The lightbulb in the circuit shown here has a resistance of $12 ~\Omega$ and consumes $5.0 \mathrm{~W}$ of power; the rod is $1.25 \mathrm{~m}$ long and moves to the left with a constant speed of $3.1 \mathrm{~m} / \mathrm{s}$. What external force is required to give the rod a speed of $3.49 \mathrm{~m} / \mathrm{s}$, everything else remaining the same?