Terminal Velocity Essay

Unformatted text preview: Physics Extended Essay Cover Contents uuuu Abstract...“a............m.m......,..m....,. .... m........°.a...."uPagQB 4 Hypathesisnuum aaaaa ...... ....s.....Page 4 Backgmund Informatienma...a....,....°... ......... n...........Page 4 Proceduresm....,....,.,,..,...a.mum............,...... Page ’7 Raw Resufits Tables,..a,.m....e..w, ..... 9 Galculation Tablesem..mg....m....,.”.,m.m.,..n..Page 1% Graph 3333 ,9.....°.........Page 11 Graph .... 12 Graph .... .... ......Page 13 Graph ,,,,,, ,,,,,, ..... .....Page 14 Graph Sm. .... 15 Graph 16 Goficlusion""mum."....e.,...,........“unsung...",......W...Page 1‘7 Evaluationwm.Wu...“...."9.9....m."mm.WW......,.....°.Pagel’7 BibliagmphyaWWW.....mm,.,.,m..ammm.n.,...m.a......Pagel9 Aim The aim of this experiment is to analyze how the air resistance and gravitational pull are related in a parachute. i will do this by investigating which type of parachute has a lower terrninai velocity by changing shapes, surface area, and material of the parachute and by keeping as first constant the gravitational puil on the parachute and its mass and as second constant the height at which the parachute will start its descent. Hypothesis i expect that the best material will be plastic since it doesn’t allow any air to pass through it. The best shape in my opinion will be the circle since being uniform without any angles it should curve in such a way that the air will come out from underneath the parachute so the one that wiil glide down more slowiy will be the largest since it has more air facing it so more resistance and less speed. Lastly the best string length wili be the longest since it ailows the parachute to be more stable. Background Information Mainly there are two forces acting on a parachute; Gravity and Air resistance. Gravity is the downwards force, it’s the force that pulls the parachute towards the ground. It is the force of attraction between matters. Aithough its one of the weakest forces in nature it still manages to keep galaxies together and us attached to the earth, This force was put in forrriuiae by Sir isaac Newton, an English mathematician, in his general law that governs gravitational forces: “Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of their distances apart.“ Put into formulae its: Fg “Elam; f OR 1 Advanced Physics Fifth Edition Tom Duncan Where: F = Force in Newton’s G = 6.67::(10'11 = Gravitational Constant M1: First Mass in Kilo grams M2 = Seemed Mass in Kilograms r = Distance in metres between m1 and 1112 In a Vacuum the parachute independently from the mass, surface area, material or shape, it would fall with an acceleration of 9.8 m s '2. For the parachute to glide down there has to be another force acting on it working as an opposite force to gravity and pulling the parachute upwards. This force is air resistance; it increases as the speed of the parachute increases. The more surface area there is of the parachute the higher the air resistance Since there is more air facing the parachute and applying resistance to it. Initially the parachute gliding down at the very moment it has been released it has acceleration due to gravity of 9.8 m s'2 downwards. Parachute not yet been released Maximum downwards pull Zero air resistance After it has been released the parachute gradually decelerates since there is air resistance acting upwards on it... Parachutes during the descent. Downward velocity decreases Upward pull increases. ...until it reaches its terminal velocity. Terminal velocity occurs when there is no acceleration and the resultant force on the parachute equals to 0 since both forces balances each other out (F g=Far). This means that it happens when air resistance equals the gravitational pull on the object. In this period of the glide the velocity of the object remains constant. Terminal velocity is not always the same; a larger surface area of the parachute means a lower and earlier terminal velocity whilst a higher mass specially if small and dense means a higher and later terminal velocity. So terminal velocity depends from the size of the parachute, how much mass put on it and also from the shape of the parachute. Parachute with upper and downward force balanced Procedure The tools that are needed for this experiment are the following: > Paper is the first material of the parachute to be tested Thin cotton sheet is the second material that will be tested Thich cotton sheet for example a towel is the third material to be tested Pieces of strings of different lengths Different weights to be used as the mass dragging the parachute towards the earth More than lKg of pongo to keep the gravitational pull always constant A balance to weigh each component of the parachute and be sure that each parachute has the same gravitational pull VV VVVV In this investigation there will be four experiments: Experiment I : Best shape ofparachute The constants in this experiment will be the length of the string that attaches the mass to the parachute, the mass that drags the parachute down, the material of the parachute and the shape. Circles will have to be cut out of paper of radii 10 cm, 15 cm, 20 cm, 25 cm and 30 cm. Strings of length 40 cm will have to be attached to paper shapes on one end