Tension or Normal Force?

One interesting physics conversation this semester has been about how we categorize forces. One future physics teacher in particular kept being concerned about whether to call something a tension force or a normal force. For example, consider the following situations:

• A chain, consisting of many links, hangs vertically. The very top link has a rope wrapped around it, which keeps the whole chain fixed to the ceiling.
• A rope is wrapped around a box and pulled by a person.

What kind of contact forces act on the top link? What kind of contact forces act on the box?

I think many students learn to associate types of forces with kinds of objects. For example, objects like ropes and strings exert tension forces. Objects like walls, ramps, and tables exert Normal forces. Springs, of course, exert spring forces. This kind of object-focused categorization means having to have a category for forces from a hand, like “Applied Force”

If this is how you think about forces (in terms of object categories), both the link and the box have tension forces exerted on them by the ropes, because ropes exert tension forces.

Another way to talk about forces, however, is to focus on mechanism. This is how I, and many other physics teacher I know, talk about force. Normal forces are contact forces arising from surfaces or points of contact that press into each other. In other words, Normal forces are compression forces. Tension forces are contact forces that result in points of contact that involve stretching. Friction forces involve sheer. Compression, tension, and sheer are about what’s happening at a point of contact not about what kind of object is exerting the force. A hand that pushes, of course, is just a normal force, because your skin cells are being squished not stretched.

It took me a while to really get insight into the students’ concern, but as we talked more and more I realized his concern resulted from the juxtaposition of these two ways of categorizing force. In the two scenarios above, the part of the rope that is contact with the object is being compressed. If  one is attending to the mechanism, then you’ll conclude that it’s a Normal force. If you are focusing on the kind of object it is, you’ll conclude it’s a tension force. This contradiction troubled the student.

The question remained, however, how should we resolve the conflict? At first, I was being a very bad debater. I just kept repeating my own arguments about normal forces being compression, dismissing altogether the issue of what kind of object it was. Now, I do think that categorizing based on mechanism is more useful than categorizing based on objects, but merely repeating my view was not going to help us understand the real issue. It wasn’t helping either me or the students get a deeper understanding. The real issue came about by thinking about grabbing someone by their shirt and pulling them toward you. In this case, if we choose the person’s naked body as the object of analysis, then the shirt is compressing against the person’s back pushing them forward, meaning there is a normal force. However, if we choose the object of analysis to include their shirt, then we could conclude that the shirt/person system was experiencing a tension force. If you get really picky about the exact boundaries and how the hand grabs the shirt, you might even conclude that the force exerted by hand on the shirt/person  are some combination of normal forces and friction forces. The key point is that we could certainly draw the boundary somewhere around the person (e.g., including most of but not all of the shirt) where the force at the boundary is a tension force.

The thing we realized is this: The ambiguity about whether something is compression or tension goes away when you attend to both mechanism carefully and attend to system boundary carefully. Small changes in the exact location of the system boundary (naked body or naked body + clothes) matter for whether the points of contact at the boundary are in tension or compression. That’s because even a single object can have places that are in tension and that are in compression. If you slice the boundary over a region that is compressed, your going to have normal forces. If you slice the boundary over a region that is being stretched, your going to have tension forces.  The shirt example helps, I think, because of it’s a subtle shift in boundary.

With the rope around the box, if you are serious about only including the box in your system, then there is no tension force. However, if you drew the boundary around the box a bit farther out, such that the rope around the box was in the system, then the force acting on the system is a tension force. The truth is, as an object, a lot of the rope is in tension.  One thing you realize in thinking about this is that tension forces can’t arise with out adhesion or bonding.  If you haven’t adhered a rope to an object, it can’t exert a tension force.

What’s interesting is that this is the complete opposite of what I’ve often heard said to students. Students are often told that ropes can only pull, not push.