$2\mathrm{.}63$ Figure P$2\mathrm{.}63$ shows a total gas force $F$ applied to the top of a piston.

$($a$)$ Copy the drawing and sketch the force paths through the piston, through the piston pin, and into the connecting rod.

$($b$)$ Making appropriate simplifying assumptions, identify the stresses in the piston pin and write an equation for each.$*$ State the assumptions made, and discuss briefly their effect.