W$4$th $15\mathrm{.}19$: Pascal's Barrel. A circular wine barrel $71\mathrm{.}0cm$ in diameter will burst if the net upward force exerted on the top of the barrel is $623N.$ A tube $1\mathrm{.}30cm$ in diameter extends into the barrel through a hole in the top, as indicated in the figure. Initially, the barrel is filled to the top and the tube is empty above that level.

a$)$ What weight of water must be poured into the tube in order to burst the barrel?

b$)$ This weight corresponds to a burst pressure. How does it compare with atmospheric pressure? Evaluate the ratio of the burst pressure to atmospheric pressure.

$($Answers: $0\mathrm{.}209N$ and $1\mathrm{.}02)$