Answer:
W=2001.24 newton meters
Caution: check units and arithmetic - I often make errors.
Step-by-step explanation:
Work is force times distance.
Denote height by h where h=0 is at ground level.
Denote the mass of the bucket and rope at height h by m(h).
The rate at which the bucket loses mass with height is (20-16)/10=0.4 kg/m
The rate at which the rope between the bucket and the top of the building loses mass is 0.4 kg/m
The initial mass of the bucket and rope is
The mass at height h is
The force required at height h is
m(h)g
where g is the gravitational acceleration.
g=9.81 meters/sec/sec
The work required is
Where a=0 and b=10
g(244-40)=204g
W=2001.24 newton meters