Aheavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. how much work is done (in ft-lb) in pulling half the rope to the top of the building?

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]

the simple machine has three main features. they are:

fulcrum is the center point or pivot point of the machine. effort is input force/ applied force. load is external force/ output.

the keisha 's machine labels are

x : load

y: fulcrum

z: lever