A large measuring cylinder will be filled to the top with golden syrup.this will be done slowly and at a shallow angle so as to prevent bubbles from forming which would otherwise compromise the reliability of the results. Seven steel ball bearings of different diameters will be selected and their radii measured using a micrometer. Four markers, three centimetres apart from each other, will be placed vertically down the measuring cylinder which will have five centimetres of syrup between the top of the cylinder and the first marker.
This five centimetre gap is to allow the ball bearing to reach terminal velocity before measurements are taken so it passes each marker at about the same speed.
Each marker will be assigned a stop-clock so when the ball passes each marker, the appropiate stop-clock will be started swilst the previous clock is stopped. This will give three similar times that can be used to find an average time and velocity for the balls.
The ball bearing will be removed after each experiment so as not to affect the next experiment.
A THOUGHT TO SAFETY
* No golden syrup will be consumes as it may have come into contact with hazardous materials in the lab and so be toxic, harmful or irritant.
* Any ball bearings that drop on the floor will be immediately picked up so they are not slipped on.
* Any syrup spills will be cleaned up so they not present a slipping hazard
Equipment
* Steel ball bearings x 2
* Screw gauge micrometer = accurate to 0.
01mm
* Golden syrup
* Measuring cylinder = accurate to 1mm
* Stop clocks x 3 = accurate to 0.01mm
Accurracy
Since the true value for the viscosity of golden syrup is not known. I will gauge my accuracy by the class average. If my value close to the class average then I will have a suitable value for the viscosity of golden syrup.
Table of results
Time = the time taken for the ball bearing to fall 3cm through the golden syrup
Ball radius
Time(sec)
1
Time(sec)
2
Time(sec)
3
Average
Time(seconds)
Millimetres
metres
1.57
1.57×10-3
27.09
27.09
26.62
26.983
1.72
1.72×10-3
18.18
17.96
17.96
18.033
4.20
4.20×10-3
5.39
5.47
5.41
5.423
4.75
4.75×10-3
4.12
4.50
4.46
4.363
5.55
5.55×10-3
3.70
3.46
3.56
3.573
6.35
6.35×10-3
3.24
3.22
3.09
3.183
7.67
7.67×10-3
3.13
2.55
2.56
2.747
Velocity = distance travelled(m) / time taken(s)
3cm = 0.03m
Table of ball bearing velocity
Ball radius(m)
Radius(m2)
Average time taken
Veloctiy(ms-1)
1.57×10-3
2.481×10-6
26.983
1.111×10-3
1.72×10-3
2.976×10-6
18.033
1.664×10-3
4.20×10-3
1.764×10-6
5.423
5.534×10-3
4.75×10-3
2.256×10-6
4.363
6.876×10-3
5.55×10-3
3.080×10-6
3.573
8.396×10-3
6.35×10-3
4.032×10-6
3.183
9.425×10-3
7.67×10-3
5.891×10-6
2.747
1.092×10-3
Error
Sample time = 26.983
26.983 = 26.980 or 26.990
If it were to equal 26.980 then the velocity would still round to 1.111×10-3
And if it were to equal 26.990 then the velocity would still round to 1.111×10-3
The average time is accurate to 0.01s due to the combined accuracy of the three separate times. The error bars produced for the velocity are so small they are worth no real merit and so were omitted from the graph of results.
Analysis
Stoke’s law states:
Upthrust + viscous drag = weight
This holds true because when the ball bearing has reached its terminal velocity weight and the sum of upthrust and viscous drag are equal.
The equation can be re-arranged to give the viscosity() of golden syrup.
The density of steel has been found to be 7647kg/m
The density of syrup has been found to be 1490kg/m
By looking at the graphs line of best fit the gradient has been found to be 250
So if we input this data into the equation we get
250=19.69(7647-1490)
250= 120677.2
9
9 = 482.71
250 x 9 = 120677.2 viscosity( ) = 53.6Nsm-3
9
9 =120677.2
250
Conclusion
The viscosity of the golden syrup was found to be 53.6Nsm-3
What could have affected the reliability of the results?
The sensitivity of my eqiupment: Drawing error boxes on my results was considered however due to the scales used in the graph the ywould not be useful. The radius was squared to reduce to the percentage error of the results taken by the ruler however this could not completely remove the error. Also the stopwatches were only accurate to 0.001 seconds.
The ball bearings could have slid down the walls of the cylinder and the resulting friction could haveslowed down the ball bearings.
The temperature of the syrup may have fluctuated during the experiment thus changing the viscosity of the syrup between tests
As the ball bearings were removed some of the golden syrup may also have been taken so not enough syrup may have been left for the other ball bearings to reach terminal velocity before reaching the first marker.
The stopwatches may not have been stopped and started at the same time in each experiment. That moment was when the bottom of the ball passed the top of a marker and if it had not been viewed horizontally each time then the results for finding the velocity and its average may not have been accurate.
The screw gauge could be clamped to different pressures so the results may have varied where consistency was required.
Sketch shows how
Viewing angle can
Changes at what time
The above moment was reached
Limitations
Since it was a human jugding when to take results, this experiment would not work for fluids of such a low viscosity that objects could pass all the markers before the eye could follow and track it. Computers and electronic sensors would be needed to replace the human element in the experiment.
If the experiment could be done again lasers would be used instead of my eyes and the markers. More accurate results would results from more accurate measuring devices would be needed such as screw gauge micrometers that measure whilst clamping with the same pressure each time.
Each experiment would be repeated more so as to get a morea ccurate average and the experiment would be done in a temperature controlled environment so the viscosity remained the same.
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