When you apply the brakes to a car and it slows down, there are two kinds of friction and I am getting confused.
On the one hand, there is friction between tyres and road. This friction
a) Is the only external force on the car, so ultimately according to Newton's law this must be equal to mass x acceleration and should be responsible for slowing down.
b) Is static and performs no work. This is weird. How can this force slow down the car but produce no work? How about the kinetic energy theorem?
On the other hand, there is friction in the brakes. This friction
a) Dissipates mechanical energy into heat, so you might say that actually it is this force that slows down the car.
b) But, all interaction at the brakes is internal to the car-system, so cannot produce any center-of-mass acceleration.
So it seems one force is responsible for the acceleration and another force is responsible for dissipating the energy. I could accept this, but it sounds weird. Should I just leave it at that or is that wrong?
EDIT: This question is not a duplicate. I understand different types of friction and the forces present in the problem. The answers to other questions do not answer this one. This one can be summarized as "How can static friction with the road produce acceleration but no work, and kinetic friction in the brakes produce work but no acceleration?" Other questions are different.