I thought of a maths problem for myself to solve, as it seemed like a good problem to try to get my head around. My issue is that I got stuck at the first hurdle. I was reading up about the braking systems on f1 cars and it said they the drivers put around 1500N of force through the brake pedal, and the coefficient of friction between the brake pads was about 0.6 at optimum temperature. I would have thought that this would have then given the car a decelerative force of 900N. f1 cars weigh 700kg, so this would give a deceleration of 1.28ms^-2. This is very far from the real value, as f1 cars decelerate at up to 5g, which is 49ms^-2. Can anybody figure out where I have gone wrong as I have been thinking about it for well over an hour by now.
You are missing at least two things here.
First, the total braking force is not directly applied by the driver's foot. All modern road cars, and F1 cars, have a servo assisted braking system so the driver's foot controls the amount of braking force, but doesn't create all of it directly. But having said that, a total force of 1500N would be reasonable for a road car. I don't know about the specification for F1 cars.
Second, that force is then multiplied by the hydraulic braking system when it is applied to the wheels. A hydraulic (fluid filled) system transmits pressure, i.e. force/area, not force. If the area of the pistons in the "wheel cylinders" that operate the brake calipers is say 10 times as big as the area of the "master cylinder" which is operated by the drivers foot (boosted by the servo system mentioned earlier), the fluid pressure will be the same in all the cylinders, but the force acting on the brake shoes will be 10 times bigger because the area is 10 times bigger.
The downside of that is that the piston in the master cylinder (and the driver's foot) has to move 10 times as far as the brake pads, but that isn't a big problem because the pads themselves only move a fraction of a millimeter from "off" to "full on."
To summarize, the force decelerating the car can be much greater than the force the driver applies to the brake pedal.