vianca15
31.03.2020 •
Mathematics
A cable that weighs 8 lb/ft is used to lift 650 lb of coal up a mine shaft 600 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
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Ответ:
1830000 ft*lb
Step-by-step explaination:
Work done = fd
f=force:
d = distance
f = 650 + 8x lbs, x is current amount of cable in shaft
dW = fdx = (650+8x)dx
x ranges from 0 to 600 then the total work is:
W = integral(x=0 to x=600)((650+8x)dx)
W = (650x+4x^2)[x=0, x=600]
W = (650*600 + 4*(600)^2) = 1830000 ft*lb
W = 1830000 ft*lb
Riemann sum approximation:
W = sum(i=1 to i=n)(650+8xi*)(xi - x(i-1))
x0 is 0, xn is 600 (or x0 is 600, xn is 0)
assuming the partition is a constant interval deltax sum can be written as:
W = summation(i=1 to i=n)(650+8xi*)deltax
Ответ:
Would you be able to solve it that way ?
They're both the same number.