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At the instant shown in $($Figure $1)$ the collar at $\backslash ($ A $\backslash )$ on the $\backslash (2\mathrm{.}0-\backslash$mathrm$\{$lb$\}\backslash )$ rod $\backslash ($ A B $\backslash )$ has a velocity of $\backslash ($ v$\_\{$A$\}=8\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Part A

Determine the kinetic energy of the rod after the collar $\backslash ($ A $\backslash )$ has descended $3$ ft $.$ Each collar is attached to the rod using a ball$-$and$-$socket joint. Neglect friction, the thickness of the rod, and the mass of the collars.

Hint: Use the angular velocity component of the rod that is directed perpendicular to the rod's axis.

Express your answer in foot$-$pounds to three significant figures.

$\backslash ($ T$=\backslash )\backslash (\backslash$mathrm$\{$ft$\}\backslash$cdot $\backslash$mathrm$\{$lb$\}\backslash )$ Figure