Question

2 lb/ft robe is used to life 800lb of coal up a mine shaft 500ft deep. Find the work done?

I need help solving this I have no idea where to start, all I know is I have to use integrals to solve

Answer 1

what I know the interval is
a=0 b=500
amount of coal = 500lbs
weight of rope = 2 lb/ft
weight of rope = 1000lbs

I'm completely lost

Answer 2

I know

Work = force * distance
and
Force = acceleration * mass

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcI/Work.aspx
it has an example almost exactly like this problem
the Force is just the total weight at any given time

Answer 4

So I got the solution

\[\int\limits_{0}^{500}3(500-x) + 1000dx = 875,000\]

what units is this in? also is this answer correct?

Answer 5

sorry this is the answer for a question where the coal weighs 1000, and the cable weights 3lbs/ft and the shaft is 500ft deep

Answer 6

total weight = 2(500) + 800 =1800lb=816.5kg=8165N(taking g=10)
displacement=(1/3.281)x500=152m
Work done = Weight x displacement=8165 x 152=1241080 J

Answer 7

yes answer is correct and units are ft*lbs since the Force is in terms of lbs