EXTENDED ESSAY

PHYSICS EXTENDED ESSAY hzy444 An Extended Essay in Physics INVESTIGATING A SUGAR ROCKET RESEARCH QUESTION - How does radius of rocket and amount of propellent in it affect the thrust velocity and maximum altitude of a sugar rocket? Word Count: 3934 hzy444 Page 1 of 26

PHYSICS EXTENDED ESSAY hzy444 Table of Contents INTRODUCTION ................................................................................................................. 3 BACKGROUND INFORMATION ............................................................................................ 4 LAUNCHING THE SUGAR ROCKET ................................................................................................. 7 EXPERIMENT 1 ................................................................................................................... 8 TECHNICAL DATA OF THE ROCKET ................................................................................................. 8 SAMPLE CALCULATION ............................................................................................................... 11 1.1. HYPOTHEISIS ................................................................................................................................... 13 RAW DATA FOR EXPERIMENT 1 ......................................................................................... 14 PRECAUTIONS – .......................................................................................................................... 18 DISTANCE - TIME GRAPH ............................................................................................................ 19 CALCULATING THRUST ................................................................................................................ 20 EXPERIMENT 2 ................................................................................................................. 22 HYPOTHEISIS .............................................................................................................................. 24 RAW DATA FOR EXPERIMENT 2 ................................................................................................... 24 DISTANCE – TIME GRAPH ............................................................................................................ 27 CALCULATING THRUST ................................................................................................................ 28 CONCLUSION .................................................................................................................... 29 BIBLIOGRAPHY ................................................................................................................. 29 Page 2 of 26

PHYSICS EXTENDED ESSAY hzy444 BACKGROUND INFORMATION On a rocket 4 type of forces act on it i.e., Thrust, Drag force, weight and lift force. Newton’s second and third law is applied in understanding and calculating the components of the rocket. CONSTRUCTING THE SUGAR ROCKET In this experiment, the simple version of the sugar rocket was made, where I personally used a PVC pipe of different base lengths. I’d taken 6 different types of PVC pipes of base lengths as follows: - 1. 18mm PVC pipe 2. 20mm PVC pipe 3. 25mm PVC pipe 4. 32mm PVC pipe 5. 40mm PVC pipe 6. 50mm PVC pipe The vertical length of the rocket was used differently in order to fill same amount of propellant in each different base length rockets. The top of the body of the rocket was sealed using semi-wet white cement which later on got dried making it a hard-tight seal (Figure 3). According to a study, the external temperature of the environment also affects the flying of the rocket, like heat so the body of the PVC pipe was painted white as white is a good reflector of heat. Page 4 of 26

PHYSICS EXTENDED ESSAY hzy444 FIGURE 3. I am using, powdered sugar and KNO 3 as the main fuel of the rocket, that will be filled after the white cement is dried. Both the materials have to be mixed in a fixed ratio like if, I am using 100g of total propellant to fill in the rocket than 65g has to be of KNO 3 and 35g has to be powdered sugar. It means that the ratio used to mix them in 7:13 (7 proportion of powdered sugar and 13 has to be KNO 3 ). Then when the propellant is filled in the rocket, it has to be compressed in order to fill the tiny air gaps between the powdered fuel, the air gaps may disturb the flight in the mid-air by a slight and sudden decrease in acceleration. Thus, the fuel needs to be compressed. Firstly, I did several tries but many times the rocket didn’t lift off the ground and the fuel got burned up at the launch pad itself. After some research I got to know about an efficient method to make a good propellant using the same two materials i.e., powdered sugar and KNO 3 . After mixing them properly using a spatula, it needs to be placed on a non-stick pan and then heated on low flame until the sugar caramelizes the whole mixture, making a semi-molten paste. The paste needs to be filled fully before the paste gets dry. In the meanwhile, when the paste is still hot, we need to use a 3.5mm iron rod to make a hole from exact centre till the other end of the rocket (Figure 4). The top of the body of rocket was supported by a balance stick (made of wood) which was 3 times as long as the body of rocket. The balance stick was sticked using 2 strong cello tape, which was as long as the circumference of the Curved Surface Area of the body of the rocket. Page 5 of 26

