2022年物理降落傘速率實驗報告

1、Motion Laboratory ReportBackground information / Introduction: The investigation is to test whether the increase of the surface area of an object would cause a change in the velocity since there is more air resistance for a larger surface area. The theory will be tested through the experiment of dro

2、pping different sizes of parachutes attaching to a juice box. Purpose: To observe a free falling object (with a parachute made of plastic bags attached to it), in case that the influential factors (the size of the object, the height of the releasing point, the vertical distance between the parachute

3、 and the object etc.) stay constant, how does changing the surface area of the parachute affect the velocity of the falling object?Hypothesis: If the surface area of the parachute increases, then the downward average velocity of the object would decrease due to the increased air resistance.If the ob

4、ject is falling down with the force of gravity, applying Newtons Second law : Force = Mass x Acceleration, the falling object has “massgravity” of force. Since the earth is not a vacuum, then there would be air resistance acting upward as the mg of force is pulling the object downward: “Air resistan

5、ce is a friction-like force that opposes the motion of objects that move through the air The amount of the air resistance force depends on the speed, size, shape and cross-sectional area of the object” (BC Science, 399) and “how thick the fluid is that is going through” which is the air itself.Air r

6、esistance is velocity dependent, because “air resistance is the result of collisions of the objects leading surface with air molecules” (The Physics Classroom). If the object has a greater speed of velocity, the object would hit the particles harder and would interact with more particles in the air

7、per second. This creates greater frictions between the object and the air and thus creating more air resistance to slow down the falling object. In addition, the formula for calculating the force of air resistance is “Fair = (1/2)CSV2”(百度) where C represents drag coefficient, p represents air densit

8、y, S represents the surface area, and V represents velocity. In the case of the investigation, where the drag coefficient, and the air density are constant, the relationship between the force of air resistance and velocity can approximately be written as “Fair = SV2”. The V in the investigation is a

9、lways negative because the object is falling downward. Therefore, from the equation, it can be predicted that Fair is directly proportional to S, and to the square of V. However, since V is negative, as the number decreases (which means there is greater velocity downwards), the square of it will sti

10、ll be positive, therefore it would increase Fair. “Eventually, the force of air resistance becomes large enough to balance the force of gravitymass. At this instant in time, the net force is zero Newton; the object will stop accelerating” (The Physics classroom), and reach to terminal velocity. Beca

11、use the larger surface area of a parachute would increase the amount of air resistance, which means that it would reach terminal velocity in a shorter amount of time, thus decreasing the average velocity of the falling object.Therefore, it is assumed that if the surface area of the parachute increas

12、es, it would create more force of air resistance, reaching to terminal velocity in a shorter time period, and thus decreases the average downward velocity. Variable: Independent Surface area of the garbage-bag parachutes30cm x 30cm; 40cm x 40cm; 50cm x 50cm; 60cm x 60cm, 70cm x 70cmDependent Velocit

13、y of the falling objects (cm/s)Constant Size of the object (a cut-open juice box with 4.7cm in length, 3.8cm in width, 6cm in height) Height between the parachute and the object (10cm)Distance between the releasing point and the point where the object touches the ground (2.3m)Distance between the fi

14、lming position and the dropping area (4.5m)Surrounding conditions (same place when dropping the object, same place when video tapping )Materials: Capable laptop computer with Logger Pro 3.8.5 installed X1Portable Camera / Camera phone X1Camera/ phone USB X1Plastic bags cut in square - Size 30cm x 30

15、cm X1- Size 40cm x 40cm X1- Size 50cm x 50cm X1- Size 60cm x 60cm X1- Size 70cm x 70cm X1Cut-opened empty Juice box X6(with length 4.7cm, width 3.8cm, height 6cm and weighted 4.5g)Strings20.8 cm X427.2 cm X433.9 cm X440.7 cm X447.6 cm X41m long ruler X130cm long ruler X1Needle X1Diagram:Safety:Use t

16、he needle carefully and make sure it does not do harm to people Stand on the ground firmly and make sure people do not fall from the 2.3m tall place. Do the experiment under the supervision of an instructor. Follow the instructions carefully Environmental concerns: The process of making the parachut