and to the mass on the other end that will be of more or less 1 kg since it will vary depending on how much the parachute weights. The total mass of the whole system will have to be constant at 1 Kg. The parachute will then be dropped from a height of 20 m so to allow the parachute to reach its terminal velocity. For this experiment to be correct there has to be no external force acting on the parachute for example wind. Ex erimenr 2: Best ska e o arachute For this experiment the constants will be the length of the string that attaches the mass to the parachute, the mass that drags the parachute down, the material of the parachute and its surface area. After having cut the paper into circles of radius 10 cm, l5 cm, 20 cm, 25 cm and 30 cm there will have to be cut squares of the same area so of side length 17.7 cm, 26.6cm, 25.40131, 44.3cm and 53.170111. Strings oflength 40 cm will have to be attached to the paper shapes on one end and to the mass on the other end. The mass as before will be of more or less lKg since it will vary depending on how much the 7 parachute weighs. The total mass of the whole system wiii have to be 1 Kg always constant. The parachute will then be dropped again from a height of 20 m so to allow the parachute to reach its terminal velocity. For this experiment to be correct there has to be no external force acting on the parachute for exampie wind. Experiment 3: Best material for the parachute In this experiment the constants will be the length of the string that attach the mass to the parachute, the mass that drags the parachute down, its surface area and the shape of the parachute for all four different materials. The four materials tested are paper, thin cotton sheet, thick cotton towel and plastic. Circles of 300m in radius will have to be cut out from all four materials. Strings of length 40 cm will have to he attached to the paper shapes on one end and to the mass on the other end. The mass as before will be of more or less lKg since it will vary depending on how much the parachute weighs. The totai mass of the whole system wiil have to be constant at 1 Kg. The parachute will then he dropped again from a height of 20 in so to allow the parachute to reach its terminal velocity. For this experiment to be correct there has to be no external force acting on the parachute for example wind. Experiment 4: Best String Len gth This experiment will have as constants the material of the parachute, the mass dragging the parachute down, its surface area and the shape of the parachute. Always with the same thick cotton parachute of radius 30 cm, strings of different lengths 100m, 15cm, 20cm, 250m, 30cm, 350m, 400m, 45cm, 500m, 550m, 600m Will have to be attached to it on one side. On the other side of the parachute there will be a mass of more or less lKg since it will vary depending on how much the parachute weighs. The total mass of the whole system will have to be constant at 1 Kg. The parachute will then be dropped again from a height of 20 In so to allow the parachute to reach its terminal velocity. For this experiment to be correct there has to be no external force acting on the parachute for example wind. Results Radii of the circle parachute cut Time for the parachute to touch the ground / Seconds Time for the Squared parachute to reach the ground / Seconds Time for the circle parachute to reach the ground / Seconds Area of the parachute cm2 Material of the parachute Time for the parachute to touch the ground / seconds Paper 1.458 Thin cotton sheet 0.826 Thick cotton towel 0.986 Plastic 1 .5 1 2 Length of the string / cm Time for the parachute to reach the 1 round / Seconds 10 15 0.742 20 0.892 25 30 35 1.182 49 1.233 1.299 1.362 1.431 1.458 45 50 55 60 Calculations V=S/T Radit 0f the circle Average Velocity of the arachute / cm 1 arachute / m/s 1,786 1,539 Area of the parachute / c1132 Average Velocity of the circle parachute / m/s Average Velocity of the Squared parachute / m/s Material of the parachute Average Velecity of the parachute / rn/s Paper 1.344 Thin cotton sheet 2.372 Thick cotton towei Plastic Length of the string / cm Average Velocity of the parachute / m/s 10 15 2.641 20 2.197 30 35 40 50 55 60 10 LA .w 96 EEQEE ygggén . u 3. Conclusion As it can be seen from the results calculations and graphs my hypothesis was correct. Experiment number one made a straight-line graph that suggests that the parachutes radius is directly proportional to the time. From the table of results it can be said that the parachute with the lower velocity so the best one was the 30 cm radius, the one with the biggest surface area. Experiment number two showed from the graphs that the perfect shape a large parachute should have is circular. In small dimensions instead the parachute should be squared, this occurs since the 2 graphs intersect which means that a longer time is taken for the descent at low surface areas. The best material should be plastic as shown in the results of experiment three since plastic has the lowest Average Velocity while the last experiment made clear that the best string was the longest one so the 600m one. Evaluation Several difficulties had been encountered while doing this experiment. The rnaj or and most damaging to the errors is that the 20 M height where