5.2.3 Tension Force

When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force, represented by a capital T⃗. The direction of the tension force is always along the direction of the string or rope, as you can see in FIGURE 5.5. The commonplace reference to “the tension” in a string is an informal expression for T, the size or magnitude of the tension force.

FIGURE 5.5 Tension.

The figure illustrates a sled on a horizontal surface being pulled by a rope. The rope is tied to the right side of the sled and is inclined toward the upper right.
FIGURE 5.5 Full Alternative Text

NOTE   Tension is represented by the symbol T. This is logical, but there’s a risk of confusing the tension T with the identical symbol T for the period of a particle in circular motion. The number of symbols used in science and engineering is so large that some letters are used several times to represent different quantities. The use of T is the first time we’ve run into this problem, but it won’t be the last. You must be alert to the context of a symbol’s use to deduce its meaning.

We can obtain a deeper understanding of some forces and interactions with a picture of what’s happening at the atomic level. You’ll recall from chemistry that matter consists of atoms that are attracted to each other by molecular bonds. Although the details are complex, governed by quantum physics, we can often use a simple ball-and-spring model of a solid to get an idea of what’s happening at the atomic level.

MODEL 5.1 Ball-and-spring model of solids

Solids consist of atoms held together by molecular bonds.

  • Represent the solid as an array of balls connected by springs.

  • Pulling on or pushing on a solid causes the bonds to be stretched or compressed. Stretched or compressed bonds exert spring forces.

  • There are an immense number of bonds. The force of one bond is very tiny, but the combined force of all bonds can be very large.

  • Limitations: Model fails for liquids and gases.

The figure illustrates a box and the magnified view of its surface.

In the case of tension, pulling on the ends of a string or rope stretches the spring-like molecular bonds ever so slightly. What we call “tension” is then the net spring force being exerted by trillions and trillions of microscopic springs.