Answer:
Total work done = 15,306.25 lb.ft
Explanation:
First of all, we know that;
Work done = Force x Distance.
Thus,
Work done to pull bucket (Wb) = 500 x 30 = 15,000 lb.ft
Now, work done by pulling the rope is given as a function of the length of the rope. Thus;
Wr =(x,x=0∫) F(x) dx
=(35,0∫) 0.5x dx
= 0.5[x²/2](35,0)
Thus,Wr = 0.5[(35²/2) - (0²/2)] = 0.5[612.5] = 306.25 lb.ft
Total work done will be the sum of that done to pull the bucket and that done to pull the rope.
Thus, Wt = Wb + Wr
Wt = 15000 + 306.25 = 15,306.25 lb.ft