Was driving home last night when I noticed that my car was slowly drifting side to side. It felt weird like when a tire is low/flat. So I gradually slowed down from 50mph to 40mph. Note, I did this carefully and slowly. My antilock brakes kicked in. Like holy hell how slick does a road have to be for a small deceleration like that to kick in antilocks?

So it made me think of a math question:
If a typically sized sedan (weighing 2 tons) decelerates from 50mph to 40mph and the antilock brakes kick in, what it the frictional coefficient of the surface of the road? Also assuming typical non-bald all season tires.
Multiple choice:
a) slick
b) really slick

  • 4
    Yeah, in proper conditions you can slide for hundreds of feet from only like 10mph. Really gets the heart racing when there's an intersection coming up and you thought you were being careful, but then you discover that friction broke since the last time you used it.
  • 3
    Though the mass of the car does not go into the equation. I could actually calculate the friction coefficient if you either gave how much time it took from 50 to 40, or what way you made during that time.
  • 3
    I learned from a coworker that some lady did a Dukes of Hazard style leap with her car about 45 minutes previous to my passing through that area. She spun around 180 and was going 70mph backwards. She hit a snow pile and launched air born. She landed on top of another snow pile. She was okay, but I bet she needed to change her shorts. She was going southbound and nearly went into the northbound lanes during this. She is very lucky how her flight ended.
  • 2
    @Fast-Nop My perception of time at the point of noticing my antilocks were engaged is suspect. I really have no idea what the details were. Adrenaline may have been involved.
  • 2
    @Fast-Nop Lets say my decel time was 5 seconds. How slick is that?
  • 7
    @Demolishun Let's say v is the speed, t is time, a acceleration, and g is the earth's gravity acceleration.

    v1 = 50mph = 80km/h = 22.2m/s
    v2 = 40mph = 64km/h = 17.8m/s

    Since a = dv/dt, and assuming constant deceleration, we have:

    a = (22.2m/s - 17.8m/s)/5s = 0.88 m/s^2.

    Given that g = 9.81m/s^2, the friction coefficient is:

    µ = a / g = 0.09.

    That would be a typical range for ice on the road, i.e. "really fucking slick".
  • 4
    Pardon my first attempt of this shitty meme.

    Winter tires: exist
  • 2
    @electrineer it's rather like this:

    Winter tires: *exist*

    But not bad for the first attempt, mate. You're really good at it.
  • 0
    @electrineer hell some of us are doing good to afford a set of used tires when we need them.

    @Demolishun it could be that one wheel was slipping while the other wasn't. On modern cars your abs works along with your traction control to help keep all the wheels in sync with each other
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