o/Example 29. The forces
between the rope and other
objects are normal and frictional
forces.n/If we imagine dividing a taut rope up into small segments, then
any segment has forces pulling outward on it at each end. If the rope
is of negligible mass, then all the forces equal +Tor−T, whereT, the
tension, is a single number.
If you look at a piece of string under a magnifying glass as you
pull on the ends more and more strongly, you will see the fibers
straightening and becoming taut. Different parts of the string are
apparently exerting forces on each other. For instance, if we think of
the two halves of the string as two objects, then each half is exerting
a force on the other half. If we imagine the string as consisting of
many small parts, then each segment is transmitting a force to the
next segment, and if the string has very little mass, then all the
forces are equal in magnitude. We refer to the magnitude of the
forces as the tension in the string,T.
The term “tension” refers only to internal forces within the
string. If the string makes forces on objects at its ends, then those
forces are typically normal or frictional forces (example 29).
Types of force made by ropes example 29
.Analyze the forces in figures o/1 and o/2.
.In all cases, a rope can only make “pulling” forces, i.e., forces
that are parallel to its own length and that are toward itself, not
away from itself. You can’t push with a rope!
In o/1, the rope passes through a type of hook, called a carabiner,
used in rock climbing and mountaineering. Since the rope can
only pull along its own length, the direction of its force on the
carabiner must be down and to the right. This is perpendicular to
the surface of contact, so the force is a normal force.force acting on carabiner force related to it by Newton’s
third law
rope’s normal force on cara-
binercarabiner’s normal force on
rope
(There are presumably other forces acting on the carabiner from
other hardware above it.)
In figure o/2, the rope can only exert a net force at its end that
is parallel to itself and in the pulling direction, so its force on the
hand is down and to the left. This is parallel to the surface of
contact, so it must be a frictional force. If the rope isn’t slipping
through the hand, we have static friction. Friction can’t exist with-Section 3.2 Force in one dimension 163