Hypothesis:
Based on the above relationship, I believe that the more massive the object, or the higher it is dropped from, the larger the resulting crater will be.
Methods:
Materials:
- 4 balls of differing mass
- A Tupperware container (measuring .11 x .20 x .33 m.)
- Sand
- A meter stick
- A scale
Procedure:
- Pour sand into a container to a depth of .035 m.
- Put the meter stick on the inside wall of the Tupperware container such that it is oriented vertically with the 1 m mark on the top. Tape it to the sides in order to maintain stability and consistency.
- Carefully mass each ball. Use a piece of tape to keep each ball stable while they are on the scale. After each ball has been massed, mass the piece of tape and then subtract this from the mass of each object to obtain their real mass.
- At the 10 cm mark on the meter stick, drop one of the balls. Carefully lift it out of the resulting crater, making sure that the width and depth of the crater is not affected.
- Repeat once again at the 10 cm mark, to help balance out any potential outliers.
- Repeat steps 4 and 5 at the 15 cm and 20 cm marks on the meter stick.
- Repeat steps 4 through 6 for the other 3 balls. Record all data in a table.
Variables:
The independent variables are the mass of the object dropped and the height from which it was dropped. The height from which the object is dropped is controlled by the fact that each object is only dropped at a specific height. This height level is consistent for each trial.
The dependent variables are the crater depth and diameter. Because crater volume is determined from these, it can also be classified as a dependent variable.
Data:
*The height of drop is not 10, 15 or 20 cm as described in the procedure because the depth of the sand in the container was taken into consideration.
**The volume was generated from the formula . The units are cm for purposes of readability.
Columns 6 and 7 are processed data, generated from the raw measurements of crater depth and width.
Graphs:
The graphs which compared volume crater depth to the height of the drop were generated using data from each individual object, in order to ensure that mass was kept constant. The graphs which compared volume crater depth to the mass of the object used trials which occurred at a given height, regardless of which mass they were associated with.
Volume crater depth graphed with respect to the height of the drop:
Volume crater depth graphed with respect to the mass of the object dropped:
Analysis:
From these graphs linear relationships can be observed in mass of the object vs. volume crater depth and the height from which the object is dropped vs. volume crater depth. The positive linear relationship that can be seen in each graph supports the relationship . When is changed but m is held constant changes proportionally, and when m is changed but is held constant also changes proportionally. This confirms this relationship, to be true. The error was .1 cm when dropping each object from the specified height, leading to corresponding errors in the graphs of mass vs. volume crater depth and the height of the drop vs. volume crater depth. This corresponded to 1.54% for the drops from .065 m, .870% for the drops from .115 m, and .606 % for the drops from .165 m. These errors were less than 5%, and thus had no consequential impact on the observation of these relationships.
Conclusion:
The formation of craters can be described as a transfer of kinetic energy into potential energy. It is this transfer that determines how mass and the height from which the object is dropped affect the width and depth of the crater formed. Described by the equation it provides critical insight into crater formation. According to this equation, as m or change, changes proportionally. This occurs because g (gravity) and d (density) are constants. If m is kept constant while is changed then changes proportionally. Similarly, if is kept constant while m is changed then changes proportionally. My experimental values confirm this. Linear relationships were present in every single graph of height vs. volume crater depth and mass vs. volume crater depth, with errors of less than 2% in each case. My hypothesis was proven correct, as the larger the mass or the higher the object was dropped from, the larger the crater created.
The weaknesses of the experiment were present in the inaccuracy of dropping the object at a consistent level and the methods used to determine the depth of the crater. Using my hand to drop each object was not consistent enough, inducing inconsistency in how high the object was dropped, creating an error of .1 cm. The experiment was also weaker because in order to measure crater depth the object had to be carefully removed first. This inherently weakened the crater, sometimes causing the depth to be slightly changed from what it had initially been. The experiment was limited by the fact that only two trials were conducted for each height for a respective mass. Three trials would have been better, as a more accurate average could be defined than if only two trials were conducted. This would also help to eliminate outliers better, because there would be two other data points to average with, versus only one.
If the experiment was repeated, then each of these weaknesses or limitations could be addressed. The inconsistency associated with using my hand could be eliminated by using a clamping system to drop each ball. This would eliminate much of the induced error, as the clamp could be set at a given height without any unsteadiness or inaccuracy. The problems associated with measuring crater depth could be resolved if a set of steel balls of differing mass were used. A magnet could then be used to extract each ball, rather than lifting each one out with my fingers. This would allow for easier and gentler extraction, again helping to eliminate inconsistency. Also, more trials could be conducted, helping the experiment to achieve a more accurate representation of the data. If these changes were implemented then the experiment would become more accurate.