$($i$)400$ mm radius brake drum contacts a single shoe as shown in Figure $1$ in Page $2$ and sustains $200N-m$ torque at $500$ rpm $.$ For a coefficient of friction $0\mathrm{.}25,$ determine: $($a$)$ Normal force on the shoe, $($b$)$ Required force F to apply the brake for clockwise rotation and counter clockwise rotation, $($c$)$ The dimension c required to make the brake self$-$locking, assuming the other dimensions remains the same and $($d$)$ Heat generated.

$($ii$)$ For long shoe brakes deduce the expression for equivalent coefficient of friction with neat sketch.

$-350-$a$-$R $4001000$Figure $1.-350-1000-$R$4$X$)$