Lets say I am hurtling along at 100mph in my car and I decide to brake to zero mph. Stopping distance is no concern.
If we disregard air resistance and other frictional factors - IOW, only the brakes can stop the car, what would be the best strategy for using the least amount of brake pad material. Stop on a dime or brake slowly over a mile. Assume that brake activation places the transmission in nuetral.
Hmm… very interesting. You’re looking for the relationship between the force of friction applied with the brakes and the resultant wear, in other words. Does the basic high-school physics F(friction) = k F(normal) work here, or do things get more complicated? How would heat factor in?
WAG time. Brake pad wear will be a function of both applied pressure and time (or distance - depends on how the problem would be most easily solved). My feeling is that the optimum is somewhere intermediate, but maybe favoring hard braking. Towards the extreme of very hard braking, there could be so much pressure that the brake pad starts to fail for reasons other than normal friction and wear. At the other end, just as light or moderate pressure works best for most abrasive tools, the same could cause more brake pad wear. But that’s, as disclaimed above, a total WAG.
I know this is cheating, but apply the brakes and lock the wheels instantaneously, slowing to a stop on the skidding tires. All of the kinetic energy is dissipated by the tires as they’re skidding, not by the brakes.
Being serious, I like lazybratsche’s guess. From what I understand, optimal brake performace is had somewhere between cold and glowing hot, though that optimal performance point might be much different that the optimal efficiency point (energy dissipated per brake mass removed). Intuitively, it would seem that higher temperatures would cause faster wear, but that’s just my gut feeling. So my WAG answer would be stopping semi-aggressively with somewhat warm brakes, but not so agressively that the brake temperature goes into that “high-wear zone”.
I’m interested to see what others have to say. Is there an automotive brakes engineer in the house?
Not an automotive brake engineer, but I do dabble in brakes.
The lightest application of brakes will give the longest life.
When I taught my son to drive, I taught him to always look way ahead. If the stoplight at the end of the block is red, coast. Lose some speed that way and then brake lightly. He now gets about 3 times the average pad life on his car then other drivers with the same model.
Answering the OP, if stopping distance is of no concern, I would take my foot of the gas and let the car coast. When it got to say 10mph apply the brakes.
No wear on the tires, and little wear on the brakes.
Yeah, but the OP specifically stated that he wants the answer irrespective of other sources of friction, meaning this hypothetical car can’t coast to a stop. In reality, this sort of light braking is very likely best, but that’s because more of the work of stopping a car is done by things other than the brake pad: air resistance, rolling resistance, internal friction, etc.
Here’s my WAG. Hypothetical car on a level surface without wind resistance using frictionless tires (why does this sound familiar?).
If you consider that the momentum of the car is going to be stopped by transferring the energy into heat absorbed by the brake pads, I think that a long, slow braking process would create less wear on the brakes. The act of braking hard and stopping immediately would create higher brake pad temperatures (thus causing more wear due to the higher temperature) compared to allowing the brakes to bleed off speed more gradually over a longer distance.
I drove my sister’s car for a weekend when its clutch started playing up, she took my car to a concert in exchange. Basically (as described in my thread on the subject) the car had trouble engaging 1st and 2nd gear. I had to look ahead to traffic lights and guage my speed so I could arrive and breeze through in third gear, so as to avoid changing down. Driving suddenly became a lot more fun 
Let me back this up with some basic tribology: brakes (particularly disc brakes) don’t function via metal-to-pad friction the way most laymen believe they do. What happens is that the heat generated by initial contact forms a very viscous, gel-like collusion between the pad and the rotor disc. The pad never actually contacts the rotor in a mechanical sense; it makes a connection via this layer, and slows the wheel by viscous drag. Too much heat–i.e. from braking too hard or for too long a period, when the rotor can’t convect away all of the built-up heat–causes this layer to break down and premature wear of both the pad and possibly the rotor. (This is exacerbated by contaminants between the rotor and pad that cause pitting or grooving of the rotor, allowing the fluid to channel away.) As long as heat never builds up to a level that causes excessive breakdown of this viscous layer, braking force will remain constant and brake wear will be nominal. Hard braking causes disproportionate wear of both the brake and rotor. It’s certainly plausible that someone who habitually brakes easily and gently will get several times the operational lifespan than someone who brakes sharply.
So, in short, Rick’s answer is absolutely correct; the lightest application of brakes will make the pads last the longest and prevent premature rotor wear. Coasting to a slow speed and then braking not only reduces the amount of total work the brakes need to do but also lets the rotors stay cool and function at optimum efficiency.
