The same ball bearing must be used for a variety of reasons, the weight and volume must remain constant so that a selection of data can be compared. Each ball bearing has a different surface texture, some are dull in colour and slightly rough while others are shiny and smooth, this could have an effect on the amount of friction and hence the speed of the ball.
Preliminary investigation:
A preliminary investigation was undertaken to help with the designing of the experiment.
It has been found that the ball must be moving at its terminal velocity for stokes law to be applicable, therefore a small investigation was undertaken to find where the terminal velocity occurs at different temperatures. Velocity was measured at three temperatures, the first temperature used was room temperature. Marks were made at 8cm intervals down the tube one from the top and two below. The time taken to pass through each section was recorded and repeated three times. Only the last two values were found to be of equal time, meaning the ball had reached terminal velocity. It was from this point that the actual boundaries to be used in the investigation were marked on. This was repeated for two other temperatures, one around 40o C and the other around 5 o C, it was found that terminal velocity occurred at the same time.
Suitable ball bearing weight and radii were found also. The diameter should allow the ball to easily move through the liquid in the tube, if the ball was too wide friction from the sides of the cylinder would act upon it, slowing it down. A suitable mass of ball also needed to be found as the greater the mass the faster the ball fell, therefore adding to the inaccuracies of timing caused by the slow human reaction. A ball of mass 1.5g and with a diameter of 7.13mm was decided upon
An appropriate drop distance was also found. The ball bearing should be able to drop a reasonable distance, because the further it drops the less the effects of human error through timing. The distance of 11cm was used as it was large enough to decrease the effects of human error and also lines up with some of the markings on the measuring cylinder, making it easier to judge the position of the ball.
The temperature needs to be controlled in two ways, one for heating the honey and one for cooling the honey. The temperature of the honey has to be controlled through a water-bath style of set-up (the honey cannot be heated directly as it would burn).
The removal of the ball in the preliminary experiments was proving difficult. The honey had to be removed and the ball then cleaned and dropped again. This seemed illogical, because changing the honey draws more errors into the experiment (the differing densities). A magnet was used to remove the ball from the honey, resulting in minimum loss of honey, keeping the same honey sample.
Experimental setup:
Apparatus setup.
The apparatus will be setup as in diagram 3. The honey level marking will allow the honey volume to be kept at a constant value so that the terminal velocities occur at the same times (due to same amount of time travelling through honey).
Method of removal of ball:
A magnet will be used to remove the ball due to the sticky nature of honey. The honey is left to drain off the ball so that only a small amount of honey is lost in the process.
Temperature control methods:
Heating the honey
When reaching the higher temperatures it is required that the honey is heated using a Bunsen burner. A stirring rod is also used to mix the honey and create a constant temperature throughout.
Cooling the honey
Ice is added to the water surrounding the measuring cylinder to cool the honey, again the honey is stirred to produce a constant temperature throughout the honey.
Apparatus:
Plan:
- Before beginning the experiment all equipment will be checked, i.e. functionality of the stopwatch and heating equipment.
- Next the apparatus will be setup as in diagram 3.
- Stability of the apparatus will now be checked.
-
The markings will be added using a pen and ruler, the distance markings are made with a gap of 11cm. The volume marking will be made at the 100cm³ mark. This level of honey allows the ball enough time to reach terminal velocity (as found in the preliminary investigation) and also allows the ball to start at its rest position. If the ball was dropped through the air and into the honey it could accelerate past its terminal velocity (in honey), meaning it would be travelling faster than it should as it moved through the honey. Therefore the ball is dropped from the surface of the honey with its initial velocity equalling 0ms-1
- A micrometer screw gauge will be used to accurately measure the diameter of the ball bearing in use.
- The stop watch will be setup and readied while the correct temperature is being met. The hot temperatures will be met by heating the honey to the desired temperature (through the transfer of heat energy from the hot water). The colder temperatures are met in a similar way, by reducing the temperature of the water. Once the thermometer has reached the desired temperature the experiment may begin.
- The ball can now be release from the surface of the honey, timing can begin once it moves past the first mark and timing will end once it passes the second mark. Each temperature will be repeated 3 times so an average can be calculated, any anomalies spotted and repeats made if necessary.
- Care will be taken on removal of the ball bearing, so as not remove large amounts of honey. If any honey should be lost it can be topped up to the pre-marked line, it should then be stirred to help maintain a constant temperature throughout the substance.
- Experiment repeated until an adequate amount of results are gained.