PHYSICS EXTENDED ESSAY hzy444 EXPERIMENT 1 In the following experiment, I have used 6 PVC pipes of different radius using a particular mass of propellant i.e., 0.118kg. For measuring the diameter of the body of the rocket a Vernier Calliper was used. To measure the volume of the rocket, the empty rocket was filled with the propellant till the top and then it was poured into a weighing scale to quantify the amount. The total mass of the rocket was also measured in the same way, by putting the whole rocket on the kitchen scale. The mass of the empty rocket was also measured to know the mass of rocket after the propellant gets burned up, which will be later on used to verify the thrust. TECHNICAL DATA OF THE ROCKET The thickness of the PVC pipe was also measured to find the inner radius of the rocket. Inner radius will help us to verify the volume of the rocket by using the formula, Volume of Cylinder = π r 2 h --------- [1] Table 1. RADIUS OF PIPE (cm) TRIAL TOTAL DIAMETER (cm) AVERAGE VALUE (cm) UNCERTAINITY (cm) 1.8 1 2.13 2.13 0.01 2 2.13 3 2.13 2.0 1 2.66 2.66 0.01 2 2.66 3 2.66 1 3.16 Page 7 of 26

PHYSICS EXTENDED ESSAY hzy444 2.5 3.16 0.01 2 3.16 3 3.16 3.2 1 3.86 3.86 0.01 2 3.86 3 3.86 4.0 1 4.82 4.82 0.01 2 4.82 3 4.82 5.0 1 6.02 6.02 0.01 2 6.02 3 6.02 Table 2. TOTAL DIAMAETER (cm) THICKNESS OF THE PIPE (cm) INTERNAL DIAMATER OF ROCKET (cm) WITH UNCERTAINITY (mm) 2.13 0.16 1.8 18 ± 0.01 2.66 0.33 2.0 20 ± 0.01 3.16 0.33 2.5 26 ± 0.01 3.86 0.33 3.2 32 ± 0.01 4.82 0.41 4.0 40 ± 0.01 6.02 0.51 5.0 50 ± 0.01 The following two tables 1 and 2, shows the data of the body of the rocket with the uncertainty. The data collected in the Table 1, shows the total diameter of the rocket including the thickness of the body. Three trials of each PVC pipe were taken in order to find the uncertainty of each rocket. The uncertainty was calculated using the formula, Uncertainty = MaxValue − MinValue 2 The least count was taken as the uncertainty as the data collected to the total diameter of the pipe was same. Uncertainty helps to quantify the data more precisely. Table 2, was made to Page 8 of 26

PHYSICS EXTENDED ESSAY hzy444 height. A sample calculation will be shown that how height of other rocket is found by the data got in 20mm PVC pipe. SAMPLE CALCULATION 20mm pipe, r=1cm h= 15.7 – 0.7 =15cm π = 3.14 Volume of Cylinder = π r 2 h = 3.14 x (1) 2 x 15 = 47.12 cm 3 To find the height of 18mm pipe , r = 0.9cm h =? π = 3.14 Volume of Cylinder= 47.12cm 3 Volume of Cylinder = π r 2 h 47.12 = 3.14 x (0.9) 2 x h h = 47.12 3.14 x 0.81 Page 10 of 26

