The dynamics of a single rope used to transmit force is clearly quite
simple: the rope just transmits an applied force. When pulleys are
used in addition to ropes, however, more complicated situations can
arise. In a dynamical sense, pulleys simply act to change the
direction of the rope; they do
not change the magnitude of the
forces on the rope. Just as we assumed the ropes to be massless, we
will similarly assume that the pulleys we work with are massless and
frictionless, unless told otherwise. The simplest case involving a
pulley involves a block being lifted by another block connected to a
rope:
Figure 3.2: The Tension in a Rope and Pulley System
This diagram represents a small block on the left in the act of being
lifted by a larger block on the right. Notice the forces T and -T:
even when used in addition to a pulley, the rope must still experience
two equal and opposite tension forces. From the figure it may seem
that the rope actually experiences two forces in the same direction,
making the situation impossible. The presence of the pulley, however,
changes the situation to make it physically tenable. When analyzing a
rope and pulley situation it is useful to define a direction not in
terms of up or down, but in terms of the shape of the rope. In the
situation above, we can define the positive direction on the rope as
pointing upward on the left side of the pulley, and pointing downward
on the right side. When we define direction in this way the rope does
actually experience two equal and opposite forces.
