Question $10.[10$ Marks$]$

A single$-$cylinder four stroke engine is coupled to a flywheel that is in turn connected to a mechanical load. The load does not vary. The engine runs at a nominal speed of $250ra\frac{d}{s}.$ The output of the engine is shown in Figure $11.$

Figure $11$: The torque output of a single$-$cylinder four stroke engine

$($a$)$ What is the mean torque output of the engine $T_m?$

$($b$)$ If we assume the load is equal to $T_m,$ explain why the largest speed variation would occur between $=0$ and $=158\mathrm{.}8.$

$($c$)$ For a coefficient of speed of $C_s=0\mathrm{.}05,$ what mass moment of inertia I should the flywheel have?

$($d$)$ What is the flywheel speed when $=0$ and $=158\mathrm{.}8?$

$1$

$2$

$($e$)$ What would happen to the system if the load was connected before the flywheel

$[3]$

had reached operational speed?