A graph can be plotted alongside the experiment to help spot anomalies as the experiment is being carried out. This way, the scientist can go back and redo that particular point to ensure that it was an anomaly and not a development of the original pattern.
Prediction:
From the derivation I can predict that the higher the viscosity the slower the ball, due to the derived inverse relationship:
η∝ 1
v
η = 2 r2 (ρ steel - ρfluid) g
9 (s/t)
I predict that the lower the temperature the higher the viscosity. In the simplest case a comparison between liquids and solids could be made. If we say that a solid has a huge viscosity and a liquid has a medium viscosity, we know from everyday life that to change the state of a liquid to a solid we need to cool the liquid down. Consideration of the actual science behind it shows that weak temporary bonds exist between molecules in a sample, these bonds are created due to the fluctuation of the molecules polarity (brought about by the random movement of electrons through the molecule). We can therefore say that when given energy (from the heat) the molecules will be less affected by these small ‘clinging’ forces and will be able to move more freely and hence the sample becomes less viscous with an increase in temperature.
η∝ 1
T
Time plan:
A total of one hour will be spent performing the experiment:
It will take 15mins to setup the necessary apparatus
It will take 35mins to record results (including disaster time)
It will take 10mins to pack away equipment
Safety:
Safety is an important aspect of this experiment. It is important that care is taken when using the busen burner and goggles are worn whenever it is being used. The vicinity of other investigations around the work area should also be considered with care. Ball bearings, when not in use should be positioned somewhere safe as they can both be easily lost and also represent a danger as a tripping hazard.
Ranges:
A range of temperature from 0-30ºC will be used at approximately 5ºC intervals.
The distance used will be 11cm.
Reliability:
The data will be plotted as the experiment takes place so that any anomalous results can be located as the experiment takes place and these temperatures can be repeated. By ruling out anomalies the investigation becomes much more accurate and meaningful. The graphs below illustrate how extra investigative work into possible anomalies can shift the line of best fit considerably. Each temperature is repeated three times allowing at average to be produced.
Sensitivity:
It is important that sensitivity is considered through the experiment as even with a perfect setup and experimental technique, non-sensitive equipment can render results useless.
The micrometer screw gauge can be read to an accuracy of ±0.005mm with an accuracy of ±0.01mm.
The standard ruler used to measure the dropping distance can be read to an accuracy of ±0.5mm with an accuracy of ±1mm.
The timer can be read to an accuracy of ±0.01s with an accuracy of ±0.01s. This level of accuracy is not suitable, considering that the timing is initiated and terminated through human reaction.
The scales can be read to 0.01g with an accuracy of 0.01g.
The thermometer can only measure to the nearest degree but the concentrated heating method that will be used means that the temperature the thermometer is reading may only be one part of the overall temperature.
Accuracy:
It is crucial that the flow of fluid past the ball is laminar, as Stoke’s law depends upon this fact. Therefore all courses of action must be taken in order to keep the flow laminar. Simple things include using a smooth ball and dropping the ball down the centre of the tube. The diagram below shows a fluid flowing down a tube, the layer against the glace is affected largely by friction, the friction of this layer affects the other layers until the most central layer has the least friction from the side of the tube.
The viscosity of the liquid remains constant at a constant temperature and pressure. But if the ball should veer off and make contact with the glass, the formulas would become invalid and the overall friction would change causing the ball to slow.
The measuring distance must be kept constant throughout the whole experiment this is ensured by the two measuring markings.
A constant temperature throughout the whole fluid must be achieved; this can best be done by quickly transferring the measuring cylinder from the heat source to the workbench and conducting the experiment right then. The measuring cylinder can then be returned to the heat for the second and third results.
Not only must heat dispersion be achieved but also keeping the heat at the correct temperature, maintaining temperature is an important consideration.
When recording the times human error will occur, from the delay of seeing the ball pass the line, to actually pressing the start and then stop buttons. Using a large measuring distance, this effect can be lessened significantly.
The ball must also be given enough space for it to be able to reach terminal velocity before passing past the lines.
Results:
Constants:
The constants can be identified and measurements can be given before actually recording drop times.
