Method
Procedure
- Attach the meter-stick to the table clamp with tape so that the height from which the “meteor”, in this case a golf ball, is dropped.
- Fill the plastic food containers with .500 kilograms of sand.
- Fill each one with a different amount of water (0 mL, 350 mL, and 700 mL) to represent different surfaces of planets and allow this to sit over two days.
- Measure the weight of the golf ball and record the weight.
- With the simply sand container, place it underneath the table clamp where the golf ball will be dropped. Level off the sand with the Popsicle stick.
- Take the clamp on the table clamp to 50 cm and prepare to hold the golf ball in the clamp. Tighten the clamp to hold the golf ball in place.
- Release the golf ball onto the sand box.
- Take the golf ball out of the sand and measure the diameter of the crater created with the metal calipers. Make sure to only measure the edges of the sand depression and record this number.
- Repeat this same procedure with the different heights (50 cm, 60 cm, 70 cm, 80 cm, 90 cm).
- Repeat this procedure with the other sand boxes to record their data as well.
Diagram
Controlling the Controls:
The way that the controls will be managed is by using the same ball, leveling the sand off in the same manner, and releasing the ball from the same heights from the clamps. Additionally, the leveling off process must be delicately dealt with because of the risk of error.
The experiment was repeated three times at the five different heights for each sandbox. Furthermore, the ball was dropped “at rest” from the heights. Additionally the measurements were taken with the metal caliper as the diameter of the crater with the impressions made on the sand, which had been set to dry for 24 hours.
Results:
Raw Data Table
Below are the tables with data from each of the five different heights from the three different sandboxes.
The Uncertainty of the Diameter of the Crater is estimated to be of the smallest unit of measurement on the metal caliper (1 mm).
Also the uncertainty of the weight of the ball (the “meteor”) is estimated to be of the smallest unit of measurement on the scale (.01 grams)
The original sandbox (sandbox with no water) was very dry and caught the meteor, absorbing it into the sand.
The 350 mL sandbox caught the meteor and allowed it to rest on the surface.
The 700 mL sandbox enveloped the meteor halfway into the surface.
Sandbox With No Water
Sandbox with 350 mL of Water
Sandbox with 700 mL of Water
Measurements were taken from the edges of the depressed landing pad.
Occasionally, an obviously wrong diameter was obtained, but these were ignored.
Analysis
Now under analysis, one must consider the two equations derived:
and .
All things considered, the equations need to be put out of the exponential to a logarithmic form to yield a straight line.
Therefore the graph will be vs. , yielding 3 graphs and calculations.
Before the graph, the averages of the trials at each height must be taken to yield a singular number to graph. Using this number, the averages will be put in the new natural log equations.
The table below shows the averages of the trials at the heights for each sandbox.
Sandbox With No Water
Sandbox With 350 mL of Water
Sandbox With 700 mL of Water
Now a data table of the calculations (natural log of the diameter of the craters) and (natural log of the energy from the crater) is shown below with its graph as well. will be the y-axis, while will act as the x-axis.
H will be taken in centimeters, D will be taken in centimeters, g will be taken using , and m will be taken using grams.
Sandbox With No Water
The equation of the linearization is
This graph keeps in mind the error and uncertainty.
Sandbox With 350 mL of Water
The equation of the linearization is
This graph keeps in mind the error and uncertainty.
Sandbox With 700 mL of Water
The equation of the linearization is
This graph keeps in mind the error and uncertainty.
Conclusion
The slopes of the lines found show the gradient at which energy affects the diameter of the crater created. Therefore the uncertainty of the slope must be found using the equation .
For the Original sandbox
For the 350 mL sandbox
For the 700 mL sandbox
So therefore, the slopes with uncertainties are as follows:
For the Original sandbox
For the 350 mL sandbox
For the 700 mL sandbox
Therefore the values calculated for the slopes with uncertainties show how energy can affect the size of craters. As hypothesized, the slopes for the original and 350 mL sandboxes were positive, however the 700 mL sandbox had a negative slope.
This can be explained since the dry and 350 mL sandboxes acted more like the Earth’s surface than the 700 mL sandbox. The two with positive slopes were on a dry and damp surface much like the surface that yields itself to many of the famous craters, such as those in Flagstaff, Arizona. The sandboxes acted as deserts and regular terrain where craters occur. The 700 mL sandbox showed the terrain of a beach because it displayed a soft and very moist terrain. This allowed the sandbox to catch the meteor, decreasing the crater size as it had more height from which to catch from.
Finally, the experiment validates the hypothesis that energy would increase crater size since it shows true through 2 of the 3 examples, with the third acting as a different terrain.
Improvements
By no means was this experiment full proof and void of mistakes. First, the experiment should be narrowed to one terrain in one sandbox. The multiple sandboxes made the numbers more difficult to deal with and made the densities of the sandboxes different. There should be one density to yield results that could be compared across the board.
Additionally, there should have been more trials taken. Three trials was serviceable and showed a trend that was matched with an average, but the more trials the more accuracy. The results could have been affected had a sixth or tenth trial had taken place, but since there were so many sandboxes this would not be possible. This highlights the need for the simplification in terrain and therefore the limiting of terrains created by the sandboxes.
Finally the last improvement would occur with the measuring of the craters. The metal calipers would yield numbers that were useable, but it would be more accurate to have a different way to measure it. Molds that solidify the diameter of the crater would be useful in yielding accurate results. Still, this metal caliper error could be nullified by more trials on a singular sandbox.
Overall the experiment was quite the success since it validated the hypothesis posed and shed light on the formation of craters, which is a long misunderstood aspect of physical geography.