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

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data

    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.)


    2. Relevant equations

    Pascal's law

    Force * arm



    3. 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: Mar 17, 2013
  2. jcsd
  3. Mar 17, 2013 #2
    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?
     
  4. Mar 17, 2013 #3
    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...?
     
  5. Mar 17, 2013 #4
    Why would the force at the piston equal F?
     
  6. Mar 17, 2013 #5
    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?
     
  7. Mar 17, 2013 #6
    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.
     
  8. Mar 17, 2013 #7
    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?
     
  9. Mar 17, 2013 #8
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