The formula used in calculating for values of work is given as:
W = F d
However on the above formula, the force
is constant but i this case, it is changing. Therefore we make use of the
general form with the integral notation:
W = ∫F(x) dx
with limits of x from 0 to 25 since only half of the rope is be pulled
The equation for F (x) is equal to the product
of mass density and length x:
F(x) = 0.5x
Substituting this into the integral work equation:
W = 0.5∫x dx
W = 0.5(0.5) [x2^2 – x1^2] ---> x from 0 to 25
W = 0.25 [25^2 -0]
W = 156.25 ft * lbs