17、es may results in wasting plastic bags. Since plastic bags are not able to decompose naturally in the soil, it is needed for the manual processes to either burn them. The burning plastic bags release dioxin gas which is a compound that is 50-100 times more toxic than potassium cyanide. The dioxin wo

18、uld enter the ecological food chain from soil, picked up by plants, further concentrated in primary and secondary consumers and eventually consumed by humans. It can also enter the human body directly by human inhaling which could cause cancer and the damage in skins, immune system, reproductive sys

19、tem and endocrine system etc. To reduce the use of plastic bags in the investigation, it is practical to just use one piece of plastic bag that is 70 x70cm. The other scales of the plastic bags can be cut from the 70 x70cm scale. Also it is essential to put the used plastic bags into the recycle bin

20、 after the investigation. The wasted juice boxed will be put into the relevant recycle bin and other disposal will go into the garbage can in order to maintain a clean and healthy environment. Procedure:Procedure for Experiment with parachutesMeasure a place that is 2.3m high with the 1m ruler, wher

21、e there is no obstacle and you can drop the object from the height. Two people carry the four corners of the 30 x30 cm parachute with each of their hands. One person stands 4.5 meters far vertically in front of the dropping area, facing towards the dropping area.*Make sure that the strings are not t

22、angled up, and the garbage bag is not crumbled; it is the juice box that is in the 2.3m high position instead of the parachute.The two people hold the four corners of the parachute 2.3m high (as measured) from the ground while the filming person stands in place and prepare to video tape the process

23、of dropping. Make sure the camera is neither angled up nor down. *be careful of the safety hazard in which people might fall from the 2.3m high place. The person clicks filming about three seconds, and then the two people carefully release the parachute at the same time. (Leaving three seconds befor

24、e the actual dropping would allow an easier manipulation and procession of the data later on)Make observation as the object goes down. The person clicks stop after the juice box and the parachute reach the ground. Label the video clip on the camera / phone. Ex: “30 x30cm Atpt1”Repeat step 2-6 for te

25、n times. Repeat step 2-7 by using 40cmx40cm, 50cmx50cm, 60cmx60cm and 70cmx70cm parachutes. Procedure for Experiment without ParachutesOne person carries the juice box (without the parachute) 2.3m high from the ground while the other person stands in place and prepares to video tape the process. Mak

26、e sure the camera is neither angled up nor down. The person clicks filming about three seconds, and then the person holding the juice box carefully release the box.Repeat step 5-7Repeat step 10-12 for ten attempts. Manipulation of Data Connect the camera / the phone with the laptop computerImport al

27、l the video clips taken for the experiment into a new folder. Make sure the video clips are in either “.mov”, “.mpeg”, “.wav” or “.avi” format.Open Logger Pro 3.8.5Click insert and movie on the Logger Pro program and upload the video clip from the new folder.Click on button Click this button on the

28、right of the video to set the scale. Set the scale: create a line on the video vertically from the releasing point to the point where the parachute falls onto. Then insert 2.3 m for distance and unit on the pop-up window. (This step calibrates the video)Move video until the parachute is just about t

29、o leave the handsUse to click on the top edge of the juice box frame by frame to plot its motion. Click on the program and then click to find the best fit linear line of the resulting graph. (ignore the red line because it records the horizontal motion) Record the slope (which is the velocity m/s fo

30、r the falling object) of the linear line in excel. Change the data from Velocity m/s to Velocity cm/s.Repeat Step 4-12 for all the 60 attempts. Record all the data in excel table.Calculate the average for each of the attempts on excel.Graph the data.Setting up the juice box and the parachutesUsing t

31、he needle to poke a small hole on each top corner of the cut-opened juice box. Thread the needle with the 20.8cm long stringTake the needle with the string through the small hole from outside.Tie the string; make sure the string does not slide away. Tie the other side of the string on one corner of

32、the 30cmx30cm plastic bag by threading the needle through the corner with the string. Repeat step 2-4 for the other three strings. Repeat step 1-5 for all the other four scales where using 27.2cm long strings for40cmx40cm plastic bag, 33.9cm for 50cmx50cm, 40.7cm for 60cmx60cm and 47.6cm for 70cmx70