the experiment should have been done was always windy so the parachute would have been 1clown away making a significant error in the results if it was tested there. It was decided that the experiments would have been done in a closed environment so with no wind but on the other hand doing it in this place made it impossible to have a height constant of 20m. The experiment was done from a height of 1.96 in. This change didn’t allow an accurate calculation of the average velocity since it didn’t allow the tested parachute (specially the smaller ones) to reach their terminal velocity. The small parachutes initially had a downwards acceleration due to gravity and before the parachute opened up and started to do resist to air making an upwards force, the parachute had already touched the ground. The results that were taken 1 still took them in consideration since they still gave an approximate idea of what the velocity would be. The second difficultyl encountered was the mass I used. In the planning it was decided that the mass dragging the parachute down would have been of lKg so the downward force was 10 Newtons. Doing the experiment I discovered that this mass was extremely high and that it dragged the parachute down too rapidly and it didn’t allow it to open well enough so to create an upwards force and reach the terminal velocity. To avoid this to happen I drastically reduced the mass to 0.1 Kg and this change provided a much more accurate reading for the big parachutes. On the other hand for the smaller parachutes I realized that 0.1 kg wasn’t enough since they behaved in the same way as described above; the results so couldn’t be extremely l2 reliable though since they still followed a general trend or pattern I still considered them while analyzing the results. All the results were approximately how I expected apart from in the experiment of the best material. First of all I expected paper to be the best material though it was plastic, furthermore I didn’t expect the cotton parachutes to be so faster than the plastic and paper. This is probably caused by the fact that air in paper and even more in plastic is trapped completely inside the parachute and released on the sides while in the cotton parachutes some air passes trough them making the air resistance less so a lower upwards force. On the other hand it can also be said that plastic is lets less air pass trough the material than paper does, this is why its average velocity was lower than the one of paper. The results of the different shapes and different dimensions of the parachute as variables followed a similar pattern that was: between the largest variable and the second largest there was the biggest gap, then the more the dimension became smaller, the more the difference between results was smaller. The experiment of the different lengths of string instead didn’t have this pattern, what happened is that it decreased slightly the more the strings were short but only at about 20 cm it had a significant decrease. This is probably because parachutes having 20 cm and less of string length could not reach their terminal velocity before the parachute reached the ground so the air resistance was not significant in the tests. This experiment as I described at the beginning of the evaluation had many difficulties so first of all to improve the experiment these difficulties should be dealt with, a height of 20 m with no wind and a smaller mass of approximately 0.05 Kg should he used. in addition other tests should be done using other materials for example nets to see if the theory of air blocked in the material is the cause of difference in results for the tests on plastic and cotton, and other shapes should he used for example rectangles and triangles. A last way of improving the results of the experiment is, since it will be done from a height of 20 m, a timer could be started when the parachute has traveled for three meters and stopped when the parachute reaches the ground. This allows the results to be more precise since only the section where the parachute has reached its terminal velocity is measured; the acceleration part where the upward and downward forces are balancing out is not counted. To extend the experiment a ticker tape timer could be used so it could be seen exactly how much time the parachute takes to reach its terminal velocity and the exact velocity at each stage of the acceleration. l3 Advanced Physics Fifth edition 2000 htt ://www.the0r .eaItechedu/ e0 le/ atricia/ ravto .html September 2003 http://schoeidiscovery.com/1essenptans/programs/foreesandmotion/ September 2003 h sieszene/Iesson/OZferees.htm :23 O :53 O 9 3 ‘-_. htt i/fwwwseienee'e September 2003 htt ://Www.cu1“tin.edu.au/curtin/de t/ h s-sei/ September 2003 ravit fin dex2.htm ht‘t ://www.eurtin.edueu/curtin/de t/ h ssci/ raVit fhistea, /hist0r .htm#ke tel“ September 2003 htt ://Www.curtin.edu.eta/cuttin/de' t/ h“s~scé/ ‘aVi fintermed/mter.htm September 2003 btt ://www.theor atficia/ ravto .html .ealteehedu/ 60; 1e/ October 2003 http :// \R’W’W’Slb . 00ml seed/ en/ notes/ 31g gut .htm October 2003 http://www.slb.eom/seed/en/lab/p araehute/res.htm October 2003 14 ...
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The Terminal Velocity of a Paper Helicopter