Stranger
Wait… so is this gel formed by the brake pad melting? I don’t get it.
If we are doing this as a controlled expirement (not for driving normal driving purposes) I’d say the way to go for least wear on the brakes is to hit that brake pedal to the floor, lock the brakes immediately, and skid from 100 mph to a stop.
I don’t even think the brakes would heat up much less wear down.
Look for a large,unmovable object. 
It would eventually reach zero speed if it were…errr…placed on a device…that could rotate backwards…yeah that’s the ticket
Yes. There’s an interesting reversal of function; initially, a brake pad or lining is a composite material with a matrix or binder in which is embedded heat-resistant abrasive particles or fibers. When the brakes are engaged, the particles rub against the rotor, rapidly heating up and liquifying the surrounding matrix. Now, the matrix creates a collusion in which the particles are suspended, which gives the whole mass more cohesion that the binder would have alone. When a contaminant like water or oil gets on the rotor it interferes with this collusion and often causes a kind of skipping or squealing behavior; ditto for pads that are unevenly worn or improperly supported.
By the way, most brake shops and many pad manufacturers often suggest turning down the rotor every time you replace the pads. While rotor warpage can occur, it is generally the result of someone overtorqing the lug nuts with an impact wrench, not from ordinary wear. Unless you’ve had problems before with the braking performance or there is visiable pitting or gouging in the rotor, it is neither necessary nor advisable to turn down the rotors when you replace the pads; doing so gives the rotor less thermal capacity and less rigidity, and most modern rotors are optimized for performance verses minimum unsprung weight, so taking off more material unnecessarily is detrimental to overall performance.
Stranger
You’re going to have serious issues slowing a car with frictionless tires using anything other than rocketry.
Open the door and stick your foot out.
I don’t want to get into a whole draw-out argument here, but this idea of the brake pad surfaces melting under normal use seems contradictory to me, and flies in the face of everything I understand about braking. As I understand things, one type of brake fade is, in fact, caused by the liquification of the binding agent. Now, it’s possible that small amounts of melting are necessary for normal braking, while large amounts lead to fade. But, I’ve seen many brake pads and shoes in my day, and if there were melting occurring under normal usage, I’d expect to observe signs of it, such as scalloping at the trailing edge, where fluid flow has cooled and refrozen. But, I’ve never seen anything like this that I can recall. Not to call your claim into question, but do you have a decent cite online I can take a look at?
Always drive uphill.
Turn the steering wheel sharply and spin out (or start going in a circle). Either way, the car will come to a stop with zero wear on its brake pads. Wear on tires, suspension and steering are beyond the scope of this OP. Even with “perfect tires” that don’t lose any energy, there would still be an energy bleed due to interactions with the less-than-perfectly rigid road/planet. If you’re on a perfectly rigid planet, you’ve got bigger problems.
Huh. Consider my ignorance fought. This is exactly why I subscribed…
Let me make sure I understand this. The brake pad contains two materials, one a fibrous network throughout the pad, and the other some sort of chemical (the binder) embedded in this network that melts and becomes a viscous fluid when braking. This fluid is very cohesive, and adsorbs (adheres?) to the brake disc and the other material in the pad, creating drag between the two surfaces.
Is this mostly right? What are the typical substances used for each component of the brake pad?
This is correct. To be clear, a small portion of the braking force is provided by direct metal to metal (or metal to ceramic, depending on the pads) friction, but mostly this just heats up the pad so that the binder that is typcially some kind of high temperature phenolic resin (like that used in thermal protection systems in rockets). The “network” need not be fiberous–more often, it is a particulate matrix–but in the past silocate fiber (asbestos) was used as a matrix. Within a elevated certain range this provides the drag that is the primary braking force; at still higher temperatures, the fluid layer loses viscosity and you get “brake fade” where the braking materal glazes or even vaporizes, measurably reducing braking force.
This is an active area of tribological research, and what I’m providing here is the very basic explanation; I’m not an expert on tribology (which is a fascinatingly tedious subject to do research in; that is to say, it doesn’t bring in the chicks like astronomy or finite element analysis, but it does give you a bizarre, counterintuitive view on how many common things work) but I’ve done some casual reading on the topic above and beyond the minimum exposure in engineering school. If you submit this as a question to Cecil, perhaps one of the resident SDSAB members, or a “guest contributor” (wink wink nudge nudge) will do a real writeup with references and all.
Stranger