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Introduction

 

For my Physics IA, I will be exploring the question of how the density of a medium affect the velocity in which a ball falls through it.

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Whilst looking at a rock fall into the water at the beach one day, I noticed that the rock fell significantly slower than it would have if it were to fall through air. I then thought of the reason for this, the first thing obviously being that they have very different densities.

 

The exploration will examine whether there is in fact a relationship between the density of a medium, and the velocity in which a ball will travel through it. The exploration will attempt to identify and explain the different forces acting on the ball, and how these in turn will affect its velocity.

 

I hypothesise that there will be a negative correlation between the density of the medium and the average velocity of the ball. I predict this will be because by definition, density has more mass per meter squared, the ball should therefore require more energy to push through this heavier mass of the medium, thus reducing its velocity as loss to friction.

 

 The Experiment

 

The experiment conducted was simple yet effective in measuring and recording the velocity of a material as it fell through different mediums. The primary idea of the experiment was to create a transparent cylindrical tube and fill it with the required medium. The tube would be able to contain any liquid and would be fixed perpendicular to the table so that a hole was left on the top of the tube. The tube would have two light gates attached to it, one on both ends of the tube. These will serve as detectors once the ball is released into the tube and will accurately read the time taken for the ball to pass through the chosen medium.

 

The experiment will measure the velocity of the ball in the medium through the simple formula of    where the velocity calculated is the distance travelled over the time taken to get there. The time is therefore measured by the light gate and the fixed distance will be exactly the distance between the two lasers on the light gate which will produce readings accurate to the nearest hundredth of a second. By recording the data of the ball’s velocity through the medium, we will then be able to analyse their relationship to density of the medium on a graph.

 

The forces acting on the ball will determine its velocity. The experiment is therefore exploring the extent to which the forces acting on the ball are affected by the difference in physical properties of the medium it travels through.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1 and 2 shown above illustrate the experiment that will take place. As shown in Fig.1, a ball is dropped from the surface of the medium. Once the ball is detected by the first light gate, a timer is automatically started. As it reaches the bottom of the tube, and is detected by the second light gate, the timer is stopped.

 

Average and Terminal Velocity

 

Ideally, the density of the medium should be compared to the terminal velocity of the ball travelling through it. The different physical properties of the mediums will vary the time is takes for the ball to reach terminal velocity. It was therefore decided that the average velocity of the ball shall be measured as to maintain a uniform and reliable set of data. The values are very similar nonetheless, as objects reach terminal velocity very quickly in denser mediums. An assumption we will make, therefore is that the ball travels at terminal velocity whilst falling through the tube

 

 

 

Uncertainty

Due to the lack of factors in the experiment and the reliability with the use of both precise and accurate apparatus, our data uncertainties will be very low, but certainly not negligible. To calculate the uncertainties, we must first know the places in which the experiment could lose absolute accuracy: This is limited to the measuring of the distance between the light gates, the data collection of the light gates, the mass of the weighed ball and the measuring of the ball’s dimensions for which we will explore in more detail later on. The following list illustrates the measurements, their uncertainties and the reason for their uncertainty.

 

 

 

Measuring:

Uncertainty:

Reason of Uncertainty:

Distance (cm) between light gates

Human error whilst measuring the ruler eg. Eye level or misreading.

Light gate (s)

Digital misreading/inaccuracy

Mass of the ball (g)

0 error on balance or inaccuracy

Dimensions of ball (cm)

Misreading of ruler/misalignment (eyelevel misreading)

Density of the liquids ()

Density can be changed by slight changes in room temperature.
Impurities and humidity can change true density value

Figure 3 shows the maximum uncertainties possible in the measurements of the experiment.

 

Controlling the experiment

 

Now that we have established the uncertainties of the experiment, we must ensure that it is done under conditions that will not alter the outcome of the experiment, for that renders our results unreliable and thus our entire experiment becomes undemonstrative of any conclusive findings. Whilst doing the experiment, we must therefore ensure that the experiment is done under controlled conditions. Figure 4 will list the controlled variables in the experiment as well as the reason why it is important for them for stay controlled for the duration of the experiment.

 

 

 

 

 

 

Controlled variables

Reasons

Atmospheric Temperature

Temperature is able to affect the densities of materials. It is important that the density of each material remains fixed at the room temperature of 25°C.

Volume of Medium in tube

If the volume of liquid in the tubes are different, the pressures in the tube will be different, and could therefore affect our results.

Same ball used

The ball will remain the same. Mass and its dimensions such as cross-sectional area will therefore all be the same with the same uncertainty.

Figure 4 is a table listing the controlled variables in the experiment. Ie. The aspects that must remain the same during the experiment

 

Now that we have established the conditions and aims of our experiment, the experiment took place. Four different mediums were used for the experiment. Each liquid was filled from above light gate 1 so that the majority of the tube was filled with the liquid. The distance between the two light gates was measured to be 0.01 if we include the potential uncertainty. The distance was long enough to produce accurate and precise readings

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The independent variable in this experiment will therefore be the medium of liquid.The dependant variable will be the velocity of the ball in the different mediums.

 

The relationship between the density and viscosity of a material is surprisingly completely un-related. It is first logical to compare their definitions, as this will indicate the critical difference between the two. Viscosity is

 

“the state of being thick, sticky, and semi-fluid in consistency, due to internal friction. a quantity expressing the magnitude of internal friction in a fluid, as measured by the force per unit area resisting uniform flow.”1

 

So how does this compare to our understanding of what density is and the difference between them? Firstly, we must consider what gives rise to either of these two things. Because density is simply mass per unit volume, you can increase the density either by increasing the atomic mass of the atoms that make up the liquid or somehow pack the liquid molecules together. Generally, things such as molten metal will be very dense because of their high atomic masses and tight packing of the molecules.

 

Viscosity on the other hand, is another story entirely. Viscosity is the liquid’s resistance to movement under a certain force. Therefore, the speed at which a liquid flows under an applied force is going to be equal to the force divided by the viscosity

1 “NIST Chemistry WebBook, SRD 69.” Thermophysical Properties of Fluid Systems, US Dep of Commerce, webbook.nist.gov/chemistry/fluid/.

 

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