Date: Sat, 04 May 2002 09:25:08 -0400
Author: James Frysinger
Subject: Re: Stopping Power
Yes, the watt is an SI unit, but I would not use the suggested equation to
calculate stopping power. The brakes on a car must dissipate the car's
kinetic energy (in joules) and if that energy is divided by the time (in
seconds) it takes to dissipate that energy then the brakes' stopping power
could be given in watts.
The essence of the problem is the force which is measured in newtons and the
distance measured in meters. Unless the car skids, the tires are static with
respect to the road so, within this rolling frame of reference, no real work
is done. The work is done (and the heat is dissipated) in the area of contact
in the braking system. The force that should be measured is the shear,
frictional force exerted by the brake pads on the disks (or shoes on the
drums) and the distance is the relative tangential displacement where they
come into contact.
Do a gedanken experiment to show that the gravitational field (and hence the
vehicle's weight) have nothing to do with the problem. Repeat the experiment
on the Moon. If the car's mass and velocity are the same at the start of both
the terrestrial and lunar trials, the same amount of kinetic energy must be
dissipated. In each of the two experiments, ensure that the same (kinetic)
frictional force is exerted by the brake pads and one can see that the
vehicle will stop within the same time interval. The two vehicles have
different weights (the one on the Earth being about 6 times as large) and
their speeds are the same at the start of the experiment. Thus the proposed
equation incorrectly predicts the stopping power (rate of dissipation of
kinetic energy). One must only ensure that the transmitted force at the area
of contact does not exceed the maximum available static frictional force in
order to prevent skidding. Once skidding starts, then some of the stopping
power is provided by the relative motion of rubber on asphalt. Even in South
Carolina, skidding stops are not considered the norm.
The above ignores the energy lost in the flexion of the tires and the
internal work done by this process in them. Since the vehicle weight on the
Earth is larger, more flexion will occur and hence more internal work will be
done. But nearly all of a car's kinetic energy is dissipated by the brakes in
a non-skidding stop and energy loss in the tires due to flexion is a process
that occurs even before braking occurs.
This is an excellent question to put before a class near the end of the unit
on work and energy! Thanks for suggesting it, though that was not your main
point, Duane. It also serves to show that, while unit analysis can reveal
errors in an equation, one can be misled by unit analysis into assuming that
an equation is correct, as this radio station may have done.
On Saturday, 2002 May 04 0826, you wrote:
> Letting the unit do the talking, speed (m/s) times weight (N) gives
> (N.m/s) which is (J/s) which is a (watt). Is that not a SI unit?
> -----Original Message-----
> From: Duane Warn
> Sent: Thursday, May 02, 2002 11:11 AM
> Subject: Stopping Power
> Hi all,
> The new advertisement on the radio for wearing seat belts uses
> Stopping Power.
> Stopping Power = Speed X Weight .... It's simple physics!
> I think this should be added to the set of new SI units.
> Boise State U.