A Simple Brake System
Before we get into all the parts of an actual car brake system, let's look at a simplified system:
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You can see that the distance from the pedal to the pivot is four times the distance from the cylinder to the pivot, so the force at the pedal will be increased by a factor of four before it is transmitted to the cylinder.
You can also see that the diameter of the brake cylinder is three times the diameter of the pedal cylinder. This further multiplies the force by nine. All together, this system increases the force of your foot by a factor of 36. If you put 10 pounds of force on the pedal, 360 pounds (162 kg) will be generated at the wheel squeezing the brake pads.
There are a couple of problems with this simple system. What if we have a leak? If it is a slow leak, eventually there will not be enough fluid left to fill the brake cylinder, and the brakes will not function. If it is a major leak, then the first time you apply the brakes all of the fluid will squirt out the leak and you will have complete brake failure.
The master cylinder on modern cars is designed to deal with these potential failures. Be sure to check out the article on How Master Cylinders and Combination Valves Work, and the rest of the articles in the brake series (see the links below), to learn more.