Untitled Essay, Research Paper
Physics CAT One
Extended Practical Investigation
Report
Student Number:Purpose The Purpose of this investigation is to explore how the terminal
velocity of a sphere falling through glycerol varies with the temperature of the glycerol
and the size of the sphere.Introduction In the early stages of the project it was intended to investigate how
the speed of a sphere falling through glycerol varies with the size of the sphere.
However, after analysis it was decided that the investigation would be more callenging if
a second variable was incorporated. There are many constants that could have been
manipulated such as, amount of glycerol used, distacnce over which times were taken,
distance sphere was allowed to fall before timing was taken and the temperature of the
glycerol. After much consultation it was decided that the temperature of the glycerol
should be varied. Once this had benn incorporated into the investigation some scientific
concepts related to the viscosity of a liquid had to be attained. (Refer to article). In conducting the experiments an attempt was made to attain results
that could, produce graphs that showed the terminal velocity of a sphere related to the
temperature of the glycerol and the terminal velocity of a sphere related to its size.Apparatus used• 600 ml of glycerol (density 1.26/ml. Assay 98.0 – 101.0%)
• Small ball bearings of radius: 3.175mm
3.960mm
5.000mm
6.000mm
7.000mm• 900 ml measuring cylinder
• Stop watch
• Thermometer
• Some type of heating and cooling device to varie the temperature
of the glycerol
• TweezersVariables and Constants The variables that have been used in this investigation are the size of
the ball bearings and the temperature of the glycerol. The constants that have been used
in this investigation are the amount of glycerol used, the size of the measuring cylinder,
the intervals at which time were taken, the distance the sphere was allowed to drop before
times were taken and the number of tests taken.Method To begin experimentation the distance over which the sphere accelerates
to reach terminal velocity had to be determined. This was done by systematically varying
the distance over which the sphere was allowed to fall then finding the point at which the
spheres acceleration is zero. It was found that for the sphere to reach terminal velocity
it had to be allowed to fall 6 – 7 centimeters before an accurate, constant reading could
be taken. It was found that the distance needed for a sphere to reach terminal velocity is
only slightly changed when the temperature of the glycerol is varied (+/- 0.2cm). To attain that the sphere had reached terminal velocity by varying the
distance that the sphere fell before timing began, the distance was varied from 2cm to
10cm. Starting at 2cm the measuring cylinder was marked at 2cm intervals and times were
taken for each interval. the times taken were analysed to determine if the rate of descent
of the sphere was constant for each reading. To ensure that the sphere had reached
terminal velocity a full 10 cm of descent was allowed. Using ‘Stokes law for the terminal velocity of a sphere falling under
gravity’ and the relationship of mg = U + F at terminal velocity the above result is
proven. These calculations can be seen in the results section. For all experiments room temperature was recorded at 20oc. The first part of the experiment was to vary the size of the ball
bearing but not the temperature. A sphere of 3.175mm in diameter was dropped from just
above water level and allowed to fall 6 cm before timing began. Once the sphere had fallen
the initial 6 cm timings were taken at intervals along the measuring cylinder every 200ml
(10cm). This experiment was repeated 4 times and an average was taken.
The experiment was then repeated using ball bearings of sizes 3.960mm,
5.00mm, 6.00mm, 7.00mm, 9.00mm. Each individual experiment was repeated 4 times and an
average was taken. All results are shown in the results section. The second part of the experiment was to vary the temperature of the
glycerol but not the ball bearing size. A sphere of 3.175mm was chosen to be used in all
experiments, due to its extremely slow descent rate. The same procedure as above was used
except five temperatures of 7oc, 12 oc, 15 oc, 17 oc and 20 oc for the glycerol were used.
Results The averaged results obtained from the experiment are presented in the
following tables and graphs. (For full documentation of all the results obtained refer to
appendix 1.)Size of Sphere Timing Interval No Averaged
Results Averaged Velocity Temperature
Timing Interval No Averaged Results
Averaged Velocity
3.175mm 1 2 3 1.4371.6001.637
6.178 cm/s 7oc 123
5.5758.1158.095 1.24 cm/s
3.960mm 1 2 3 0.7500.9820.970
10.240 cm/s 12oc 123
2.6504.4754.400 2.24 cm/s
5.000mm 1 2 3 0.5000.6900.680
14.598 cm/s 15oc 123
2.3753.6573.755 2.68 cm/s
6.000mm 1 2 3 0.7850.6550.627
15.600 cm/s 17oc 123
2.1252.9352.977 3.36 cm/s
7.000mm 1 2 3 0.3400.3600.360
27.777 cm/s 20oc 123
1.4801.6021.627 6.17 cm/s
Chart One
Note that there is a reflex error for all the recordings of +/- 0.1
seconds. Also, the first timing interval cannot be used for any calculations as the sphere
has not yet reached terminal velocity. This is a graph representing how the velocity of a 3.175mm sphere
varies with the temperature of the glycerol.
