Your supervisor, Dr. A. Nick, has been contacted by a commercial entity that is interested in constructing a new and exclusive leisure resort in the French Alps. The developer has identified a number of potential sites for their resort but is concerned about the potential for avalanches in the region.
In order to determine the most suitable location for the planned resort the developer has requested that your supervisor’s team conduct modeling to enable the company to better predict the run-out distance for avalanches in each of the sites they are investigating. Dr. A. Nick has suggested you should investigate this problem using a model experiment.
A schematic of the apparatus available to conduct the model experiment is shown in figure . In summary, the apparatus consists of a ramp in which a straight chute is connected seamlessly to a horizontal sheet by a smooth curve. At the start of a test, a quantity of granular material is held behind a trapdoor at the top of the chute.
To initiate a test the trapdoor rotates about a hinge thereby releasing the granular material to travel down the ramp. The distance that the granular material travels beyond the bottom of the ramp is known as the run-out distance x, as shown in figure . The horizontal sheet at the base of the ramp is marked with a graduated scale to facilitate the measurement of x.
The apparatus is designed in such a way that its geometry can be extensively varied. In particular, it is possible to vary the length of the chute L (0.1 ≤ L ≤ 2 m), the width of the chute W (0.05 ≤ W ≤ 0.5 m), and the angle θ (10 ≤ θ ≤ 60) at which the chute is inclined. The trapdoor is of a fixed width Wtrap = 0.05 m and freely rotates about the hinge when a latch fixing the trapdoor in position is removed. The radius R of the curved section of the ramp cannot be varied.
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