Answer
$3857.3 J$
Work Step by Step
Work done to lift the bucket:
$$(10 kg)(9.8 m/s^{2})(12 m) = 1176 J$$
Work done to lift the rope:
$$\int_{0}^{12} 7.84(12-y) dy= 564.5 J$$
Work done to lift the water:
$\frac{36 kg}{12 m}=3kg/m$
$3(12-x)=36-3x$
$$\int_{0}^{12} 9.8(36-3y) dy= 2116.8J$$
Add all the work done on the bucket, rope, and water:
$$1176J + 564.5J + 2116.8J = 3857.3J$$