This is a graph representing how the velocity of a sphere varies with
the diameter of that sphere.Analysis of Results Chart One demonstrates that as expected the terminal velocity of the
sphere increases as the temperature of the glycerol and the size of ball bearings
increase. Graphs one and two visually illustrate this point and it can be seen by the
positive gradient shown. It is interesting to note that the change of velocity with the
temperature is signifigantly greater as the temperature becomes higher (15oc to 20.5 oc).
The reason for this is directly related to the change in viscosity as the temperature is
varied. As the temperature increase the viscosity becomes less and so the sphere is able
to move freely through this less viscous liquid thus having a greater terminal velocity. A
chart of temperatures and their relative viscosities for glycerol is shown in appendix
two. A hypothetical relationship can be developed between velocity and temperature. The
shape of the graph, although not smooth, is a curve and therefore it is reasonable to
suggest that the relationship would invole T to the power of something: ie) v = kTn (where
k is a constant). Thus, Log10v = Log10k + n Log10T, where n takes the gradient value. If a
graph of Log10v vs. Log10T is plotted it may be possible to form a relationship.(Graph 3) A line of best fit for the above graph gives a gradient of 2.69.
Therefore a hypothesis for the relationship between velocity and temperature is V =
kT2.69. Of course for the results to be most accurate the sphere would ideally have
reached terminal velocity when the times in graph three were taken. An attempt has been
made to calcualte the terminal velocity at 20oc using stokes law and the relationship mg =
U + F at terminal velocity so that it can be compared to the velocity found at this
temperature.THIS GRAPH SHOWS HOW VELOCITY VARIES WITH TIME Refering to the graph the velocitites of the ball bearings for each
temperature are shown. These results can be proven using Stoke’s Law (for a detailed
description of Stoke’s Law and other related physics concepts refer to the article),
but due word limit restrictions these calculations have been removed. From chart one a relationship between the size of a ball bearing and
its velocity can also be formed. Studying graph two it can be seen that there is a gradual
curve which indictes that it is reasonable to suggest that the relationship would once
again involve T to power of something. Therefore a relationship could be formed using a
Log-Log graph, shown below. Using a line of best fit the gradient can be found as 0.638. Therefore
the relationship between the Log of Velocity vs. Log of Diameter is V = kD0.638. All
discrepancies in calculations for graph five and the same as for graph three.DifficultiesDifficulties encounted during this investigation are:
? Trying to establish weather the sphere had reached terminal velocity before timing
began.
? Trying to maintain the temperature attained once the glycerol has been heated or
cooled.
? Human errors when timing.
? Human errors in general.
? Transfering the glycerol from the measuring cylinder to bottles without loosing any.
? Trying to hold the ball bearings just above the glycerol without dropping them in.
? Trying to perform as many tests as possible (in an effort to get a more accurate
average) within the time allocated in class.Although every difficulty was hard work to around, trying to establish weather the sphere
had reached terminal velocity before timing began was the main difficulty encountered.Errors% error in distance = 0.15cm x 100 = 1.5%
10cm 1% error in time = 0.36s x 100 = 4.4%
This is in regard to
human error in 8.1 1
responding with the stopwatch.% error in velocity = 8%
% Error in temperature = 7 x 100 = 32% This
allows for a possible increase
20
1 or
decrease in temperature whilst
the experiment was taking place or
for the chance that the thermometer
wasn’t calibrated correctly
Error in radius = 1%
This accounts for human error in 1
reading the
measurements or that
the radius’ of the spheres used was
not uniform.
% Error in velocity calculations
using Stoke’s Law and mg = U + F = 1%Success of The Investigation The aim of this investigation was show that the terminal velocity of a
sphere falling through glycerol varies with the temperature and the size of the sphere.