PHYSICS EXTENDED ESSAY hzy444 h = 47.12 2.54 h= 18.55cm Table 4. INNER DIAMETER OF PIPE (cm) TRIAL S MASS OF EMPTY ROCKET (gram) MASS OF THE ROCKET (gram) AVERAGE VALUE (gram) UNCERTAINTY 18mm 1 0.070 0.188 0.180 0.01 2 0.070 0.188 3 0.070 0.188 20mm 1 0.062 0.180 0.180 0.01 2 0.062 0.180 3 0.062 0.180 25mm 1 0.058 0.176 0.176 0.01 2 0.058 0.176 3 0.058 0.176 32mm 1 0.053 0.171 0.171 0.01 2 0.053 0.171 3 0.053 0.171 40mm 1 0.045 0.163 0.163 0.01 2 0.045 0.163 3 0.045 0.163 50mm 1 0.042 0.160 0.160 0.01 2 0.042 0.160 3 0.042 0.160 Table 4, is created with the aim to find the mass of the empty rocket as well as mass of rocket with the propellant, which will further help in finding the thrust produced by each type of Page 11 of 26

PHYSICS EXTENDED ESSAY hzy444 Independent Variable – The independent variable during this investigation was the radius of the body of rocket. Dependent Variables – The dependent variables during this investigation are thrust and velocity of the rocket. The motion of the launching of the rocket was recorded by a high- speed camera of 300 FPS. The video was then inserted in the LoggerPro 3 on the computer and then velocity was calculated by the slope of distance-time graph. Table 5. RADIUS OF THE ROCKET (m) TRIAL MAXIMUM HEIGHT (m) AVERAGE VALUE (m) UNCERTAINTY 18 ± 0.01 1 348.38 344.76 18.84 2 361.79 3 324.11 20 ± 0.01 1 422.37 420.56 10.20 2 409.27 3 429.66 25 ± 0.01 1 391.70 389.28 7.45 2 380.23 3 395.92 32 ± 0.01 1 266.77 257.16 9.86 2 247.04 3 257.68 40 ± 0.01 1 47.09 56.60 7.84 2 62.77 3 59.94 50 ± 0.01 1 0 0 0.01 2 0 3 0 Figure 5. Page 13 of 26

PHYSICS EXTENDED ESSAY hzy444 The following table itself says that the 20mm radiused rocket showed the best result by reaching a height of up to 420m. Then the 25mm radiused rocket showed good result by flying up to 390m, followed by is the 18mm rocket – then 32mm rocket and then by the 40mm PVC pipe. I was so surprised to see that the 18mm rocket had so much velocity that the total flight time was only 6.3seconds. The table 5 demonstrates the total maximum height that different rocket achieved with their respective uncertainty of the maximum height. In all the 3 trials of 50mm rocket, the propellant got burned at the launch pad itself. The uncertainty of the maximum height was noticed in the least radiused rocket i.e., 18mm rocket as the height of the rocket was tall that the burning of the propellant was too uncertain as in the 3 rd trial, the initial thrust was too less to lift off the ground. The combustion of any material is so uncertain that no human can predict, which leads to uncertainty in maximum height of any rocket as the external environment do affect the flying of the rocket. The maximum height that is shown in the table is the total displacement of the rocket from the initial point to the final point reached in the air. It was noticed that the combustion of the propellant went on increasing as the radius of the rocket was increasing. The combustion does not take place only from the centre but also from the periphery. As the fuel starts combusting the rate of Page 14 of 26

PHYSICS EXTENDED ESSAY hzy444 PRECAUTIONS – i. Working with fire can be too dangerous so I used 2-3 firecracker fuse to bind the fuse together, in order to run away from the launch pad for full safety. ii. I personally do not recommend to caramelising the propellant when in powdered form in a household kitchen. iii. A full body protective gear was used while making the fuel, by wearing a face shield, heavy cotton full-sleeved t-shirt and heat resistant gloves. iv. The area around the launch pad was cleaned by avoiding the dry grass which might later on lead to spread of fire and the area was also cleared by flammable items. v. A good fire extinguisher and 2 litre bucket full of water was carried when conducting the experiment, in case if the propellant burns too quickly. Table 6. RADIUS OF ROCKET (cm) AVERAGE FLYING TIME (s) 1.8 7.3 2.0 8.2 2.5 7.6 3.2 6.9 4.0 3.2 5.0 0 The following table shows the total flying time of the rocket from the launch pad to the maximum height that the rocket reached. DISTANCE - TIME GRAPH The following table will be used to find the thrust. The velocity in is obtained by the slope of the distance-time graph. The maximum velocity that the rocket attained was seen in the Page 16 of 26

