Question $2$

$($a$)$ In a $4-$cylinder $4-$stroke internal combustion engine, the cylinder bore is $78$ mm and the stroke length is $95$ mm $.$ In a test, the brake mean effective pressure is $850$ kPa and the speed is $2400$ rpm $.$

$($i$)$ What is the total displacement volume of the engine? Express your answer in $\backslash (\backslash$mathrm$\{$mm$\}^\{3\},\backslash$mathrm$\{$~mL$\}\backslash ),$ and $\backslash (\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

$($ii$)$ Calculate the work done by gas on one piston in one full cycle.

$($iii$)$ Calculate the power output of the engine.

$($b$)$ Explain the term "normalisation of deviance" with reference to at least one well$-$known example of a failure or error in mechanical engineering.

$($c$)$ An electric motor has its highest efficiency at a speed of $1520$ rpm $.$ It propels a car with wheels of diameter $0\mathrm{.}46$ m $.$ When the car is driving at $\backslash (45\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ),$ the motor should be running at maximum efficiency.

$($i$)$ What gear ratio from motor to wheel should be used?

$($ii$)$ Name and sketch two types of mechanism that could provide the required gearing.