Sunday, 8 November 2020

The raindrop explodes

 The raindrops were hitting the roof of the car so hard in the summer that it was possible to see them bouncing up again. I was wondering how to analyse this. Normally when an object bounces back from a surface I use conservation of momentum. Here it is definitely not going to be an elastic collision. Some of the kinetic energy will be dissipated as sound. I looked up the terminal velocity of a falling raindrop. These were large drops - about the size of a house fly - so this source suggests 10 m/s. A spherical drop of 6mm diameter would have a volume of 0.11cm^3 and thus a mass of 0.11 grams. This would give a kinetic energy of 0.0055J. Suppose the whole drop bounces back up 2cm, an assumption, then the drop would have been given kinetic energy=mgh after the impact =0.00002J. In other words, most of the kinetic energy on impact is dissipated. It is obvious that the linear momentum of the drop is not conserved. So to justify conservation of linear momentum, the roof of the car must move slightly, thus producing the sound.