PHYSICS EXTENDED ESSAY hzy444 rocket with the radius 25mm. The camera was kept 100m away on a terrace to track the rocket from the initial point to the maximum point. After the video was recorded it was then put in a software named LoggerPro 3 to analyse the video and the data it obtained from it. The least velocity more than 0 was seen in 40mm radiused rocket i.e., figure 10. The data obtained from the following graph is very important as it will later on help to find the maximum thrust that the rocket has attained in each type of rocket. The 25mm radiused rocket attained the maximum velocity followed by 20mm, 18mm, 32mm, 40mm and 50mm rocket didn’t lift off the rocket so it was not able to achieve any height or velocity with respect to time. The best result among all the 3 trials was put in the software to analyse the best data. Table 7. RADIUS OF ROKCET VELOCITY ( m ⋅ s −1 ) 1.8 53.07 2.0 55.02 2.5 56.08 3.2 41.75 4.0 19.82 5.0 0 The following table shows the data obtained from the LoggerPro 3 in a tabular form. CALCULATING THRUST Thrust is the force that is produced by the propellant filled in the rocket which makes the rocket go up in the air. I got thrust easily by the LoggerPro 3 app by the video analysis mode, but to verify the thrust which was observed from the data and to verify it I manually used the formula check whether the maximum thrust shown is right or not, Thrust = v ( ∆m ) ( Δt ) , Page 17 of 26

PHYSICS EXTENDED ESSAY hzy444 According to Table 8 and the data obtained from LoggerPro 3 matches with a little bit of variation in 18mm and 32mm radiused rocket. Both the data obtained shows that the 25mm radiused rocket has achieved the maximum thrust of up-to 8.53N. The data obtained in the last column was multiplied by 9.8 as the rocket is going against the gravity so the gravity constant has to be multiplied by the final amount in order to get the maximum thrust. The best result after the 25mm rocket is seen by 18mm followed by 20mm, then 40mm and lastly by 32mm radiused rocket. 50mm rocket didn’t had any velocity so finding thrust for the same is not possible theoretically as well as practically. Hence, it is proved that the hypothesis does not match the data got after processing the raw data, as I expected that there might be a linear increase or decrease in thrust or velocity with the change is size of the rocket. Page 19 of 26

PHYSICS EXTENDED ESSAY hzy444 EXPERIMENT 2 In the following experiment, I have used 5 same radiused PVC pipe to make the rocket body. The only difference lies in the height as in this experiment I am increasing the amount of propellant by 18grams. I am using a 20mm PVC pipe to conduct the experiment because as we observed in the experiment 1 that the 20mm rocket showed the best result by attaining the maximum height among all sized rocket. To measure the data of the rocket, same methods which were used in Experiment 1 will be used in the Experiment 2 for e.g., maximum height, thrust and acceleration. The technical data like the volume of each rocket was also measured by the same formula of Volume of Cylinder, the height of the pipe and the weight of the rocket as well as the empty rocket will be in the same way. The diameter of the rocket remains the same as it was in last experiment. 1 Table 9. MASS OF PROPELLANT (gram) TOTAL HEIGHT OF THE BODY (cm) HEIGHT OF THE BODY AFTER 0.7cm SEAL (cm) VOLUME OF THE ROCKET (cm 3 ) 82 11.1 10.4 34.85 100 13.4 12.7 39.88 118 15.7 15.0 47.12 136 18.0 17.3 54.33 154 20.3 19.6 61.54 The table 7, is a very crucial table as it helps to find that what vertical length of the PVC pipe needs to cut in order to get the total height of the rocket. The increasing height of the rocket shows an arithmetic progression as the height of the rocket in each case increases by 2.3cm, as the amount of propellant is being increased. Table 10. HEIGHT TRIA MASS OF MASS OF AVERAGE UNCERTAINITY Page 20 of 26