Re: [Phys-l] stopping distance

[Scott Goelzer <s.goelzer@comcast.net>]

I started a thread on this a while back and never really got a  
concrete answer.

Searching for data will find that trucks take longer to stop. Some  
sources cite as much as 66% more.

For a locked and sliding tire, it's not so hard to explain in terms  
of µ (mu) changing. A sliding patch increases in temp and decreases  
in term of µ. The derivation below assumes that µ is constant.
> F_net=F_fr
> ma =u * F_n
> ma = u * ma_g       (assuming we are on a horizontal surface)
> here the masses cancel.


For a rolling tire near the static friction limit, I still have  
problems understanding how to explain stopping distances with the  
simple friction law. It makes more sense in terms of energy.

It would seem that if the force of static friction is proportional to  
the weight and rolling tire is not changing physical properties much,  
then mass should not matter for a expertly stopped truck - but it  
does. Even a 'super' transmission capable of almost locking the  
wheels used exclusively for engine braking could not slow the truck  
faster than the force of static friction allows.

My best _guess_ is that the surfaces of the braking system change due  
to heating as the truck stops and the force of friction falls below  
that of the optimal static friction force. The truck takes longer to  
stop - much more KE to lose. I sat waiting on a runway for 1.5 hours  
after an airline pilot aborted a takeoff (kiss the knees!) - the  
stated reason was to let the brakes cool.

I've never been happy with the simple friction laws. Similarly  
friction is supposed to independent of area -  but this does not work  
for surfaces with high intermolecular attractions. Try friction vs  
area experiments with plastic wrap on plastic wrap.


Scott


PS The short version for air brakes is that they make pneumatically  
coupling and uncoupling the truck to the trailer MUCH simpler than  
hydraulically. They also enable a clever fail-safe mechanism in case  
of pressure loss.

<http://www.newbiedriver.com/ABCsUpdates/AirBrakes101.htm>




**********************************
Scott Goelzer
Physics Teacher
Coe-Brown Northwood Academy
Northwood NH 03261
603-942-5531e218
sgoelzer@coebrownacademy.com
**********************************


On Jan 5, 2007, at 9:21 AM, Paul Lulai wrote:

> I am sure others will have more thorough anwers, but I will try to  
> contribute:
> --
> 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.
> --
>
> I believe the assumption and the braking model are both a part of  
> the problem.  If we do a Force analysis, we find the masses 'cancel  
> out' when analyzing the acceleration of the car.
> F_net=F_fr
> ma =u * F_n
> ma = u * ma_g       (assuming we are on a horizontal surface)
> here the masses cancel.
>
> *However*, this is assuming that the frictional force stopping the  
> car is caused by the frictional interaction between the wheels &  
> the ground.  This is not true, even when brakes lock up.
> The frictional breaking force exists between the pads/calipers and  
> disks/drums.  This force does Not change Due to the mass of the  
> car.  It is a design of the breaking system.
>
> Regarding large trucks, I have been told two versions.  I can only  
> relay what I've heard.
> 1-They are able to use their drive-train in a funky reverse mode to  
> slow then down.
> 2-Air brakes-- I do not know any more.
> --I know my response here is very un-satisfying.
>
>
>
> Paul Lulai
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