I have a Work word problem I need help completing?
1 Answer
See below
[Be careful about units. I have pretty much never used the old Imperial System before.]
Explanation:
The net upward force on the bucket,

#T# is the tension in the rope 
#m = m(t)# is the mass of water
Newton's Second Law:
The bucket travels at constant velocity

#implies 2 dot m = T  ( 4 + m)g# 
#implies T = 2 dot m + ( 4 + m)g#
Because the bucket is leaking at constant rate:
It also travels at constant velocity:
Thus:
So
And
#implies T(s) =  0.8 + ( 4 + (50  0.2 s))g#
The work done by
#W = int_0^(100) T(s) \ ds #
Using
Reality check:

Assuming no leak, it would be
#54 * 32 * 100 = 172,000# so it is correct order of magnitude and lower. 
The bucket still retains
#60 "%"# of the water so you would expect it to be closer to the ideal noleak position