How to Stop a Car: The Physics Behind Brake Systems

 How can the small amount of pressure applied by your foot manage to stop massive, hundreds of kg, car moving at incredible speeds? The answer is physics, simple area, and pressure physics to be exact. 

When you apply force to the brake pedal, it pushes a non-compressible liquid through a tube to translate this applied force. The liquid, typically oil, is then pushed through tubes. The tubes can curve and snake around the car and can fork into two allowing the applied force to be translated anywhere the tubes end. The real magic of the braking system though comes in the form of hydraulic multiplication.

Consider what we know about pressure, area, and force,

F = P/A

Based on this simple equation we can see that to increase force we can either increase pressure while the area remains constant or decrease area while pressure remains constant. In both of these cases, the force will increase. As we can see in the diagram below, if A2 is greater than A1 then F2 will be greater than F1. So let’s consider that the piston on the left has a radius of 2 inches while the piston on the right has a radius of 4 inches. When considering the areas of the pistons, A1 is now π(2)2 = 12.6 in2 while A2 is π(4)2 = 50.7 in2. So if F1 = 10 N, F2 will now equal 40.4 N! In this case doubling the radius of the piston, quadruples the force it exerts. Now imagine that force exerted by F2 is applied to the tires of your moving car and instead of doubling the radius we triple, quadruple, or multiply the radius of the piston to even greater degrees on the right. This incredibly multiplied force is then applied to the moving tires to create a frictional force that will start to slow their rotation and we can start to see how the simple push of your leg can stop the hurling chunk of metal you are driving.