From the results shown I believe that the investigation was a success.Conclusions As a result of this investigation it can clearly be concluded that as
the temperature of glycerol increases, viscosity decreases and therefore any sphere
falling through the glycerol will experience an increase in terminal velocity. Also the
rate of increase in velocity is greater as the temperature rises. This is because the less
viscous the state of the glycerol, the more freely the sphere is able to fall. It can also
be concluded that as the diameter of the sphere increases the weight of the sphere
increases and therefore its terminal velocity increases.BibliographyDe Jong, Physics Two Heinman Physics in Context, Australia 1994
McGraw-Hill Encyclopedia of Physics 2nd edition, 1993Appendix OneSize of Sphere Test 1 Test 2
Test 3 Test 4 Average
3.175mm 1 1.5802 1.9503 1.940 1.2801.4101.570
1.5501.5401.410 1.3401.5001.630
1.4371.6001.637
3.960mm 1 0.7502 1.0403 1.050 0.7500.9100.910
0.7200.9700.950 0.7801.0100.990
0.7500.9820.970
5.000mm 1 0.5302 0.6303 0.670 0.4400.4800.470
0.5300.7400.610 0.4800.5100.590
0.5000.5900.590
6.000mm 1 0.7402 0.6403 0.580 0.6600.6500.670
0.9600.6600.660 0.7800.6700.600
0.7850.6550.627
7.000mm 1 0.3102 0.3603 0.340 0.3600.3500.370
0.3300.3600.350 0.3500.3700.380
0.3400.3600.360
Temperature Test 1 Test 2 Test 3
Test 4 Average
7oc 1 5.4252 8.0503 8.060 5.9008.2508.150
5.3008.1008.050 5.6008.0608.050
5.5008.0508.060
12oc 1 2.7002 4.5403 4.420 2.8004.6004.700
2.6004.5004.450 2.5004.3004.400
2.7004.5004.400
15oc 1 2.3002 3.6303 3.920 2.3003.6003.800
2.4003.7003.700 2.5003.8003.600
2.3003.5303.920
17oc 1 2.0402 2.8903 3.360 2.0002.9003.000
2.2002.9502.950 2.3003.0002.900
2.0002.8903.060
20oc 1 1.4402 1.6003 1.640 1.5001.6001.650
1.4501.6101.630 1.5301.6001.590
1.4401.6001.640
Appendix Two This chart demonstrates that as temperature increase there is a
signifigant decrease in the viscosity.Temp. oc Viscosity cp
-42 6.71×106
-36 2.05×106
-25 2.62×105
-20 1.34×105
-15.4 6.65×104
-10.8 3.55×104
-4.2 1.49×104
0 12,100
6 6,260
15 2,330
20 1,490
25 954
<30 629
Physics CAT One
Extended Practical Investigation
Report
Student Number:Purpose The Purpose of this investigation is to explore how the terminal
velocity of a sphere falling through glycerol varies with the temperature of the glycerol
and the size of the sphere.Introduction In the early stages of the project it was intended to investigate how
the speed of a sphere falling through glycerol varies with the size of the sphere.
However, after analysis it was decided that the investigation would be more callenging if
a second variable was incorporated. There are many constants that could have been
manipulated such as, amount of glycerol used, distacnce over which times were taken,
distance sphere was allowed to fall before timing was taken and the temperature of the
glycerol. After much consultation it was decided that the temperature of the glycerol
should be varied. Once this had benn incorporated into the investigation some scientific
concepts related to the viscosity of a liquid had to be attained. (Refer to article). In conducting the experiments an attempt was made to attain results
that could, produce graphs that showed the terminal velocity of a sphere related to the
temperature of the glycerol and the terminal velocity of a sphere related to its size.Apparatus used• 600 ml of glycerol (density 1.26/ml. Assay 98.0 – 101.0%)
• Small ball bearings of radius: 3.175mm
3.960mm
5.000mm
6.000mm
7.000mm• 900 ml measuring cylinder
• Stop watch
• Thermometer
• Some type of heating and cooling device to varie the temperature
of the glycerol
• TweezersVariables and Constants The variables that have been used in this investigation are the size of
the ball bearings and the temperature of the glycerol. The constants that have been used
in this investigation are the amount of glycerol used, the size of the measuring cylinder,
the intervals at which time were taken, the distance the sphere was allowed to drop before
times were taken and the number of tests taken.Method To begin experimentation the distance over which the sphere accelerates
to reach terminal velocity had to be determined. This was done by systematically varying
the distance over which the sphere was allowed to fall then finding the point at which the
spheres acceleration is zero. It was found that for the sphere to reach terminal velocity
it had to be allowed to fall 6 – 7 centimeters before an accurate, constant reading could
be taken. It was found that the distance needed for a sphere to reach terminal velocity is
only slightly changed when the temperature of the glycerol is varied (+/- 0.2cm). To attain that the sphere had reached terminal velocity by varying the
distance that the sphere fell before timing began, the distance was varied from 2cm to
10cm. Starting at 2cm the measuring cylinder was marked at 2cm intervals and times were
taken for each interval. the times taken were analysed to determine if the rate of descent
of the sphere was constant for each reading. To ensure that the sphere had reached
terminal velocity a full 10 cm of descent was allowed. Using ‘Stokes law for the terminal velocity of a sphere falling under
gravity’ and the relationship of mg = U + F at terminal velocity the above result is
proven. These calculations can be seen in the results section. For all experiments room temperature was recorded at 20oc. The first part of the experiment was to vary the size of the ball
bearing but not the temperature. A sphere of 3.175mm in diameter was dropped from just
above water level and allowed to fall 6 cm before timing began. Once the sphere had fallen
the initial 6 cm timings were taken at intervals along the measuring cylinder every 200ml
(10cm). This experiment was repeated 4 times and an average was taken.
