Master and Output Pistons in Car Breaking System: Calculating Force and Movement

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Homework Statement



the breaking system on a car utilises a master pistion that is 10 cm in dimeter. the four outout pistons (one on each wheel) are 2cm in diameter

a) if 500 N of force is applied to the master piston, what is the output force on each of the wheel pistons?

b) if the master piston moves 5cm, how much does each output piston move?

c)how is this not a free lunch?


Homework Equations



unknown. missed class the day this was done and I cannot foind an example like it.



The Attempt at a Solution



I figured that the force would just be divided by four but looking at C that must not be right or that wouldn't be there.

b) for the output piston i would think it would be 10/2 x 5= 25 cm. but I am not sure about this answer.
 
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Think in terms of pressures transmitted by the working fluid from and to the piston surface areas. Consider the pressure in the working fluid to be everywhere the same. Also consider that the total volume of working fluid is constant.
 


i still don't get it, what is the formula for it, could you show me a sample calculation?
 


What is the pressure in the working fluid if a 500N force is applied to the 10cm diameter piston? (hint: what is the formula for pressure given force and area?).