Answer
$16, 245 ft-lbs $
Work Step by Step
The magnitude of the gravitational force acting on the man +Can of paint $=(160+m)lbs$
When we are moving in the upward direction, then we have
$F \cdot dr=(185-\dfrac{9r}{s}) dr$
Work done, $W=\int_C F\cdot dr= \int_0^s (185-\dfrac{9r}{s}) dr$
Here, $C$ is a vertical line segment joining the lower and upper part of the silo, so we get
Thus, the work done is given by: $W=\int_C F\cdot dr=[185r-\dfrac{9r^2}{2s}]_0^s=185 (s)-4.5 (s) =16, 245$ ft-lbs
