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• scarlet

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Physics IA: Investigating the relationship between “gas law” and water rocket. It has been my childhood memory to play with water rockets. When I was in my 3rd grade in primary school, my science teacher taught us the way to fire rockets into 5 stories high, only with water pressure. This scientific wonder stunned me and over the years, I have been thinking of the optimal conditions to create a water rocket that would fly the maximum vertical height. The physics internal assessment provided me with an excellent chance to investigate on this topic and test my findings. Physics that is involved in this experimentation is energy and gas law, which requires me looking into details like bottle shape, water, pressure, in order to answer the topic question. What I am going to do about this experiment is that I will be looking at the variation of water volume and air pressure, finding out the relationship between them, by applying gas law through data collecting and graph plotting.

Number of attempts

Volume of water (ml)

0 1 2 3 4 5 6 7 8 9 10

0 50 100 150 200 250 300 350 400 450 500

Time (s) 0 0.010 0.012 0.015 0.018 0.022 0.026 0.030 0.035 0.038 0.042

Height (m) 0 6.37 6.29 6.20 5.92 5.46 4.98 4.36 3.89 3.27 2.99

Guage Pressure (Pa) － 3867.07 2995.90 2192.07 1698.24 1282.30 1014.89 830.64 669.40 596.60 518.60

11 12 13 14 15 16 17 18 19 20

550 600 650 700 750 800 850 900 950 1000

Control variable The bottle I used Pressure pump with gauge

Same space (outdoor, in the afternoon) Same weather condition (at around 26.5°)

0.044 0.047 0.048 0.050 0.051 0.051 0.052 0.052 0.052 0.052

2.45 2.12 1.77 1.34 1.36 1.21 0.994 0.687 0.343 0.172

Dependent variable Volume of water (50 mL at a time) From 0 mL to 1000 mL beaker

485.90 443.04 430.17 406.28 395.17 395.17 384.57 384.57 384.57 384.57

Independent variable Maximum height (measured in Meters) Pressure being read from the gauge (167.4 psi as average value) Reading on the Altimeter (measured in Meters)

The table below shows the data collected during the experimentation To do the experiment, I first need to prepare a plastic bottle with a volume of 1000 mL and put it under a tripod to stable it. Then I need to prepare a beaker with a measurement from 0 mL to 1000 mL, because it is used to measure the volume of the water used when the water rocket launches. After that, A pressure pump which is connect with a pressure gauge will be used in order to find out how much air I have pumped into the water rocket to make it leave the land. Then, a plastic tube will be used in order to connect water rocket and the pressure pump. Lastly, an altimeter will be stuck on the top of the bottle because it is used to record the height the rocket flew. The problem I realized during the experiment is that the rocket actually spins and stays in the air when it reaches its maximum height. After the rocket lands, the bottle is almost empty. The diagram below shows the equipment that are used during the experiment: Water rocket A 1 liter staright body plastic pepsi water bottle Bubble wrap To wrap around the rocket to protect the apparatus that is stuck on it (which is the altimeter) Pressure guage Connected to the bicycle pump in order to take measurements in each trail Tripod A launch pad for stabling the water rocket Altimeter Connected to the water rocket in order to record the height Mobile Phone Taking videos and check how long the rockect stays in air when it reaches its maximum height

Tape Bicycle Pump

Use to stable the pump and the rocket , also stabling the altimeter, bubble wrap and the rocket A tool for pumping air into the water rocket

Through out the entire experiment, the time (T) represents how long the rocket stays in air when it reaches its maximum height in each trail.

Graphs are plotted in order to show the relationship between each quantity.

This graph is plotted with the raw data collected during the experiment. It shows that presure and volume are inversely proportional. It can also be proved with the ideal gas law equation PV = nRT.. The equation for ideal gas law will be applied in order to explain the variation of pressure volume with the water rocket. For R is the universal gas constant, T is temperature of the gas in K, n is the amount of ideal gas and V is the volume of the container with the gas. The equation shows the pressure, volume as well as the temperature of certain amount (n) of ideal gas. P is the absolute pressure. 1 will be plotted in order to V find the relationship between the gauge pressure and the volume, based on the formula: nRT P= V 1 Therefore, P is ∝ V Moreover, another graph of P against

According to the graph above, it indicates the inverse relationship between gauge pressure and the volume, which comes out with a linear graph, plotted with a line of best fit. As a result these 2 graphs are demonstrated as a strong model of ideal gas law. Eventhough Absolute pressure wasn’t used in the experiment I did, the graphs has show the similar conclusion and relatinoship between each variables. In the actual experimentation, inefficiency and losses in energy are expected to see. During the process of launching the water rocket, there is a drag force acting on it, which is gravitational force, calculated with the formula: mgh. For m is mass, g is garviatational force ( 9.81 ms -1) and h is the height. N × m3 2 m PV =Nm PV =

Where Nm is defined as work done in this case. Another graph will be ploted for PV against mgh. Where P is absolute pressure. Mass will be calculate with the formula : Density of water(kg/m³) x volume of water( m 3 ¿ .The density of water is 997 kg/m³