33、cm. Data Collection: Raw dataSurface Area (cm)Velocity (-cm/s)Atpt 1Atpt 2Atpt 3Atpt 4Atpt 5Atpt 6Atpt 7Atpt 8Atpt 9Atpt 10Average0 x 0376.2376.6394.9389.3394.9386.1382.7398.3370.8388.7385.8530 x 3096.74123.9110.2106.3103.7121.890.8692.67109.9126.8108.28740 x 40 89.8472.6078.0795.4276.4684.8674.8892

34、.2986.07111.686.20950 x 50 80.6282.4273.7774.85116.183.9670.8263.9273.8176.3979.66660 x 6072.7755.0272.8788.2181.2783.0268.5668.9092.5575.3775.85470 x 7070.8259.5855.1463.7672.8659.4475.0552.1372.0364.2764.508Processed DataSurface Area (cm)Velocity (-cm/s)0 x 0385.8530 x 30108.28740 x 4086.20950 x 5

35、079.66660 x 6075.85470 x 7064.508Observations: The parachutes swing back and forth as they fall down.The surface of the plastic bag becomes a semi-sphere shape as it falls down.The juice box reaches the ground first.Sometimes the juice box might flip as it just reaches the ground.Graph: Sample: The

36、first attempt for trial 40 x40 cmGraph without the outlier 0 x0 cm dataGraph with the outlier Analysis: Length of the string to make the height between the parachute and the juice box to be constant:Pythagorean Theorem: a2+b2 =c2Ex: 30cm x 30cm trial: ( eq f (30-4.7,2) )2 + ( eq f (30-3.8,2) )2 = 33

37、1.6325 cm2331.6325+ 102 = 431.6325 cm2 eq r (431.6325) 20.8 cm Average VelocityFormula for calculating the average: x = EQ F(1,n) (x1+x2+.+xn) average = EQ F(1,10) (attempt1 +attempt2 +attempt10)Ex: 30cm x 30cm trial: EQ F(1,10) (96.74+123.9+110.2+106.3+103.7+121.8+90.86+92.67+109.9+126.8) = 108.287

38、 cm/sTransform from Velocity m/s to Velocity cm/sEx: 30cm x 30cm first attempt:1 m = 100 cm0.9674 m/s x 100 =96.74 cm/sConclusion & Evaluation: The data and graphs carried out from the investigation support the hypothesis that as the surface area of the parachute increases, the average velocity cm/s

39、 decreases. For example, the highest point on the graph, if including the 0 x0 cm2parachute increment, is at the x-axis of 0 x0 cm2parachute with downward velocity 385.85 cm/s, which represents that the increment has the highest average velocity in cm/s. If not including the outlier of 0 x0 cm2parac

40、hute increment, then the highest point is at 30 x30 cm2parachute increment, the smallest surface area among all tested increments, with downward velocity of 108.287 cm/s. The lowest point on the graph is at the x-axis of 70 x70 cm2 parachute with downward velocity of 64.508 cm/s. The downward veloci

41、ty for the surface area 40 x40 cm2 parachute is 86.209 cm/s, for 50 x50 cm2 is 79.666 cm/s, and for 60 x60 cm/s is 75.854 cm/s respectively, which clearly shows a decreasing trend line, and thus shows that the amount of downward velocity is decreasing as the surface area of the parachute gets larger

42、. The enlarged surface area of the parachute causes the increased possibility of more successful collisions happening between the air molecules and the surface area of the parachute per second. Therefore, it has a greater force of air resistance. In addition, the resulting data can also show to supp

43、ort the hypothesis that air resistance is velocity dependent by using the formula Fair = SV2 extracted from the formula Fair = (1/2)CSV2 which mentioned previously. Using the sample graph of 40 x40 cm2 parachute as an example, the first part of the graph has not reached terminal velocity yet, where

44、the downward velocity cm/s is higher than the average. Suppose the downward velocity of that part is 90 cm/s, then substituted into the simplified formula: Fair = (40)(40)(-90)2, and Fair would assume to be 12960 k unit; then substitute the average velocity in: Fair = (40)(40)(-86)2, and Fair would