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The Terminal Velocity of a Paper Helicopter

Introduction.

Terminal velocity is the resulting occurance when acceleration and
resistance forces are equal. As an example, a freefalling parachutist
before the parachute opens reaches terminal velocity at about 120mph,
but when the parachute is opened, terminal velocity is reached at
15mph, which is a safe speed to hit the ground at. This experiment
will be no different, as I will be examining the terminal velocity of
a freefalling paper helicopter.

Planning and Method.

Any experiment needs variations as well as fairness to be a true
success. The two variations I will include in this experiment shall
be:

1) The number of paperclips on the bottom of the helicopter.

2) The length of the helicopter rotors.

The number of paperclips changes the acceleration force while the
rotor length changes the resistance force. Finally, to make this a
fair test I shall use the same helicopter throughout the experiment.
The helicopter shall always be dropped from a height of two metres, as
this continuity makes the experiment even more of a fair test.

My method of working is that I will start off by completing the tests
involving the number of paperclips. I will then move on to the rotor
length tests, which will all be carried out with a standard weight of
one paperclip. All tests will be repeated three times, and averages
will be taken, as this will rule out the possibility of anomalous
results. The rotor lengths will be recorded in centimetres.

Predictions.

Knowing the information given in my introduction, I can hypothesise on
two things.

1) The more paperclips there are, the greater the acceleration will
be.

2) The shorter the rotor length is, the smaller the resistance will
be.

I have come to these predictions using scientific knowledge. The
heavier something is, the faster they fall, so I decided to base my
first prediction on this fact. I based the second hypothesis on the
parachutist example in my introduction.

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Related Searches

Terminal Velocity         Scientific Knowledge         Predictions         Parachute         Acceleration         Variations         Lengths         Tests        




When open, the parachute
offers a larger surface area and so slows down. I reversed this to get
the fact that a smaller surface area will offer less resistance.

Results.

No. of Paperclips

Rotor Length

Clip No.

1st Drop

2nd Drop

3rd Drop

Length/cm

1st Drop

2nd Drop

3rd Drop

0

1.15

1.27

1.33

10cm

1.89

1.88

2.00

1

1.82

1.80

1.79

9cm

1.83

2.01

1.87

2

1.71

1.69

1.78

8cm

1.77

1.75

1.82

3

1.37

1.44

1.51

7cm

1.74

1.66

1.68

4

1.27

1.36

1.48

6cm

1.65

1.65

1.58

5

1.10

1.36

1.27

5cm

1.58

1.45

1.53

The averages were needed to be able to plot graphs for this data, so
here they are.

No. of Paperclips

Rotor Length

Clip No.

Average Results

Length/cm

Average Results

0

1.25

10cm

1.92

1

1.80

9cm

1.90

2

1.72

8cm

1.78

3

1.44

7cm

1.69

4

1.30

6cm

1.63

5

1.24

5cm

1.52

Now that we have averages, we can begin to plot graphs for this data.
Both graphs contain lines of best fit and their formulas. For the sake
of continuity, the first graph plotted will be for the number of
paperclips on the bottom of the paper helicopter.

Text Box: y = -6.1699x + 12.255[IMAGE][IMAGE][IMAGE]The average data
value for 0 paperclips was too big an outlier for this results graph,
so I have discounted it from this analysis. It seems the number of
paperclips on the helicopter directly affects how long the helicopter
stays in the air. My hypothesis was therefore true; the more
paperclips there are, the less time the helicopter spends in the air.
To test my line of best fit I shall find out how many paperclips would
be on a helicopter that stays in the air for 1.1 seconds.
(1.1X-6.1699)+12.255=5.46811. So the helicopter would have on it 5.5
paperclips. Look at the arrows on the graph, and note how they meet
the line at 1.1 on the x axis and 5.5 on the y axis. Next up is the
results of the rotor length tests, which show another interesting
discovery.

[IMAGE][IMAGE]Text Box: y = 11.827x - 13.079[IMAGE]This graph tells a
similarly true story of strong correlation. The shorter the rotors
are, the less time the helicopter spends in the air. That means my
second prediction was also correct. Using the line of best fit on this
graph I shall try to find out how long the rotors would have to be to
keep the helicopter airborne for 1.7 seconds.
(1.7X11.827)-13.079=7.0269. So the rotors would need to be 7
centimetres long for this to work. Now to check this finding. Note how
the arrows on the graph meet at 1.7 on the x axis and just above 7 on
the y axis.

All in all my hypotheses both turned out to be true, albeit in the
first graph I did have to discount a data set. Had I included this
extra point, then the points collectively would have made a line that
started at the co-ordinates (1.25,0) and gone across to (1.8,1) before
continuing as the existing graph shows. In effect the graph would form
a line that looks much like a> sign. Also, the line of best fit would
have been severely distorted.



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