Problem $\backslash$# $1$

A $12-$in$-$wide polyamide A$-2$ flat belt is used to connect a $4-$in$-$diameter pulley to drive a larger pulley with an angular velocity ratio of $0\mathrm{.}5.$ The center$-$to$-$center distance is $18$ ft $.$ The angular speed of the small pulley is $\backslash (1750\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash )$ as it delivers $2$ hp $.$ The service is such that a service factor $\backslash (\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$s$\}\}\backslash )$ of $1\mathrm{.}25$ and a factor of safety equal to or greater than $1$ is appropriate.

i$.$ Estimate the centrifugal tension $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$c$\}\}\backslash )$

ii$.$ Estimate the Transmitted Torque T

iii. Allowable largest belt tension $\backslash (\backslash$left$($F$\_\{1\}\backslash$right$)\_\{\backslash$mathrm$\{$a$\}\}\backslash )$

iv$.$ Loose side tension $(\backslash (\backslash$mathrm$\{$F$\}\_\{2\}\backslash ))$

v$.$ Initial tension $(\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$i$\}\}\backslash ))$

vi$.$ Allowable power $\backslash (\backslash$mathrm$\{$H$\}\_\{\backslash$mathrm$\{$a$\}\}\backslash )$

vii. Length of the belt

viii. Check the danger of slipping