Re: Hard braking and the Physics of Coming-to-Rest


"peter" <scoular@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
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DavidM <newsNO@xxxxxxxxxxxxxxxxxxxx> writes
The car coming to an abrupt stop under gentle braking is not due to the
tyres slipping, so is not really the reverse of what larkim said.
If the brakes are applied with a low but constant force they will
gradually slow the car. During which time it's momentum exceeds the
friction between pads and discs required to make them lock. Once the
momentum of the car becomes sufficiently low, and if the braking is not
adjusted for speed, the pads will grab on the discs and probably cause
an immediate stop. The momentum of the car is now too low to make the
tyres skid. The driver will over react and lift off the brake causing
passengers to jolt forward and back in their seats.

Interesting in a strange sort of way but complete gobbledygook I'm afraid.


You don't think that the way a car can appear to come to an abrupt stop
under gentle braking is actually not because of any change in the grip of
the tyres or change in pad friction coefficient but simply the reaction to
the sudden removal of a force?

Indeed. Nothing at all unusual happens in the last few inches of braking to
a halt other than at some point the car actually achieves zero mph at which
point the acceleration changes abruptly from whatever negative value it had
been at previously to zero. The rate of change of distance with respect to
time is velocity, the rate of change of velocity wrtt is acceleration, the
rate of change of acceleration wrtt is called jerk and so on ad infinitum to
further derivatives wrtt which don't have universally accepted names but
have at some point been called snap, crackle and pop for the next three in
the series.

So that very last jolt you get if the brakes are not feathered as the car
comes to rest is not a more abrupt acceleration than the car had been
undergoing previously but an abrupt change in the rate of acceleration i.e.
jerk, something that rollercoaster designers and public transport system
designeers have to take into account if the passengers aren't to be reduced
to vomiting all over each other. To minimise the amount of jerk the rate of
acceleration itself has to be reduced just before velocity drops to zero so
as to smooth the transition to the zero point.

From a purely mathematical point of view I'm not absolutely sure why the
jerk just at the point at which velocity changes from zero to something non
zero (or vice versa) isn't actually infinite because another value
(acceleration) is changing in an infinitesimal amount of time. I guess in
the real world that transition is cushioned by the elasticity of matter to a
value that has to be both finite and generally not actually that large.

Presumably in a theoretical world if you applied a force (or removed a
force) to an infinitely rigid body it would encounter an instantaneous
change in acceleration and hence an infinite amount of jerk.
--
Dave Baker
Puma Race Engines


.

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