The densities of steel and honey can be calculated using the density formula:
ρ= m
v
Mass of empty measuring cylinder = 110.2g → 0.1102kg
Mass of measuring cylinder containing 100cm³ honey = 258.6g → 0.2586kg
Mass of honey in measuring cylinder = 0.2586 – 0.1102 = 0.1484kg
Volume of honey = 100cm³ → 1x10-4m
Density = 0.1484 / 1x10-4m = 1484kg m-3
Mass of ball = 1.5g → 1.5 x 10-3kg
Diameter of ball = 7.13mm → 7.13 x 10-3m
Radius = 7.13 x 10-3m /2 (to find radius) = 3.565 x 10-3m
Volume= (given by 4/3 Pi r³) 4/3 Pi (3.565 x 10-3)³ = 1.89 x 10-7 m³
Density = 1.5 x 10-3 / 1.89 x 10-7 = 7936.5kg m-3
g= 9.81ms-2
s= 11cm → 1.1 x 10-1 m
r= 3.565x10-3m
η = 2 r2 (ρ steel - ρhoney) g
9 (s/t)
The following table shows the recorded results (time and temperature) and then the calculated viscosity at these temperatures. I have converted the Celsius temperatures to Kelvin (+273). The times were rounded to the 0.1 of a second, even this is too accurate considering the inaccuracies involved with human error.
While carrying out the experiment an unexpected recording was made at 284K (11°C). Previously the honey had been cooled to 280K(7°C), the ball dropped and the recording made. The temperature of the honey was then raised to 284K (11°C) by gently heating the water around the honey. When the thermometer read the correct temperature the ball was dropped, but something unexpected occurred. The ball began by dropping slowly, but then accelerated beyond expectation. It was discovered that the thermometer had been held too far up the measuring cylinder meaning that there was a large spread of temperatures from the bottom of the measuring cylinder to the top. After this it was ensured that the water temperature and honey temperature were equal and also that the honey was stirred to help create a constant temperature throughout the honey.
From the graphs we can clearly see that the viscosity is inversely proportional to the temperature.
η∝ 1
T
Graph 1 shows average speed against viscosity. It was exactly the trend suggested when deriving the formula, it shows how an increase in viscosity results in a decrease in average velocity. This supports the theory of temporary induced bonds.
Graph 2 shows the relationship between temperature and average velocity. It shows how the temperature affects the velocity through the change induced in the viscosity. We can see what appears to be an anomalous result at 299K. A smooth curve was expected but this point does not follow the exact trend. The most likely cause for this result is the reaction time involved with using the timer.
Graph 3 shows the inverse relationship between temperature and viscosity, the graph proves my prediction to be valid. It appears that a 0K the viscosity will be of an infinite value as at 0K all the kinetic energy of molecules is removed meaning that the honey would be an impenetrable solid.
Graph 4 shows the relationship between temperature and the log10 of viscosity. Log10 of viscosity was used in order to reduce the spread out effect of the results. As such a straight line was produced which allows a gradient to be calculated.
Graph 4 now gives us a straight line, we can therefore apply the straight line graph rule, y=mx+c
Log10 F = mT+c
The only problem is that c is an infinite viscosity at 0K. This means that the point of y intercept cannot be found as the lines never meet.
We can therefore rearrange to:
Log10 F = c-mT
Where c is infinite.
The fact that c is infinite means that a simple y=mx+c rule cannot be applied.
The co-efficient of viscosity decreases with increasing temperature, this is due to bonds in the molecules of the honey (or any liquid). The bonds in question are temporary intermolecular bonds created by the instantaneous imbalance of electrons in a molecule. When atoms are bonded in a molecule their electrons move at high speeds in orbitals around the molecule. At any instant time more electrons may be found towards one side of the molecule, this has the effect of instantaneously polarising the molecule (with the electrons acting as the negative side and the protons in the nucleus acting as the positive side). This then induces the same effect in a neighbouring molecule, creating an instantaneous attraction, giving an instantaneous bond, this effect then travels throughout the molecules. These bonds act as a frictional force as they act against the flow of molecules (resisting the flow).
When heated the particles are given more kinetic energy, this allows the previously mentioned temporary bonds to be overcome allowing molecules to move more freely. The more a sample is heated the more kinetic energy the particles have, causing more bonds to be overcome, this therefore reduces the effect of viscosity causing the inverse relationship as seen in the above graphs. The resultant reduction of viscosity allows the ball to travel faster producing the faster times recorded in the experiment. The cooling of the liquid means that the temporary bonds are not opposed by as much kinetic energy, thus meaning that the bonds are stronger and viscosity is increased.
Limiting factors:
The angle of decent could affect the times recorded, as a ball travelling at an angle will have to cover a greater distance than one that falls directly downwards. a² + b² = c², the ball veers to the side it will still be timed passing the same point, but it will take longer than normal, as it has to cover a greater distance, s=v/t.
