The brass tube $AB(E=15{10}^6)$ has a cross$-$sectional area of $0\mathrm{.}24i{n}^2$ and is fitted with a

plug at $A.$ The tube is attached at $B$ to a rigid plate that is itself attached at $C$ to the bottom

of an aluminum cylinder $(E=10\mathrm{.}4{10}^6)$ with a cross$-$sectional area of $0\mathrm{.}40i{n}^2.$ The

cylinder is then hung from a support at $D.$ To close the cylinder, the plug must move down

through $\frac{3}{64}$ in$.$ Determine the force $P$ that must be applied to the cylinder.

The force $P$ that must be applied to the cylinder is

kips.