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We will measure the ranges,maximum altitudes and air time in order to have a better understanding of the projectile motion-As the practical situation which includes the air resistance and different kinds of errors caused by students’ carelessness s different from the theory,it is unavoidable that the results are quite different from the theoretic statistics.
The horizontal velocity is related to the range, while the vertical velocity is related to the maximum altitude. This experiment can help us reinforce the concepts related to the motion in two dimensions although the water rocket does not have the ideal situation.
A lot of equations we learned in class can help our group calculate the range and maximum altitude. Introduction Purpose: The purpose of the experiment was to reinforce the concepts related to motion n two dimensions using water rocket launches and the calculations necessary to determine launch speed and range.
Background: (1) Because the water rockets are essentially pressurized chambers, they have the same launch speed, regardless of launch angle. (2) Ignoring air drag, a projectile will take the same time for its horizontal motion and its vertical motion. 2) Neglecting air drag, the horizontal velocity of a projectile will remain constant. (3) The vertical motion will have constant acceleration, g. Equations: R = box [ vertical motion] sys = vote + h g to horizontal motion] A hypothesis: The water rocket which is launched at different angles will fly into different heights in the sky and each time it will have different ranges when it drops.
Method Materials The materials which are prepared to be used for this experiment are a timer, a water rocket, a meter ruler, a launch pad.
Procedure Firstly,we need to set the rocket on the ground so that the barrel is exactly vertical. Then we can fire it vertically two or three times, using stopwatches to clock total air time,determining average air time for the vertical launch. Secondly,we are supposed to use the vertical motion equation to find the launch velocity, FL_, which, in this case only, is equal to boy. Thirdly,we need to calculate the horizontal and vertical components of the launch velocity for each of the 300, 45, and 600 launches, and make a component vector diagram for each of the launch angles like the following diagram.
FL = 30 m/s Ivy = sin 200 m/s 200 Example: Vs.. = coos 200 m/s As result,we can calculate the range, R, for launch at each angle. Elf you are willing to set a flag on the field at that distance from the rocket,you can do t. Finally,remember to measure the launch angle and secure the rocket barrel to fire at each of the angles just once, setting a flag where the rocket lands each time and measuring only the difference in range between the two flags to use in calculating percent error. Also remember to measure and record the “air time” for each launch.
Results Important results in verbal form All of the useful lunch angles are 30 degree, 60 degree and 45 degree. The percentage errors of the data of angle Isis the Therefore, our group will mainly use the data of this angle. Calculated Range at 45 degree s 32. Mm. Vertical Displacement at 45 degree is calculated to be 15. 5 m. The measured time at 45 degree is 2. As. Discussion Discuss sources of error and calculate percentage errors on the three ranges, using the calculated range as the accepted value. Sources of errors: 1.
The people who look at the protractor may be distracted by the objective factors, so the measured time is not accurate. 2. When students measure the range, it is difficult to have the right range as we can’t measure in a straight line. 3. The water rocket may not be able to fall at the exact point on the land. It may leap because of the force. As a result, the range cannot be determined accurately. 4. The air resistance may hamper the flying of the water rocket. 5. Sometimes the water rocket may fly to the reverse direction. 6. Students may make a mistake when they write down the data .
They may put the data in a wrong place. Launch angle(degrees) Percentage errors 30 27% 45 0. 3% 60 48. 9% Plot “Calculated Range vs.. Launch Angle” for all four launch angles. Examine: The range of the water rocket is the largest when the launch angle is 50 Meaning: When the launch angle is smaller than 450, the bigger the launch angle, the larger the range will be. If the launch angle is bigger than 450, the larger the launch angle, the smaller the range will be. Plot “Vertical Displacement vs.. Time” for one of the launch angles (except 900).
Meaning: The vertical displacement is related to the time. As the time goes by, the water rocket will get higher when the initial velocity is invariable. Plot “Horizontal Displacement vs.. Time: for one of the launch angles (except 900) Meaning: The horizontal displacement is related to the time. As the time goes by, the water rocket will go farther when the initial velocity is invariable. The water rocket has the largest horizontal displacement when the launch angle is 450. What effect do you think air drag had on your results? The air drag may shorten the range of the water rocket.
The air drag will reduce the magnitude of velocity The air drag can change the direction of the water rocket and make it fall down immediately The ways that the experiment might be improved or varied. 1 . Students can use more advanced equipment to measure the air time and he range instead of using the protractor and the meter-ruler. 2. In the four experiments, we can control the pressure and the quantity of the water to remain the same. 3. Students can make a stream-line water rocket to reduce the air drag and make the stream easy to go through. 4. Students can use lighter materials to make the water rocket. 5.
According to the physical theory, the water rocket can reach its largest range when it is launched at the 45 degree. However, during the experiment, we had better launch it at the angle between 45 and 55 o reach its largest range. 6. The top of the water rocket should be pointed so the air drag can be reduced. 7. In order to increase the stability of the water rocket, students can use the tripod as the launching pad. 8. To Increase the speed of the water rocket is to increase the amount of water per unit of time. Therefore, the pressure of the water inside the water rocket and the quantity of the water are appropriate for the largest range.
Explanation of the results. These results show that our water rocket goes through a projectile motion, specially the one launched at 45 degree, because the percentage is only 0. 3%. Conclusion The air resistance and objective factors influence the examination of the theory of projectile motion. If these factors were eliminated, even though it is not possible, the results of the experiments can be more accurate and convincing. The experiments really make us understand that the range of the projectile in the motion in two dimensions is determined by the initial velocity and the air time.
The horizontal velocity is related to the range, while the vertical velocity is related o the maximum altitude. This experiment can help us reinforce the concepts related to the motion in two dimensions although the water rocket does not have the ideal situation. The biggest success is that when the water rocket is launched at the 45 angle, the range is the biggest, which concurs with the theory. References http://item. Taboo. Com/item. Tm? Sum=al z. 2. 9. 194. Sheds&id Douglas C. Conical: Chapter 2-3 PEP- pep Physics—-principles with Applications for AP Group members: Fife, Ivy. Appendix A Table A The data of the experiment.