# HW 12 Question 7 ??

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The figure below shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is 1.8 cm2, and that of the piston in the brake cylinder is 6.4 cm2. The coefficient of friction between shoe and wheel drum is 0.50. If the wheel has a radius of 34 cm, determine the frictional torque about the axle when a force of 47 N is exerted on the brake pedal.

For the hydraulic brake system, first we need to find the force the brake shoe is pushing the wheel drum. This can be done using the hydraulic pressure and force relation. Here P is same in the hydraulic system and the pressure force exerted on the cylinders are $F=PA$, where A is the area of the cylinder.  See the figure below for illustration of the forces and torque on the brake system.

Since pressure in the hydraulic system is the same, we have $$\frac {F_p}{A_1}=\frac {N}{A_2}$$

This will allow you to find the normal force the shoe pushes on the wheel drum.

Then this normal force will create friction $f=\mu mg$, which then creates a torque $\tau=fR$.

answered Nov 10, 2013 by (21,750 points)