We want to determine what a reasonable flexural rigidity $(EI)$ would be for a Cessna $172$ wing spar. We will

model the wing as shown below: assume the $5-m$ wing is pinned at the root and again $2$ m from the fuselage.

The lift distribution is constant between the supports and then tapers linearly from that value to $40\%$ of the

value at the wing tip. Along with the pin at the fuselage, there is a moment of $10w_0($note that the moment

still has units of force x length, even though $w_0$ does not$).$ The $172$ has a maximum load factor of $3\mathrm{.}8,$ so we

will use the load case where each wing produces lift equal to $190\%$ of the plane's weight. We will consider

the maximum takeoff weight $($MTOW$),$ which is approximately $1,100kg.$ Assume the wing spar is uniform;

i$.$e$.,$ it has the same $EI$ along its length. Develop an expression for the deflection $v(z)$ in terms of $EI.$ What

would a reasonable flexural rigidity be$?$