## Question:

alleviate this problem, an automobile seat restraint has been developed that provides additional pressure contact with the cranium. During dynamic tests the distribution of load on the cranium has been plotted and shown to be parabolic. Determine the equivalent resultant force and its location, measured from point $A$.

Given:

$a$ = $0.5$ $ft$

${ w }_{ 0 }$ = $12\frac { Ib }{ ft }$

$k$ = $24\frac { Ib }{ { ft }^{ 3 } }$

$w(x)$ = ${ w }_{ 0 }$ + $k{ x }^{ 2 }$

## Step-by-step

${ F }_{ R }$ = $\int _{ 0 }^{ a }{ w(x)dx\quad\quad \quad \quad \quad \quad \quad } { F }_{ R }$ = $7$ $Ib$

$x$ = $\frac { \int _{ 0 }^{ a }{ xw(x)dx } }{ { F }_{ R } } \quad\quad\quad\quad\quad \quad \quad \quad x$ = $0.286$ $ft$