Ponderous Curmudgeon
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- Feb 20, 2021
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Are you sure you are not just modelling hydroplaning? Wet traction in a car is due to reduced contact patch between tire and road due to inability to clear water from the actual tread in contact with the road, contact decreases as the speed increases due to an inability to remove increasing volumes of water, in the extreme where there is a layer of water across the entire contact area you reach a limit where the water shear becomes relevant and you are now hydroplaning. beyond that, there is the difference between static friction and rolling friction if you actually stop the tire from rotating.I did address your question; perhaps the issue here is you didn’t understand the answer.
You cannot treat a skidding car with its wheels locked as a separate or isolated issue without considering the initial conditions which occur prior to slamming on the brakes.
For argument sake let’s assume the car does skid when the brakes are applied.
On a level road before applying the brakes there are three forces acting on the car which affects its forward motion.
f₁ = ma the forward acceleration where m is the mass of the car and ‘a’ is the acceleration.
f₂ = kvⁿ the air resistance where k is a constant and n and is a positive integer.
f₃ = μN the frictional force where μ is the coefficient of friction and N = -mg where N is the reaction force and g the acceleration due to gravity.
f₂ and f₃ act in the opposite direction to f₁.
ΣF = f₁ + f₂ + f₃
If ΣF > 0 the car is accelerating and if ΣF = 0 the car is moving at a constant velocity.
When the brakes are applied there is a decelerating force or an impulse which is applied for period of time t which changes the momentum of the car.
At the end of the impulse period there is now only one force f₃ acting on the car as f₁ = 0 since the car is moving under its own inertia and f₂ ≈ 0 since the velocity becomes relatively small.
The car eventually comes to a stop as the frictional force f₃ overcomes the inertia.
The point here is it confirms the frictional nature of water when it is modelled as a composition of layers which needs to be overcome, the car moving due to inertia where the wheels are locked does not overcome the internal friction of the water layers.
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