The experiment was then repeated using ball bearings of sizes 3.960mm,
5.00mm, 6.00mm, 7.00mm, 9.00mm. Each individual experiment was repeated 4 times and an
average was taken. All results are shown in the results section. The second part of the experiment was to vary the temperature of the
glycerol but not the ball bearing size. A sphere of 3.175mm was chosen to be used in all
experiments, due to its extremely slow descent rate. The same procedure as above was used
except five temperatures of 7oc, 12 oc, 15 oc, 17 oc and 20 oc for the glycerol were used.
Results The averaged results obtained from the experiment are presented in the
following tables and graphs. (For full documentation of all the results obtained refer to
appendix 1.)Size of Sphere Timing Interval No Averaged
Results Averaged Velocity Temperature
Timing Interval No Averaged Results
Averaged Velocity
3.175mm 1 2 3 1.4371.6001.637
6.178 cm/s 7oc 123
5.5758.1158.095 1.24 cm/s
3.960mm 1 2 3 0.7500.9820.970
10.240 cm/s 12oc 123
2.6504.4754.400 2.24 cm/s
5.000mm 1 2 3 0.5000.6900.680
14.598 cm/s 15oc 123
2.3753.6573.755 2.68 cm/s
6.000mm 1 2 3 0.7850.6550.627
15.600 cm/s 17oc 123
2.1252.9352.977 3.36 cm/s
7.000mm 1 2 3 0.3400.3600.360
27.777 cm/s 20oc 123
1.4801.6021.627 6.17 cm/s
Chart One
Note that there is a reflex error for all the recordings of +/- 0.1
seconds. Also, the first timing interval cannot be used for any calculations as the sphere
has not yet reached terminal velocity. This is a graph representing how the velocity of a 3.175mm sphere
varies with the temperature of the glycerol.
This is a graph representing how the velocity of a sphere varies with
the diameter of that sphere.Analysis of Results Chart One demonstrates that as expected the terminal velocity of the
sphere increases as the temperature of the glycerol and the size of ball bearings
increase. Graphs one and two visually illustrate this point and it can be seen by the
positive gradient shown. It is interesting to note that the change of velocity with the
temperature is signifigantly greater as the temperature becomes higher (15oc to 20.5 oc).
The reason for this is directly related to the change in viscosity as the temperature is
varied. As the temperature increase the viscosity becomes less and so the sphere is able
to move freely through this less viscous liquid thus having a greater terminal velocity. A
chart of temperatures and their relative viscosities for glycerol is shown in appendix
two. A hypothetical relationship can be developed between velocity and temperature. The
shape of the graph, although not smooth, is a curve and therefore it is reasonable to
suggest that the relationship would invole T to the power of something: ie) v = kTn (where
k is a constant). Thus, Log10v = Log10k + n Log10T, where n takes the gradient value. If a
graph of Log10v vs. Log10T is plotted it may be possible to form a relationship.(Graph 3) A line of best fit for the above graph gives a gradient of 2.69.
Therefore a hypothesis for the relationship between velocity and temperature is V =
kT2.69. Of course for the results to be most accurate the sphere would ideally have
reached terminal velocity when the times in graph three were taken. An attempt has been
made to calcualte the terminal velocity at 20oc using stokes law and the relationship mg =
U + F at terminal velocity so that it can be compared to the velocity found at this
temperature.THIS GRAPH SHOWS HOW VELOCITY VARIES WITH TIME Refering to the graph the velocitites of the ball bearings for each
temperature are shown. These results can be proven using Stoke’s Law (for a detailed
description of Stoke’s Law and other related physics concepts refer to the article),
but due word limit restrictions these calculations have been removed. From chart one a relationship between the size of a ball bearing and
its velocity can also be formed. Studying graph two it can be seen that there is a gradual
curve which indictes that it is reasonable to suggest that the relationship would once
again involve T to power of something. Therefore a relationship could be formed using a
Log-Log graph, shown below. Using a line of best fit the gradient can be found as 0.638. Therefore
the relationship between the Log of Velocity vs. Log of Diameter is V = kD0.638. All
discrepancies in calculations for graph five and the same as for graph three.DifficultiesDifficulties encounted during this investigation are:
? Trying to establish weather the sphere had reached terminal velocity before timing
began.
