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

[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.)

Homework Equations

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...?

 

[voko]

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?

 

[dreamliner]

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...?

 

[voko]

Why would the force at the piston equal F?

 

[dreamliner]

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?

 

[voko]

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]

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?

 

[voko]

Review this: http://en.wikipedia.org/wiki/Mechanical_advantage