The measuring cylinder used in the experiment is very thin and as such the ball may be affected by friction caused by the closeness of the ball to the sides. Laminar flow is when the fluids flow in streamlined layers. The outer layers touching the glass experience a greater amount of friction, this friction gradually decreases as it moves towards the centre of the measuring cylinder. Therefore it is important that the ball is dropped down the centre of the cylinder this means that it will be affected by only a small amount of layer friction. The measuring cylinder’s diameter is only approximately 1cm larger than the ball’s diameter, this means that this friction is inevitable.
Another problem with the experiment is inaccurate temperature distribution. The technique used to heat the contents of the measuring cylinder relied on heating one part. This means all the heat is concentrated in one point and not spread. Although the stirring rod does serve to spread even the temperature slightly, it is not very effective. So there are different areas of heat within the honey, some with different viscosities to others. The anomalous result on graph 2 (velocity against temperature) may be the result of incorrect positioning of the thermometer within the cylinder. The thermometer may have been to close to the top of the measuring cylinder, giving a lower temperature than what was actually present.
The ball was not always dropped from the surface of the honey, occasionally it was held slightly above. This was due to the diameter of the measuring cylinder. The ball must have an initial velocity of zero as it passes into the honey, this means its acceleration begins in the honey and terminal velocity can be reached. If dropped before reaching the honey then the ball will accelerate faster (due to the lesser effects of upthrust and viscous drag) and therefore enter the honey with a greater velocity. This means that it will have to be slowed by the honey to its terminal velocity, giving a shorter time.
The sensitivity of the equipment was of a high standard. The only let down was measuring with the ruler, a more sensitive piece of equipment could have been used to give a more reliable value. The timing of course I the main factor but the sensitivity of the timer was not the problem.
The most limiting factor of them all is human reaction. The recorded time is the most important recorded factor other than temperature. The time it takes for the brain to recognise that the ball has passed the line until pressing the button and then the same process for when the ball passes the finishing line adds up to a reasonable amount. This is the most difficult factor, all the other factors remain constant.
A minor consideration is the density of the honey. As the honey is heated it becomes slightly less dense as with all liquids, during this experiment the density was taken to be a constant value but the effect of this varying density is so small that it would not make a significant difference to the results.
The level of the eye to the markings can also make a large difference to the results. For accurate readings the eye should be level with the marking in question. But it is difficult for the person timing to shift their head from the first mark to the second mark in only a matter of seconds. This could account for the anomalous result in graph 2, the reading could be the result of misreading the marking on the side of the measuring cylinder and pressing the stop button too early.
A diagram showing how the position of the ball can be interpreted differently when viewed from the incorrect angle.
Temperature control is also a problem; as soon as the honey is heated up, it begins losing heat immediately - to return to room temperature - (and when cold, it starts warming to room temperature). This is due to the radiation of the heat and convection around the work area, if left the honey would eventually return to room temperature. Due to the rapid return to room temperature the whole experiment needed to take place quickly (as the cylinder needed to be removed from the water) so that the temperature at the time of the ball dropping was very close to the recorded temperature. Ideally after each drop of the ball the measuring cylinder should be returned to its water bath so that the temperature remains constant throughout each of the three results - this is due to the amount of time it takes for the experiment to take place (esp. at colder temperatures) and also the time it takes to remove an clean the ball bearing.
Improvements for next time:
The distance over which the time taken is measured should be made as large as possible so that the associated reaction times will be of much less significance. This means that effects are lessened hence providing a greater accuracy.
Ball bearings with different radii could be used. This would allow a greater spread of results giving a better average selection of viscosities.
The main problem with the investigation was human error with the timing. This problem can be completely eliminated with the use of light gates. The light gates would have to be able to measure across a large distance due to the specific path the ball bearing takes through the honey. But once setup correctly they could time with far more precision.
The other problem with the investigation is the temperature. The way this could be solved is by heating the whole room to the desired temperature. This would require large industrial machinery, but would allow the honey to be accurately heated/cooled to the desired temperature, maintaining equilibrium of temperature throughout the honey. A more likely solution would be the use of a water bath, although this would not be as effective.
A more suitable release mechanism could be implemented so that the ball is dropped directly onto the honeys surface and is dropped centrally as well. This would help prevent the problems caused when the ball moves at angles and is affected by the extra friction imposed on it by the walls of the cylinder.
A complete change of the basic experimental setup could be used. A viscous drag viscometer could be used to measure the viscosity. The apparatus could be enclosed in the same temperature controlled room, this would allow the viscosities to be accurately measured and the results from the two investigations could be compared. One problem that may occur with this is that a metal is used to control the needle for the display. A suitable metal that is not affected by heat (through expansion) would have to be used.
