Next I decided to determine the angle at which to set the tube. I can work out the angle of the tube using trigonometry. To work out the angle I would first find the length of the side of the triangle opposite to the angle. To do this I would take away the height of the front of the tube (TF) from the height of the back of the tube (TB). Using this figure, and the length of the tube, I can then use the equation;
sinX = o/h.
X = sin-¹o X h
To determine the angle I first set the tube at the pre-determined height of 32cm and took the same results as before but positioning the tube at angles of 20, 25, 30 and 35º. My results are shown in the table below
Preliminary Angle Table
By analysing these results I decided to position the launch tube at an angle of 20º as results at this angle had the largest range and were most consistent and would therefore be easiest and best to analyse.
After setting the tube at this height and angle I will release the ball from the tube 45 times, and recording the results as described above. I will be releasing the ball five times from 9 regular 10cm intervals, between 10 and 90 cm from the end of the tube. I will then average the five results I took at each interval and take note of the results. I can attempt to predict what I think will happen by using scientific theory:
Kinetic energy = Potential energy
Kinetic energy = ½mass X velocity²
Potential energy = mass X gravity X height
½mv² = mgh
½v² = gh
This proves that mass is irrelevant as it can be removed to leave a balanced equation.
I can rearrange this equation to find the speed that the ball bearing will be travelling when it leaves the tube. I will be disregarding other interfering forces such as friction and wind resistance.
v² = 2gh
v = √2gh
This means that if I know the height of the ball bearing before it begins to move I can work out the velocity. I can use this information to determine the approximate velocity of the ball bearing as it leaves the tube. I predict that the distance the ball bearing travels will increase steady rate as the length of the tube increaces.
Results
I measured the distance that a ball bearing travelled from a launch tube of different lengths. I took each measurement in millimetres from the point directly below the tube bottom (TB), to the front of the indentation made by the ball in the sand. I took each reading five times and then found the average of these five results in order to find more accurate final result.
My results are recorded in the table below.
Results Table
The first result I took at 70cm appears to be my only anomalous result with the others all rising as the tube became longer.
Analysis
This is what my results showed:
Results Table
See graph on next page.
The graph is a smooth curve, indicating that the increase in the distance the ball travels from the tube gets smaller as the length of the tube increases. This is due to the ball getting closer to its terminal velocity. When the wind resistance of an object equals its acceleration it can no longer accelerate and has reached its terminal velocity. My prediction was wrong as I predicted that the distance that the ball bearing travelled would increase at a steady rate as the length of the tube increased. Instead, the rate that the distance that the ball travelled increased at a smaller rate as the length of the tube increased.
Evaluation
I believe my results were accurate as I measured my results in millimetres rather than centimetres. However, I would have liked to have measured them in smaller units if possible. When measuring results, I measured them from the point directly below the bottom of the tube (TB). I found this point only once, at the start of the experiment, rather than before each measurement. Although I believe that the tube remained in the same place throughout the experiment I can not be sure of this. In order to increase reliability I should have found the point directly below TB each time I measured a reading. My results were almost all reliable. I found one anomalous result. It was the first result taken at 70cm which was approximately 20mm shorter than could have been expected. In further work I could investigate the effects of the angle of the tube would be. I could also experiment with mass to back up the theory, which explains that it is irrelevant.
