A pressure vessel explodes. The method generally used for designing barricades around

something like this is to $1)$ calculate the stored energy in the pressurized vessel, $2)$ postulate a

typical fragment size, and $3)$ estimate the velocity of the fragment when it has all or part of the

stored energy in the vessel $($kinetic energy$).$

The fragment size estimated in our analysis weighs $5$ lbf $(2\mathrm{.}268$ kg mass$).$ Remember that lbf is a

FORCE, not a mass $($mass is in slugs$).$ The maximum velocity of the fragment is predicted to be

$500$ m$/$s $(1640\mathrm{.}4$ ft$/$s$).$ The fragment travels horizontally and hits a wall, which has a spring

constant, k$,$ of $14,400$ lbf$/$ft $(210$ N$/$mm$).$

a$)$ With what force will the fragment hit the wall?

b$)$ What will be the deflection of the wall when it hits?

If the wall was made of a material having a spring constant of only $1000$ lbf$/$ft $(14\mathrm{.}6$ N$/$mm$),$ and

the velocity was the same as above, what would be the

c$)$ impact force?

d$)$ wall deflection?