Our procedure for this experiment was not exactly very elegant, and looking back, we now realize that we could have made it more precise.
Firstly, we experimented with several different types of sediment in water. Sand seemed like a promising proposal, but we found that it settled much too quickly. However, we noticed that the sand left the water murky, and that this murkiness eventually disappeared. This meant that there were finer sand particles in the water that settled somewhat slower than the larger sand particles. We extracted some of this fine sand (perhaps better called dirt) by agitating the mixture, letting the sand settle to the bottom, and skimming the dirty water off the top. However, even this dirt settled a bit too quickly. Our solution was to use milk instead of water, as milk is slightly thicker than water is. This provided the ideal solution, as the line between the milk and the sediment would be clearly visible. We placed the dirt and the milk in a clear container and sealed it.
To vary the change in potential energy of the container, and consequently the agitation of the dirt particles, we decided to tie the container to a string and vary the height from which we dropped the arrangement. We decided to let the container swing from a measured angle into a wall, where it would stop abruptly and forcefully, most of the potential energy due to the height changing into agitation of the particles via the kinetic energy of the container as it swung downward. Our setup is diagrammed below.
Lacking a protractor to measure the angle at which we extended the
container, we resorted to less precise methods. (We realized later
that we could have bypassed the measuring of the angle in the first
place, but in our rush we did not see this.) We measured the length
of the string to be 0.66 m. For each trial, we extended the container
to an arbitrary angle, then mirrored this angle with a compass (which
we did have access to). Knowing the length of the arm of the compass,
and for a given angle being able to measure the separation of the
two tips of the arms of the compass, we could calculate the angle.
This angle is given by
where r is the separation of the tips and l is the length
of the arms. Given the angle and the length of the string, simple
trigonometry could be used to calculate the change in height of the
container. As the change in height is directly proportional to its
change in potential energy, this information is sufficient to test
our hypothesis of linearity. The rationale for these calculations
is given below.
The most difficult portion of the experiment was to determine, constistenly, when the dirt could be said to be settled. In reality, this determination was highly subjective. However, the rough guidelines we went by was that the dirt was completely settled when the milk had cleared to certain amount of whiteness, and there were not visible dirt particles still falling in the milk. With these questionable criteria, we collected the following data.