Physics of Fitness Fridays: Resistance Bands and Hooke's Law

Resistance bands! They are lightweight and portable and great for working out…but what does it mean when your band has a rating of “30 pounds”?

When you lift a dumbbell, kettlebell, etc, the movement is resisted by the weight of the object. (The weight of the object is the mass m times the acceleration of gravity g).

In contrast, the same motion performed with a resistance band is resisted by the tension T of the band. What is that tension?

To first order, the tension is a function of the amount of length that the band is stretched, described by Hooke’s Law. In math terms, that means that the tension T = -kx. Here, x is the distance that the band is stretched past its relaxation length, or the length of the band with no tension on it. Here, k is the spring constant of the band. k is determined by the properties of the band materials. Typically, resistance bands are made out of latex rubber.

In most cases, if you try to look up properties of bands, you don’t find much of anything. However, a few companies (such as Thera Band) actually list the range of tension forces versus extended length. So here, for a green band the force ranges from 2.0 lbs (25% elongation) to 9.6 lbs (250% elongation). These numbers are usually determined by performing stress test experiments where the force of tension is measured at different lengths.

In my infinite Covid free time, I put some of my bands to the test. I hung each band over my pull-up bar with a 1lb basket attached to the ends. I then placed different weights in the basket, measuring how much the band stretched each time. I then plotted the distance x versus the weight (mg).

So I increased the weight until almost the max rating of the band and plotted the change in length vs weight. And…it’s not a straight line!

In reality, resistance bands do NOT follow Hooke’s Law, except for a small range of weights/tensions. Instead, the tension follows a curve. So if you really want to know how your bands function, you should measure it!

But what I found here is that a weight of 30lbs stretched the band roughly 20% past its rest length. So anytime I want to achieve that resistance, I need to pull that much.

For a typical move, like this seated row, the force I’m exerting is well below the max rated value. For example, this band is rated to 60 lbs. However, the distance at which I am pulling only corresponds to maybe half that! So if you REALLY want to know what tension you’re creating, you need to measure it out. Suffice to say, ain’t nobody got time for that.

Resistance bands are a great alternative to free weights, but the resistance they provide is…complicated. Just remember that if your bands are rated, it’s pretty likely that you’re not pulling to the full force rating of the band. But you can always verify the exact performance through experimentation.

(I’m happy to perform band characterization services for a reasonable fee.)

Happy stretching!