How does the length of a piece of string or rope vary with the number of knots tied in it? I came across this question a few months ago and decided to try it out as an investigative activity to help A-level Physics students revise some basic practical skills. I’ve since seen other Physics teachers, like Frank Noschese, tweet about using it in class.

What’s the relationship between the number of knots and the length of the rope? Great #modphys graphing lab I learned from @hbarphysics! pic.twitter.com/jPlA1xdp1o

— Frank Noschese (@fnoschese) September 14, 2017

The practical aspect is straightforward to carry out, and students I’ve done this with have collected data which produced nice straight lines. This is an easy, cheap, activity which works well as a revision lesson, allowing you to remind students of key aspects of data collection and analysis, particularly ideas relating to straight line graphs. You could probably do this activity without a worksheet, but I’ve made one which you might find useful as an off-the-shelf resource. It’s a word document, so feel free to amend to suit your own needs. Click the link below to download:

A Knotty Problem

As always, I’m grateful for any feedback or suggestions for improving the worksheet, so please leave any comments you have below.

The activity can be done in about 30 minutes. It can readily be extended by supplying students in the same class with string / rope of different diameters and pooling data to investigate the relationship between diameter and length reduction per knot. I followed up the activity in class with an exam question relating to straight line graphs.