I've had an interesting conversation a day ago and we came to a stop regarding one explanation.
Conversation went about how increasing brake rotors doesn't make your car stop faster. But we came to the part where I couldn't explain how can we calculate the work done by human foot pressing on brake pedal.
When we press on pedal we exert a force on it. And this pedal travels some distance, so there is work done. Through all of hydraulic system we get a normal force on brake caliper and through it we get friction on the rotor. But let's assume that the brake rotor isn't spinning. We can press on the pedal as much as we want, but there is no friction created.
One more thing that bothers me is also equivalent of work done when we want to stop the car. We know its kinetic energy and all of this kinetic energy must transfer to heat energy of brake rotors (if we are correct, some goes to tires). I don't know the physical correct explanation of work done by foot and all this energy that transfers to heat on brake rotors. Can we even make this equal?
I know that calculation of work done by friction is straightforward. We know the magnitude of force and distance. But how do we calculate work done by normal force, which is perpendicular on the path of friction so dot product is zero?