? Trying to maintain the temperature attained once the glycerol has been heated or
cooled.
? Human errors when timing.
? Human errors in general.
? Transfering the glycerol from the measuring cylinder to bottles without loosing any.
? Trying to hold the ball bearings just above the glycerol without dropping them in.
? Trying to perform as many tests as possible (in an effort to get a more accurate
average) within the time allocated in class.Although every difficulty was hard work to around, trying to establish weather the sphere
had reached terminal velocity before timing began was the main difficulty encountered.Errors% error in distance = 0.15cm x 100 = 1.5%
10cm 1% error in time = 0.36s x 100 = 4.4%
This is in regard to
human error in 8.1 1
responding with the stopwatch.% error in velocity = 8%
% Error in temperature = 7 x 100 = 32% This
allows for a possible increase
20
1 or
decrease in temperature whilst
the experiment was taking place or
for the chance that the thermometer
wasn’t calibrated correctly
Error in radius = 1%
This accounts for human error in 1
reading the
measurements or that
the radius’ of the spheres used was
not uniform.
% Error in velocity calculations
using Stoke’s Law and mg = U + F = 1%Success of The Investigation The aim of this investigation was show that the terminal velocity of a
sphere falling through glycerol varies with the temperature and the size of the sphere.
From the results shown I believe that the investigation was a success.Conclusions As a result of this investigation it can clearly be concluded that as
the temperature of glycerol increases, viscosity decreases and therefore any sphere
falling through the glycerol will experience an increase in terminal velocity. Also the
rate of increase in velocity is greater as the temperature rises. This is because the less
viscous the state of the glycerol, the more freely the sphere is able to fall. It can also
be concluded that as the diameter of the sphere increases the weight of the sphere
increases and therefore its terminal velocity increases.BibliographyDe Jong, Physics Two Heinman Physics in Context, Australia 1994
McGraw-Hill Encyclopedia of Physics 2nd edition, 1993Appendix OneSize of Sphere Test 1 Test 2
Test 3 Test 4 Average
3.175mm 1 1.5802 1.9503 1.940 1.2801.4101.570
1.5501.5401.410 1.3401.5001.630
1.4371.6001.637
3.960mm 1 0.7502 1.0403 1.050 0.7500.9100.910
0.7200.9700.950 0.7801.0100.990
0.7500.9820.970
5.000mm 1 0.5302 0.6303 0.670 0.4400.4800.470
0.5300.7400.610 0.4800.5100.590
0.5000.5900.590
6.000mm 1 0.7402 0.6403 0.580 0.6600.6500.670
0.9600.6600.660 0.7800.6700.600
0.7850.6550.627
7.000mm 1 0.3102 0.3603 0.340 0.3600.3500.370
0.3300.3600.350 0.3500.3700.380
0.3400.3600.360
Temperature Test 1 Test 2 Test 3
Test 4 Average
7oc 1 5.4252 8.0503 8.060 5.9008.2508.150
5.3008.1008.050 5.6008.0608.050
5.5008.0508.060
12oc 1 2.7002 4.5403 4.420 2.8004.6004.700
2.6004.5004.450 2.5004.3004.400
2.7004.5004.400
15oc 1 2.3002 3.6303 3.920 2.3003.6003.800
2.4003.7003.700 2.5003.8003.600
2.3003.5303.920
17oc 1 2.0402 2.8903 3.360 2.0002.9003.000
2.2002.9502.950 2.3003.0002.900
2.0002.8903.060
20oc 1 1.4402 1.6003 1.640 1.5001.6001.650
1.4501.6101.630 1.5301.6001.590
1.4401.6001.640
Appendix Two This chart demonstrates that as temperature increase there is a
signifigant decrease in the viscosity.Temp. oc Viscosity cp
-42 6.71×106
-36 2.05×106
-25 2.62×105
-20 1.34×105
-15.4 6.65×104
-10.8 3.55×104
-4.2 1.49×104
0 12,100
6 6,260
15 2,330
20 1,490
25 954
30 629