Biomedical Engineering Reference
In-Depth Information
Fig. 5.10
Combination of a
movable pulley (
below
)
with two fixed pulleys
(
above
) guaranteeing a
mechanical advantage
up to three
F
A
F
A
F
A
F
A
20 kg
W = F
R
object, that is,
W
3
F
A
. The magnitude of force
F
A
is equal to 66.7 N and the
mechanical advantage of the system is three.
In Fig.
5.10
the movable pulley is suspended in equilibrium by the action of three
forces. On the other hand, Fig.
5.11
illustrates a combination of pulleys in which a
configuration with two fixed pulleys and a support of the load with two movable
pulleys is adopted. In this case, the same cable passes through all of the fixed and
movable pulleys, giving rise to the four forces that support the load. In static
equilibrium, these forces are of the same magnitude whose sum has the same
value as the weight of the suspended load and the mechanical advantage is four.
Therefore, the magnitude of the action force,
F
A
, is equal to 625 N, that is, one
fourth of the weight of the suspended object. Remember that the fixed pulleys just
change the direction of the force.
The configuration of Fig.
5.11
can accommodate a larger number of pulleys,
since the number of fixed pulleys is the same as the number of pulleys that supports
the movable load. Thus, for three pulleys in support, there will be six upward
vertical forces, establishing the equilibrium of the set, and the mechanical advan-
tage will be equal to six. An improvement of the configuration of Fig.
5.11
is to
place the pulleys on the same axis.
In relation to the system of pulleys that guarantee the mechanical advantage, one
last observation in relation to the work performed by the involved forces must be
made. If the friction of the system is neglected, the work performed by the action
force,
F
A
, by using the machine must be the same as the work that is done without
it, when the force
F
R
is used directly. That means that to lift an object weighing
W
ΒΌ
