Re: [Phys-l] stopping distance

[John Denker <jsd@av8n.com>]

On 01/05/2007 08:50 AM, Anthony Lapinski wrote:
> Using the Work-Energy Theorem, you can determine how the stopping distance
> is related to the car's initial velocity:
>
> W = KE
> fd = 0.5mv2
> mmgd = 0.5mv2
> mgd = 0.5v2

There's a buuunch of assumptions that go into that.
For starters, it looks like there is an unstated dependence
on coefficient of friction hidden in there somewhere.

The notions of "friction" and "coefficient of friction" are
not fundamental physics;  they are quick & dirty approximations.

> If we assume the brakes "lock" the wheels to create a skid mark, then the
> above result shows that the stopping distance does NOT depend on the car's
> mass.

Again that depends on lots of questionable assumptions.

> However, students tell me and Driver Manuals often state that the weight
> of the vehicle IS a factor (heavier = longer stopping distance). In the
> above calculation, I am dealing with an idealized case, but in "real-life"
> anti-lock brakes change the actual stopping distance depending on the
> weight of the vehicle. I've also heard that large trucks have a unique
> braking system. Can anyone elaborate on these ideas?

Among the factors involved:
 *) At some point the force will shred the tire.  This is not well
  modelled by coefficient-of-friction ideas;  at the very least
  there will be a crossovers between
    -- the coeff of static friction vs sliding friction
    -- the coeff of static friction vs shredding
  Those those are not the same, and the non-sameness depends on the
  weight of the vehicle, tire pressure, and other details.
 *) Similarly at some point the force will tear up the road surface.
 *) If the road is wet, there will be hydroplaning, which approximately
   depends on the square root of the tire pressure, which in turn depends
   on the weight of the vehicle and other details.
      http://www.mountainflying.com/hydroplane.htm

Never mind trucks, you can take two cars of comparable size and weight
and obtain radically different stopping distances, just by choosing the
tires differently (along with brakes, suspension and other details).