Jet Propulsion Rocks: Balls Oscillating On Tap

Jet Propulsion Rocks: Balls Oscillating on Tap

Jet Propulsion Rocks: Balls Oscillating on Tap[pic 1][pic 2]

Adinan Alves de Brito Filho, Bianca Barboza Bertolotto,

Caíque de Souza Benevidio, Gabriel Leal Teixeira, Gustavo Diogo Silva,

Ivan Moratori Castelani, Larissa Aguiar dos Santos, Samuel Costa Calvo Motrico,

Victoria Alves Porto, Victoria Peres Araújo Costa.

 [e-mail]

Professor: Jeroen Schoenmaker

Centro de Engenharia, Modelagem e Ciências Sociais (CECS)

Campus Santo André

Abstract

When a water jet impinges on a ball rested on a surface, an oscillation movement can be observed if certain conditions are met. These oscillations are the result of complex fluid dynamics, adhesion and viscous forces. In this study, we aim to understand the relevant parameters determining such oscillations. Through a series of trials using three types of balls under different water jet energies and surfaces, we verified that the Simple Harmonic Motion, damped or not, is fit to model these systems. Moreover, we determined the frequencies, equivalent spring constant values and regimes as a function of water jet energy.  

INTRODUCTION

From concrete structures, such as bridges or skyscrapers, to automobiles and electronic circuits, harmonic oscillators are ubiquitous systems in engineering and physics. In this work we investigate whether balls oscillated by water jets can be suitably described by harmonic oscillators models.

In theoretical context, a harmonic oscillation system is commonly described as a block of mass  attached to a spring moving on a frictionless surface. This movement is called simple harmonic motion, modeled by Hooke’s formula:[pic 3]

                                  (1)[pic 4]

where  is the force,  is the string constant and  is the dislocation of the block. [pic 5][pic 6][pic 7]

The dynamics of the system results in an oscillating movement with angular frequency given by

                       (2)                                        [pic 8]

where  is the period of the oscillation and  is the mass of the block. [pic 9][pic 10]

If the energy of the oscillation is strongly damped by friction, the movement is called overdamped. If the damping is less significant, the amplitude of the oscillation reduces continuously with time, and the movement is called underdamped oscillation. A special case of damping for non-undulatory movement is said to be critically damping as shown in Fig. 1.

[pic 11]

Figure 1: Harmonic oscillation motion regimes. MATH 24.

[pic 12]

Figure 2: Sketch of the phenomena in the case of a ball on a hard surface.

Sometimes oscillations can be observed in surprising systems such as the case of this study. A ball set at a flat surface oscillates back and forth when hit upon by a water jet. However, the movement can be damped after a few seconds. Similar oscillations are observed on a liquid surface, when the balls are floating.

OBJECTIVE

This work aims to understand the nature of the oscillations of a spherical object under a water jet. The objective in this experiment is to determine the relevant parameters for the motion of such systems considering Simple Harmonic Oscillator models for different conditions of surface, waterpower and ball material. Furthermore, we aim to comprise and predict the circumstances in which such oscillations can be damped.

METHODOLOGY

In this study, we investigated oscillations of balls under the influence of water jets considering two different surfaces that sustain the balls: hard surface and liquid surface.

We defined that we would work with ten flows for both surfaces, with similar values on both, so that the data could be compared effectively.

At first, we collected ten balls, all different sizes and materials, and classified them all using two criteria: similarity of sizes and density. In the end, we selected three of them. 

We have realized that floating balls were more apposite for regular oscillations and, to observe their motions under different water flow rates, we tried to fit their behavior in a model for simple harmonic motion and orbitals.

Depending on their weight, the balls under higher waterpower would start to orbit in their conservation of momentum. It is possible to watch a main tendency for orbiting and higher oscillations’ frequencies in the floating cases than on the hard surface, considering its friction with the ball. Therefore, we ran again trials with the same previous variations but also pushing the balls under the jet of water to observe the damping effect. It evolved from underdamped to overdamping and critical damping depending on its weight and the increase of waterpower.

[pic 13]

Figure 3: Balls used in the experiments. From left to right: Ball ‘A’ (ping pong), Ball ‘B’ (rubber), and Ball ‘C’ (silicone).

Table 1: Specifications of the balls used in the experiment.

Ball	Mass (kg)	Density (kg/m³)	Volume (m)	Nick Name	Floats or sinks?
‘A’	4,0E-6	3,56E-2	2,36E-13	“ping pong”	Floats
‘B’	5,8E-5	5,55E-2	8,95E-13	“big blue”	Floats
‘C’	1,3E-5	2,70E-2	1,03E-13	“glitter”	Depends on water power

For the liquid surface, a tray provided by the laboratory was used. The tray was placed under two disassembled universal supports and then filled with water, simulating such a surface. The height of the fall of the water was 18,5 centimeters. On the solid surface, we use the same universal support as the floor, and the height of the fall of the water was 27 centimeters.