Simple Machines - Biomechanics of the Human Body - page 87

Fig. 5.9 Representation of
a pulley-block with two
movable pulleys and a
mechanical advantage equal
to four

F A

W / 4

W / 2 W / 2

W = F R

weight of the object that we want to lift, and the direction of the force has
been changed.
The pulley-block, shown in Figs. 5.8 and 5.9 , is the system of pulleys,
constituted by independent movable pulleys that are supported by an even number
of forces. In this case, as already demonstrated, each movable pulley works in a way
that the action force necessary to maintain the system in equilibrium is half of that
needed without the combination of pulleys.
In the pulley-block with N movable pulleys, the mechanical advantage is then
given by:

F R
F A ¼

2 N ,

MA ¼ (5.5)

or more explicitly, we can say that the magnitude of the action force, F A , is the
magnitude of the resistance force, F R , divided by 2 N . In the case of Fig. 5.8 ,
the mechanical advantage is 2 1 , that is, 2. On the other hand, in the case of
Fig. 5.9 , the mechanical advantage is 2 2 , that is, 4, since F A ¼

W /4.
The system shown in Fig. 5.10 is made up by three pulleys: two fixed and one
movable. Applying the condition of static equilibrium on the movable pulley, we
verify that the vector sum of three upward forces must be the same as the weight of
the suspended object. The weight of the wheel and of the ropes has been neglected.
In the case in which we can consider the upward forces as vertical, we can say that
the magnitude of the action force F A in the figure is 1/3 of the weight of the hanging