$3.$ The schematic below shows two spheres, $\backslash ($ a $\backslash )$ and $\backslash ($ b $\backslash ),$ connected by a thin rod which pivots about a hinge at the center of the rod. Initially, the weight of the larger sphere, $\backslash ($ a $\backslash ),$ keeps the rod against the stop, which prevents the assembly from rotating counter$-$clockwise. Estimate the wind speed $($air at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )),\backslash ($ U $\backslash ),$ necessary to cause the rod to come off the stop and begin rotating clockwise. Assume that the pivot is frictionless and the drag force on the rod itself is symmetrical about the pivot and can be neglected. The spheres are steel $\backslash (\backslash$rho$=7800\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

a$.$ Write an expression for the balance of forces on the spheres.

b$.$ What drag coefficient$($s$)$ will you use for the spheres? Might you need to iterate?

c$.$ What is the velocity, $\backslash ($ U $\backslash ),$ when the rod moves off the stop? Was your drag coefficient in b correct? If not repeat until it is$.$

Soln: c$.\backslash ($ U$=64\mathrm{.}3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ show all work.