The final common application of Newton's Laws deals with tension.
Tension usually arises in the use of ropes or cables to transmit a
force. Consider a block being pulled by a rope. The person doing the
pulling at one end of the rope is not in contact with the block, and
cannot exert a direct force on the block. Rather a force is exerted on
the rope, which transmits that force to the block. The force
experienced by the block from the rope is called the tension force.
Almost all situations you will be presented with in classical mechanics
deal with massless ropes or cables. If a rope is massless, it
perfectly transmits the force from one end to the other: if a man pulls
on a massless rope with a force of 10 N the block will also experience
a force of 10 N. An important property of massless ropes is that the
total force on the rope must be zero at all times. To prove this, we
go back to Newton's Second Law. If a net force acts upon a massless
rope, it would cause infinite acceleration, as a = F/m, and the mass of
a massless rope is 0. Such a situation is physically impossible and,
consequently, a massless rope can never experience a net force. Thus
all massless ropes always experience two equal and opposite
tension forces. In the case of a man pulling a block with a rope, the
rope experiences a tension in one direction from the pull of the man,
and a tension in the other direction from the reactive force of the
block:
Figure %: The Tension in a Massless Rope
Tension and Pulleys
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 %: 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.
