=v
v=2.27 m/s

Based on this maximum velocity calculation. I can deduce that during my race I was overcoming the force of friction, however the effects are not visible in a dramatic way. Because I had to battle with the lack of friction, and all other racers had to do the same, this is why race times are slower at PCTA. 

Comments

  1. Mr GrayJanuary 1, 2018 at 8:25 AM

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

    ReplyDelete

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