Answer
$a=25.76~\text {ft/s}^2(\downarrow)$
Work Step by Step
Given:
Applied force, $F_{Applied}=10~\text {lbf}$.
Acceleration due to gravity, $g=32.2~\text {ft/s}^2$.
Mass of the object, $m=50~\text {lb}$
To Find:
Net acceleration of the object, $a=?$
The applied force on the object acts in the upward direction (+) and the weight of the object acts in the downward direction (-).
For equilibrium,
$F_{Applied}-W=ma$
$F_{Applied}-mg=ma$
$a=\dfrac {F_{Applied}-mg}{m}\\
=\dfrac {F_{Applied}}{m}-g$
Plug the given values and find the acceleration of the object.
$a=\dfrac {10\text { lbf}}{50\text { lb}}\dfrac {32.2\text { lb.ft/s}^2}{\text {lbf}}-32.2~\text {ft/s}^2\\
a=-25.76~\text {ft/s}^2$
The negative sign indicates that the acceleration is in the downward direction.
