Conclusions


The relative displacements of the splashes were as we predicted them to be. We found that the water that was displaced by the entrance of the object into the water was replaced soonest by the sphere. The water was replaced second by the cylinder and last by the cube. Furthermore, the connection between the bubble above the sphere was severed from the impression at the water's surface much sooner than the connection for the cylinder. It was typically severed a few centimeters from the surface The connection for the cube wasn't broken until the cube reached the bottom of the aquarium. Moreover, the cube was the only object that left a distinct depression at the water's surface after the connection broke. It always left a bowl shaped depression, regardless of height or angle. When connections were severed for all objects, the connection was severed slowly and the diameter of the gap would decrease slowly to naught. It is clear that the cube displaced the most water for the longest period of time, the cylinder coming in second, and the sphere coming in a close third.

With regard to height dropped, our predictions were correct as well. The amount of a bubble left above the object was much more drawn out and lasted much longer when the object was dropped from a higher height. The dispacement was therefore greater for the higher heights dropped. This distinction is most prevalent in the cube drops and least prevalent in the cube drops. The depressions left from the cube were more parabolic, though, when the cubes were dropped from higher heights.

With regard to the angle of incidence of the object into the water, there was a slight decrease in the amount of displacement as the angle from horizontal decreased. This is probably due to the presence of the vertical decreased component of the velocity. The trajectory of the object was maintained as the object entered the object, though. The distictive bowl-shaped depression also became less prevalent when the angle from horizontal was decreased.


The relative heights of the splashes for the objects were also as we predicted them to be. The only significant splash height was from dropping the cube. The other objects have small splashes, but they are very small compared to the splashes of the other objects. The bowl-shaped depression of the cube's splash simply continued above the water line and formed the majority of the splash. This part of the splash only rose about two centimeters above the surface. A thinner splash extended above it and rose about eight centimeters above it. (These estimations are done by using the 3 cm side length cube as a basis and they are only rough estimates.) This splash was not bowl-shaped and was higher in some parts than in other parts, but the upper surface remained curved. The splash of the cylinder was very similar to that of the cube, only much smaller. It had the distinctive bowl-shaped extension above the water, but no bowl-shaped depression under the water line. The sphere's splash was much smaller and not nearly as straight at the top of the splash as for the splashes for the other two objects. In fact, it was quite jagged. Thus, the splash was tallest for the cube and shortest for the sphere.

With regard to the height dropped, our predictions were correct. The splash height decreased as the height dropped decreased. It didn't decrease much, but it did decrease a noticeable amount. The largest change was with the cylinder and the smallest change was with the sphere.

With regard to the angle of incidence upon the water, the height of the splash remains about the same. Each part of the splash isn't the same, however. Instead, the splash on the side opposite the entrance of the object into the water is higher than the side closer to the entrance of the object into the water, which is barely existent.

It is therefore easy to see that the cube performs the least efficient entrance into the water since it displaces the most water and its splash is the tallest. The sphere therefore has the most efficient entrance since it displaces the least amount of water and the height of its splash is the shortest. By increasing the height from which the object is dropped, the efficiency is also decreased. Lastly, as the angle of incidence into the water decreased, the efficiency increased since the splash height decreased as did the displacement. These results were expected and the analysis was made even easier by the fact that the height of the splash and the displacement of water increase and decrease at the same times.


There are several main reasons that some of the results that we have obtianed aren't fully accurate. First of all, the objects are subject to being torqued when they are released, and rotation about any axis can lead to discrepancies in data. Although the objects were released from as close to the same point as possible each time, that wasn't neccessarily the case and that led to more discrepancies. The best way to improve upon this is to use a more automated release apparatus that will release the objects from precisely the same location and without torquing the object either. Despite these sources of error, they are minimal and the data that we have taken is still viable data that can be taken as a good base for these kinds of splashes.


Bibliography

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