# IYPT 2017 Singapore

##### But first, what is IYPT?

The International Young Physicists’ TournamentIYPT, is a physics competition centered on 17 non-examination research problems that are published yearly in late July. During the tournament, discussion-based sessions called Physics Fights are conducted and the performances of the teams are judged by expert physicists.

##### 9. Ball in a tube

A sealed transparent tube is filled with a liquid and contains a small ball. The tube is inclined and its lower end is attached to a motor such that the tube traces a conical surface. Investigate the motion of the ball as a function of relevant parameters.

This task offers several interesting challenges. In order to investigate the motion of the ball and how the relevant parameters affect it a proper apparatus was the absolute necessity.

The ball and the medium in the tube may have different densities, therefore we may observe the ball initially floating or resting at the bottom of the tube. When a centrifugal force is applied – the tube spins, the ball will start to move. But how fast should it rotate in order to move?

Further, when the ball’s density is smaller than the density of the liquid, the ball will experience a dynamic equilibium at distance:

However, the ball initially resting at the bottom of the tube won’t reach any equilibria and will only slide to the upper end.

The position-time graph (3) was obtained by videoanalysis in Tracker. Although it covers only a span of 70 seconds, we can already observe how the ball approaches stability at (2) distance and convergence time T. This motion quite resembles an overdamped harmonic oscillator, doesn’t it?

Major contributor is of course the resistance of the fluid in the tube, hence the drag is mainly dependent on a viscous friction. For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), is the drag force:

If you are interested in the equation of motion, solution for overdamped oscillator or experimental comparison with theory leave me an email.

Experiments

To investigate the relevance of visocsity, density, and size I have used different materials and liquids.

• Types of liquids used: water, olive oil, ethanol (80%)
• Types of balls: acrylic, wooden, polystyrene 4mm and 6mm in diameter.