David Beckham was not known for excellence at Physics. But his intuition about where a ball would go when he kicked it was astonishing. And though our skills are not quite so exceptional, we all rely on our intuition about the how the world is going to behave in unexpected situations.
But sometimes our intuition fails us completely.
I recently experienced such a failure. As the video shows, if a slinky spring is suspended from one end, hanging under its own weight, and then the support is removed, the slinky falls in an unexpected (to me) manner. The top of the spring moves down, but initially the bottom of the spring does not move at all until the top collides with it.
I don’t intend to try to explain this to you. But I did spend some time trying to explain it to myself. I couldn’t think how to model a slinky spring, so instead I modelled a similar situation – a set of masses connected by springs, initially suspended and then dropped.
I was able to write a short program to solve all the sums for how the springs and masses behaved, using Newton’s laws of motion thousands of times to see how the masses moved. I then worked out the extension of each spring over time and results are shown in two graphs below. The key understanding is that each mass responds only to gravity and the two springs above it and below it in the chain.
The first graph shows how the springs first stretched, with springs near the top extending more until they settle down, and then after 3 seconds the top spring is removed.
The graph below shows detail from the first graph. When released, the top springs reduce their extension quickly, but the bottom springs didn’t change their extension at all until the the upper weights made them move. If one draws a line on the graph its slope corresponds to the speed of a ‘sound wave’ propagating down the chain of masses and springs.
The model I solved considered 10 x 1 kg masses separated by springs with a regular length of 30 cm and a spring constant of 500 newtons per metre. The expected speed of sound is approximately 6.7 metres per second, and the simulation gives a result close to this.