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

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    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.
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    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.
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    @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.
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    @Fast-Nop Lets say my decel time was 5 seconds. How slick is that?
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    @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".
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    Pardon my first attempt of this shitty meme.

    Winter tires: exist
  • 1
    @electrineer it's rather like this:

    Winter tires: *exist*

    But not bad for the first attempt, mate. You're really good at it.
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