45、be 11833.6 k unit. From the result of the calculation, it is supported that the force of air resistance is directly proportional to the objects velocity. Additionally, although not shown, the two proceed graphs still have illustrated that the trend of the graph would much steeper with the outlier 0

46、x0 cm2parachute increment than without it. The downward velocity of the falling object without parachute is about three times greater than that of the falling object with 30 x30 cm2parachute, showing that there would be a huge decrease change in velocity by increasing the base area of the 4.7x3.8 cm

47、2 object to 30 x30 cm2. However, the data in detailed is inaccurate, and this can be demonstrated by the differences between the velocities of each increment, excluding the outlier. For example, the difference between the downward velocity of 30 x30 cm2 and 40 x40 cm2 parachute increment is 108.287

48、- 86.209 = 22.078 cm/s. The next two differences tend to follow a decreasing pattern by presenting 6.543 cm/s difference between 40 x40 cm2 and 50 x50 cm2 increment and, 3.812 cm/s difference between 50 x50 cm2 and 60 x60 cm2 increment. However, the difference between 60 x60 cm2 and 70 x70 cm2 incre

49、ment breaks the pattern by resulting in a difference of 11.346 cm/s. It can also be shown by looking at the graph, where there are dots going above and below the trend line without any order. The resulting data is reliable in a larger scale, but not reliable in the partial details. It is fairly prec

50、ise because the more attempts there are, the more accurately will the calculated average be, and the investigation has ten attempts for each increment instead of three as usually required. However in minor details, the repeated readings for each trial are not very close. For example for trial 50 x50

51、 cm2, with all attempts data results to be around 70cm/s to 80 cm/s, the eighth trial reaches only 63.92 cm/s. Especially for the fifth attempt where it reaches to 116.1 cm/s, it is a result that is even higher than any attempt result of the 30 x30 cm2 increment. Such would lead to the later inaccur

52、acy of the average velocity, thus affecting validity to draw conclusion. It also represents that the data is not reliable if to look into details. There are several uncontrollable factors discovered and problems occurred as we processed through the investigation. The major ones that will affect the

53、validity are the constant variables control, issues in independent variable and disadvantaging location. The disadvantaging location where we did our investigation sets the data to be inaccurate. Due to the limited locations provided in school, it is hard to find a place with 2.3m tall with no obsta

54、cles and people can stand on it safely. The place we chose is the stairs in the lobby where it has a “bump” stick out from the lateral surface of the stairs. For several times that the parachutes hit the “bump” as it falls down. For example in the middle-left of the sample graph, there is a signific

55、ant difference on the dotted trend, and that is when the parachute hits the “bump”. This would affect the accuracy of the data greatly because the change in the dotted line would first affect the auto-calculation of the slope (the velocity in m/s) in the program. Then the inaccurate velocities would

56、 go into the attempts and affect the result of average velocity. However, the ten-times attempts reduces the effeteness of the issue by little to make the resulting data still explainable. To resolve this problem, it is essential to at the line “there is no obstacle and you can drop the object from

57、the height” when finding the location to do the investigation. With such awareness in mind, the possibility of the occurred problem would decrease. The issue in the x-axis of the graph has been identified through processing the data. The x-axis of the graph seems to be increasing in a consistent rat

58、e by showing “30 x30, 40 x40, 50 x50 etc”. However, it is not consistently increasing because it is increased by centimeter square instead of centimeter. If calculated, it will be 900cm2, 1600cm2, 2500cm2, 3600 cm2, 4900 cm2 for the increasing independent variables. From that, it can tell that the i

59、ndependent variable is not constantly increasing in a linear rate but in a half-parabola shape. This would not affect the result of the data, but will influence the conclusion if to compare the relationship between each increment further on. Additionally, there are several constant variables that ca

60、nnot be controlled which would affect the accuracy of the resulting data. For example, the leading surface area for each object with parachute would not be exactly 30 cm2 because there is still the base surface area of the juice box ahead of the parachute as it falls down. Also the distance between