Problem $5.$ For a double short$-$shoe external drum brake with a drum width of $60$ mm as shown

in the following figure, find the torque capacity and required actuating force $F_a$ for $a=90mm,b$

$=80mm,e=30mm,r=40mm,$ and $=25.$ What value of $c$ will make it self$-$locking?

Assume the maximum allowable lining pressure is $1\mathrm{.}3$ MPa and the friction coefficient for the

brake lining material is $=0\mathrm{.}25.$

$(20$ marks$)$