2023年物理降落伞速率实验报告.docx

Motion Laboratory Report

Background 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 dropping 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 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 object is falling down with the force of gravity, applying Newton’s Second law : Force = Mass x Acceleration, the falling object has “mass·gravity” 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 resistance 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 resistance is velocity dependent, because “air resistance is the result of collisions of the object's 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 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)CρSV2”(Baidu) where C represents drag coefficient, p represents air density, 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 = S·V2”. The V in the investigation is always 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 still be positive, therefore it would increase Fair. “Eventually, the force of air resistance becomes large enough to balance the force of gravity·mass. At this instant in time, the net force is zero Newton; the object will stop accelerating” (The Physics classroom), and reach to terminal velocity. Because 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 increases, 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 parachutes
30cm x 30cm; 40cm x 40cm; 50cm x 50cm; 60cm x 60cm, 70cm x 70cm
Dependent
· Velocity 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 filming 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 X1
· Portable Camera / Camera phone X1
· Camera/ phone USB X1
· Plastic bags cut in square
- Size 30cm x 30cm X1
- Size 40cm x 40cm X1
- Size 50cm x 50cm X1
- Size 60cm x 60cm X1
- Size 70cm x 70cm X1
· Cut-opened empty Juice box X6
(with length 4.7cm, width 3.8cm, height 6cm and weighted 4.5g)
· Strings
·20.8 cm X4
·27.2 cm X4
·33.9 cm X4
·40.7 cm X4
·47.6 cm X4
· 1m long ruler X1
· 30cm long ruler X1
· Needle X1

Diagram:

Safety:
· Use the 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 parachutes 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 would 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 system 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 70x70cm. The other scales of the plastic bags can be cut from the 70x70cm scale.
Also it is essential to put the used plastic bags into the recycle bin 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 parachutes
1. Measure a place that is 2.3m high with the 1m ruler, where there is no obstacle and you can drop the object from the height.
2. Two people carry the four corners of the 30x30 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 tangled 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.
3. 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 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.
4. The person clicks filming about three seconds, and then the two people carefully release the parachute at the same time. (Leaving three seconds before the actual dropping would allow an easier manipulation and procession of the data later on)
5. Make observation as the object goes down.
6. The person clicks stop after the juice box and the parachute reach the ground.
7. Label the video clip on the camera / phone. Ex: “30x30cm Atpt1”
8. Repeat step 2-6 for ten times.
9. Repeat step 2-7 by using 40cmx40cm, 50cmx50cm, 60cmx60cm and 70cmx70cm parachutes.
Procedure for Experiment without Parachutes
10. One 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. Make sure the camera is neither angled up nor down.
11. The person clicks filming about three seconds, and then the person holding the juice box carefully release the box.
12. Repeat step 5-7
13. Repeat step 10-12 for ten attempts.
Manipulation of Data
1. Connect the camera / the phone with the laptop computer
2. Import all 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.
3. Open Logger Pro 3.8.5
4. Click ‘insert’ and ‘movie’ on the Logger Pro program and upload the video clip from the new folder.
5. Click on button
6. Click this button on the right of the video to set the scale.
7. 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)
8. Move video until the parachute is just about to leave the hands
9. Use to click on the top edge of the juice box frame by frame to plot its motion.
10. 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)
11. Record the slope (which is the velocity m/s for the falling object) of the linear line in excel.
12. Change the data from Velocity m/s to Velocity cm/s.
13. Repeat Step 4-12 for all the 60 attempts.
14. Record all the data in excel table.
15. Calculate the average for each of the attempts on excel.
16. Graph the data.
Setting up the juice box and the parachutes
1. Using the needle to poke a small hole on each top corner of the cut-opened juice box.
2. Thread the needle with the 20.8cm long string
3. Take the needle with the string through the small hole from outside.
4. Tie the string; make sure the string does not slide away.
5. Tie the other side of the string on one corner of the 30cmx30cm plastic bag by threading the needle through the corner with the string.
6. Repeat step 2-4 for the other three strings.
7. 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 70cmx70cm.

Data Collection:

Raw data
Surface Area (cm²)
Velocity (-cm/s)
Atpt 1
Atpt 2
Atpt 3
Atpt 4
Atpt 5
Atpt 6
Atpt 7
Atpt 8
Atpt 9
Atpt 10
Average
0 x 0
376.2
376.6
394.9
389.3
394.9
386.1
382.7
398.3
370.8
388.7
385.85
30 x 30
96.74
123.9
110.2
106.3
103.7
121.8
90.86
92.67
109.9
126.8
108.287
40 x 40
89.84
72.60
78.07
95.42
76.46
84.86
74.88
92.29
86.07
111.6
86.209
50 x 50
80.62
82.42
73.77
74.85
116.1
83.96
70.82
63.92
73.81
76.39
79.666
60 x 60
72.77
55.02
72.87
88.21
81.27
83.02
68.56
68.90
92.55
75.37
75.854
70 x 70