# Expression for pressure in a brake system - is this correct?

• dreamliner
In summary: Mechanical_advantages_of_simple_mechanismsThe arms of the lever give the bicycle an advantage in terms of mechanical advantage over a human rider.
dreamliner

## Homework Statement

Write an expression for the force applied to the brake caliper in the braking system(hydraulic) of a bicycle.

F= force applied to the brake lever
a = distance between F and the pivot point of the brake lever.
b= distance between pivot point and lever piston.
d1= diameter of the piston on the brake handle
d2 = diameter of piston on the brake caliper.(PS English is not my mother tongue, so I might have used the wrong words for the different parts of the brake system. I do hope it's possible to understand what I mean.)

Pascal's law

Force * arm

## The Attempt at a Solution

Right away I'm thinking Pascal's law.

My first thought is to write pressure, p, = F1/d1 = F2/d2. I'm a bit unsure about where to incorporate distances a and b.
I'm tempted to use force*arm and write the whole expression as p=(F1*a)/d1 = (F2*b)/d2, but is this correct...?

Last edited:
You are thinking along the right lines, but you need some more structure to it. Let's start with the forces. The force applied is F; what is its moment about the pivot? What is the moment of the force generated at the piston? How are the two related?

Well, working on the assumption that moment force is force *length of the arm the force is working on, the amount about the pivot would be the applied force F*the distance a and the moment at the piston would be F*the distance b.
The relation being that the force F is the same in both cases.

But, that's the same as what I wrote in my initial post so I suspect you might be thinking about something else...?

Why would the force at the piston equal F?

Indeed. I suspect it's a case of hurrying. "Pascal's law uses F/A. I already have a F in the assignment. Great!".

Would it be correct to use F = P*A where P would be the applied force and A would be the surface area of the pistons, and then multiply the results with the distances?

Before doing the hydraulic part, finish the mechanics. You have a lever, with given arms, and a given force applied to one arm. Find the force produced at the other arm.

dreamliner said:
Well, working on the assumption that moment force is force *length of the arm the force is working on, the amount about the pivot would be the applied force F*the distance a.

So this part is correct?

I might be about to break some major rules of physics here, but I'm pretty much guessing now... Would the force on the piston be the amount about the pivot* distance b?

## What is the expression for pressure in a brake system?

The expression for pressure in a brake system is given by the formula P = F/A, where P is the pressure, F is the force applied, and A is the surface area over which the force is applied.

## How is the expression for pressure in a brake system derived?

The expression for pressure in a brake system is derived from the principles of fluid mechanics and the basic equation for pressure, which states that pressure is equal to force divided by area.

## Is the expression for pressure in a brake system correct?

Yes, the expression for pressure in a brake system is correct. It is a fundamental equation used in understanding and designing braking systems for vehicles.

## What are the units for the expression of pressure in a brake system?

The units for the expression of pressure in a brake system are usually in Pascals (Pa) or pounds per square inch (psi). However, other units such as bar, atmosphere, and kilopascals (kPa) may also be used.

## Are there any other factors that may affect the expression for pressure in a brake system?

Yes, there are other factors that may affect the expression for pressure in a brake system, such as changes in temperature, friction, and the properties of the brake fluid being used. These factors should be taken into consideration when designing a brake system.

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