How to Calculate Torque in a Hydraulic Brake System

[sun]

Homework Statement

The area of the piston in the master cylinder is 1.8cm^2, and that of the piston in the brake cylinder is 6.4cm^2. The coefficient of friction between shoe and wheel drum is .50. If the wheel has a radius of 34cm, determine the frictional torque about the axle when a force of 44N is exerted on the brake pedal.


(Pedal)--[master cylinder]-----[brake cylinder]-----(shoe)Wheel drum

Homework Equations

torque=rF
F1=(A1/A2)F2
F=(mu)*normal force

1.8cm^2=1.8X10^-4m^2
6.4cm^2=6.4X10^-4m^2
radius=34cm=.34m

The Attempt at a Solution

I solved for F2 and got 12.4N. Is this the force that the shoe exerts on the wheel drum?
If that is correct, how do i go about solving for the torque?

thank you

 

[Shooting Star]

You have to know where the force is being applied on the wheel. Since a radius is given, it seems logical to take the force as being applied at that ditance.

Torque about a point = force*dist from that pt to line of action of force.

 

[Chandrakiran]

Hi,
I might be wrong, but I was going through the problem statement and got a doubt there.

I think you have considered A1 as aan area of Master Cylinder, then F1 should be 44 N, as it is the force applied on the brake pedal. F2 must be a force exerted by a brake cylinder. Please correct me if my thinking is wrong...

 

[Shooting Star]

Going through the problem again, I think user Chandrakiran is correct. Exerting 44 N and getting 12.4 N doesn't seem realistic. The OP had not specified which are the brake and master cylinders, and I had only anwered as to how to find the torque.

Nice work, Chandrakiran.