Disc break is studied in the breaking configuration i$.$e$.$ when the brake pads are pressed against the disc surfaces by the piston and the caliper the actions of the pads on the surface are defined as follows in the next figure

The mechanical actions applied by the right $(R)$ and left $(L)$ pads on the disc surfaces are

defined at points $M$ and $N$ on the elemental surface $dS$ as:

$d{F}_R=d{N}_R+d{T}_R=-PdS{x}_0+fPdS{e}_{}$

$d{F}_L=d{N}_L+d{T}_L=QdS{x}_0+fQdS{e}_{}$

with $P,Q$ and $f$ positive constants.

Questions:

a$)$ Determine the wrench coordinates at point O of the right pad actions on the disc,

b$)$ Similarly, without any calculations, give the wrench coordinates of the left pad action

on the disc.

c$)$ Considering the union of the actions of the two pads on the disc, give the wrench

coordinates in O $.$

d$)$ Assuming that pressures Q and P are equal:

a$.$ give the corresponding wrench coordinates

b$.$ calculate its automoment, is the wrench special?

c$.$ Determine the central axis.