Answer
The work done by the gravitational force is $~~-1578~J$
Work Step by Step
We can find the vertical component of the length of the rope in the final position:
$L_y = \sqrt{(12.0~m)^2-(4.00~m)^2} = 11.3~m$
We can find the vertical displacement of the crate:
$\Delta y = 12.0~m-11.3~m = 0.7~m$
We can find the work done by the gravitational force:
$W = F~\Delta y~cos~180^{\circ}$
$W = mg~\Delta y~cos~180^{\circ}$
$W = (230~kg)(9.8~m/s^2)~(0.7~m)~(-1)$
$W = -1578~J$
The work done by the gravitational force is $~~-1578~J$.
