Problem $1.[5$ Marks$]$

A fan is driven by a belt from a motor which

runs at $880re\frac{v}{m}in.$ A medium double ply

leather belt $8$ mm thick and $250$ mm wide is

used. The diameters of the motor pulley and

driven pulley are respectively $350$ mm and

$1370$ mm $.$ The center distance is $1370$ mm $,$ and

both pulleys are made of cast iron. The

coefficient of friction of leather on cast iron is

$0\mathrm{.}35.$ The allowable stress for the belt is $2\mathrm{.}4$ MPa $,$ which allows for the factor of safety

and for the fact that a double ply belt does not have double the capacity of a single ply

belt. $($A double ply belt has approximately $85\%$ the capacity of a single ply belt of the

same thickness.$)$ The belt mass is $970k\frac{g}{m^3}.$ What is the power capacity of the belt?