$4-$ The brass tube $AB(E=15{10}^6)$ has a cross$-$sectional area of $0\mathrm{.}32i{n}^2$ 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 $3/64$ in$.$ Determine the force $P$ that must be applied to the cylinder. Answer: $6\mathrm{.}95$

kips.