Determine the magnitude of force $\mathbf{F}$ as a function of time, which must be applied to the end of the cord at $A$ to raise the hook $H$ with a constant speed $v=0.4 \mathrm{m} / \mathrm{s}$. Initially the chain is at rest on the ground. Neglect the mass of the cord and the hook. The chain has a mass of $2 \mathrm{kg} / \mathrm{m}$.