Example $2$:

A Linear Induction Motor $($LIM$)$ is designed to propel a conveyor system. The LIM operates with a primary current frequency of $50$ Hz $,$ and the conveyor is moving at a speed of $\backslash (20\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The pole pitch $($the distance between two consecutive magnetic poles$)$ is $0\mathrm{.}1$ m $.$ Calculate the following:

$1-$ Synchronous Speed $($V sync$)$ of the LIM.

$2-$ Slip $($S$)$ of the LIM.

$3-$ Thrust force $($F$)$ if the motor input power is $50$ kW and the LIM efficiency is $\backslash (85\backslash \%\backslash ).$