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

PabsV (Nm)

mgh

5.2596035

3.115111545

10.43209

6.15197853

15.5275605

9.0959301

20.604648

11.58019488

25.651825

13.35047805

30.701967

14.61217158

35.754474

14.92514982

40.79776

15.21856692

45.86472

14.39210876

50.9218

14.62195215

55.995995

13.17931808

61.060824

12.44088504

66.1408605

11.25254579

71.211896

9.17417466

76.2901275

9.9761814

81.376136

9.46759176

86.4531345

8.263603593

91.538613

6.047326431

96.6240915

3.186998735

101.70957

1.68225804

This graph shows the relatioship between mgh and PV, which is a parabolic graph. Note that the graditent on the curve does not have any unit. The perfect case for this is when they are 100% equal to each other, which is when PV is exactly equals to mgh. The graph should be a straight line instead of a curve. If this case in taken event in real life, there may be external concerns that are taken into account: 1 2 PV =mgh+friction+ m v +leakage of water 2 In addition, I will present another table of adding absolute pressure to atmospheric pressure. In this case a new set of data will be calculated with the raw data, with uncertainty taken in account due to systematic error . With the equation of ideal gas law : PV = nRT.  P will be the absolute pressure, in which Pabs = Patm + Pgauge Atmospheric pressure is 101325 Pa  V will be volume, which will be measured in m3  T will be measured in Kelvin, which is 26+ 273= 299  R will be the gas constant Volume (m3) 1 2

Pressure ± 0.01 600 300

105192.07 104320.9

(Pabs/Pa)

Height

± 0.01 0 6.37

(m)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

200 150 120 100 85.71428571 75 66.66666667 60 54.54545455 50 46.15384615 42.85714286 40 37.5 35.29411765 33.33333333 31.57894737 30

103517.07 103023.24 102607.3 102339.89 102155.64 101994.4 101921.6 101843.6 101810.9 101768.04 101755.17 101731.28 101720.17 101720.17 101709.57 101709.57 101709.57 101709.57

6.29 6.20 5.92 5.46 4.98 4.36 3.89 3.27 2.99 2.45 2.12 1.77 1.34 1.36 1.21 0.994 0.687 0.343

Since uncertainty of both height and pressure is ± 0.01 , the V above will be defned as smallest volume base, which will be calculated : ± 0.013=3 ×0.01 0.01× 3 3 volume ∈m This gives the data above. V olume base=

Another graph of P against table

1 V

will be plotted with the new data

The graph came out to be a curve, which is almost a straight line, but it also suggested that it would never cross 0. It is because actual ideal gas does not exist in real life and can never be approached. The perfect situation of this can be defined in this way: If : PV =Constant ×Temperature PV =constant It is because the experiment is hold up under a constant temperature, so the result will be constant, which will be represented as k PV =constant PV =k k P= V P∝

1 V

Or

V∝

1 P

In conclusion, the data collected from the water rocket experiment matches, to a high extent, the gas law of PV = nRT. The more water there was in the rocket, the lower it flew, proving an inversely proportional relationship between the pressure of the gas and the volume of the water bottle. The dependent variable will be the amount of water and gas added in the water, while the independent variable will be the distance of how far the rocket went. Compare with the real life, the water rocket is a smaller model of an actual rocket. As a result, the data collected may not be accurate because there is air resistance acting on the water rocket and this will affect the results collected. In addition, the alitmeter broke during the halfway of the experiment, so the results may not be accurat as I have use another alitmeter that is same as the broken one. Still, there will be some systemetic error. The graphs and data has come up with a conclusion that in real life, PV ≠ mgh. Random errors are made through the plotting of the graph, which follows my expected trend, which are the curves and lines on the graph with the error bars and poles. While the systematic occurs due to the not quite “zero” setups on my digital apparatus. The experiment is used to carry out to explain how gas law is related to the maximum height that can be achieve when flying the water rocket. he data results, the graphs has illustrates the relationship between the pressure and volume and height achieve. In addition, they also show how pressure and volume have inversely proportional relationship. In order to improve my experiment and further development, I think I should repeat the same setup for more times, which allows me to get more data and better average results. In the same setup, I may do further development and research on velocity of 1 2 mv ) and it also helps to improve the rocket, which includes the formula (mgh + 2 the accuracy of my experiment. Moreover, I can also repeat the same experiment with different kinds of liquid of same volume, just like: water + sugar, water +oil, etc. Changing the density of liquid of water rocket is also an interesting topic for me to investigate through out this experiment, or even trying out the same setup with water of different temperature.

Reference: https://users.soe.ucsc.edu/~karplus/abe/soda-bottle-rocket.pdf (setup) http://www.wikihow.com/Build-a-Bottle-Rocket(setup) https://orbi.ulg.ac.be/bitstream/2268/36471/1/2010%20Water%20Rocket %20AJP.pdf(setup) http://www.npl.co.uk/upload/pdf/wr_booklet_print.pdf(setup) https://spaceflightsystems.grc.nasa.gov/education/rocket/BottleRocket/historyofrocket rypostconfact.htm (Nasa’s guide and explanation) https://orbi.ulg.ac.be/bitstream/2268/36471/1/2010%20Water%20Rocket%20AJP.pdf (Physics explanation on water rocket experiment)