A slinky spring hanged by its top end, its motion after it is released. A Challenge problem at the International Physics Olympiad


  Eli Raz  
ORT Braude College

Israel hosted the International Physics Olympiad this year. Eighty-three countries and 364 students (under the age of 20 years) participated in the Olympiad. The students in the Olympiad have to face two exams, one in theory, which consists of three questions that usually deal with natural phenomena. The second is a laboratory exam, where students perform and analyze two experiments. Each exam lasts for five hours. The host nation is responsible for preparing the problems and the experiments.

One of the questions that appeared in the theory exam this year required analyzing the motion of a slinky spring, initially hanging and stretched under its own weight, after being released from rest.
Experiments show that it gradually contracts from the top, while the lower part remains stationary. As time advances, the contracted part moves as a solid chunk and accumulates additional turns of the spring, while the stationary part becomes shorter. Every point in the spring begins to move only when the moving part reaches it. The bottom end of the spring starts moving only when the spring is fully collapsed and reaches its unstretched length

The analysis of spring motion from basic physics principles is a problem that goes beyond the syllabus of the International Physics Olympiad. In order to solve the problem with tools available to a high school graduate, the contestants were asked to rely on the described observational phenomenon, and hence to calculate measurable quantities, such as the time it takes from the moment the spring is released until it fully collapses to its minimal length, or the velocity of the moving part as a function of the relative mass of the stationary part.

At first glance, the problem seems technical, but it involves several thinking barriers that students had to overcome. Only 11% of the students managed to score more than half the points and only about a third of the students gained more than a quarter of the points.
Although the physical model was given to the students, the difficulty in most cases was in finding the key ideas for solving the various parts of the problem, as well as taking subtle points into account (for example, the bottom of the spring loops remains tight).

We will present a video clip of the phenomenon and the problem as given to the students, and will analyze the challenges, solution strategies, and the difficulties that the students faced. We will also present statistics of the results in the various parts of the problem.