QUESTION $3[10$ marks$]$

A vertical steam engine has reciprocating parts that weigh $95$ kg $.$ At a point on the down$-$stroke when the crank angle is $140$ the pressure above the piston is $35k\frac{N}{m^2}$ and $20k\frac{N}{m^2}$ below. The cylinder diameter is $600$ mm $,$ the connecting rod is $500$ mm long and the stroke is $250$ mm $.$

a$)$ Find the engine torque if the speed is $550re\frac{v}{m}in.$

b$)$ Write an equation to calculate $F_E$ for a horizontal engine

$(1)$