Landslide and Tsunami (Ron)

Landslide and Tsunami

Ron Yang (UWCRCN 2016)

Introduction

In the Kingdom of Norway where I started my high school, there is a beautiful mountain called Åknes lying next to three towns near the famous Geiranger Fjord. However, a system of cracks is expanding in the mountain at the rate of 3cm/year. It may result in unstable landmass cracking into the fjord and create a tsunami, which in the worst-case scenario could destroy all three nearest towns in ten minutes.

The incredible power the landslide of Åknes is able to create has drawn the attention of researchers from a number of different disciplines, as well as my interest. In this investigation different methods (dropping plasticine balls and making simulation in Algodoo) are used to investigate the relationship between different properties (height and density) of a falling object and the amplitude of the wave created.

1. Height of ball

The equipment

The investigation started with measuring the height. To analyze the relationship between the height and the amplitude of the wave created, a set of equipment was used to measure these two quantities.

As is shown in Fig.1, a transparent water tank containing a certain amount of water was set as a mini ocean. To measure the height and the amplitude a ruler stuck to one side of a water tank was used with the scale of 0.1 cm.

Fig.1

To prevent the object from having any physical or chemical reaction after the direct contact with water, and to minimize the loss of the total amount of water when taking out the object, a plasticine-made sphere, as shown in Fig.2, was used as the object that will be dropped from a certain height into the water.

Fig.2

When repeating the experiment for one value of height, a retort stand was holding the ball to make sure that every time the ball was falling from the same height. The ball was suddenly dropped by loosening the holder as illustrated in Fig.3.

Fig.3

Theory

The surface of the water was taken as the zero-height horizontal. When raised to a certain height by the a retort stand the gravitational potential energy equivalent to mgh(h stands for the vertical distance between the geometric centre of the ball and the surface of the water) is stored in the ball, which will be transferred into kinetic energy equivalent to ½ mv2 once the holders are loosened and the ball started to fall. Most of the gravitational potential energy is transfered into the kinetic energy at the moment when the ball touches the surface, while some of the energy is transfer into the internal energy due to the air resistance. When cracking into the water and creating little “tsunami”, as shown in Fig.4, the kinetic energy stored in the ball is transfered to the potential energy and heat of the water thus creates waves.

Fig.4

The amount of the potential energy of the water is reflected by the amplitude of the wave created. The motion of the ball and the water was shot by a slow-motion camera, and the amplitude was measured by the ruler attached onto the water tank, perpendicular to the surface of the water.

Measurement

To find the relationship between the height of the ball and the amplitude of the wave, the plasticine ball was raised to 5 different positions in the step of 10 cm along the same vertical axis, and was dropped for 5 times from each position to reduce the uncertainty in the experiment. The results are shown in Fig.3. The scale of the ruler used is 0.1 cm so the uncertainty of the height is ±0.05cm. For the five values of the amplitude the uncertainty is (max-min)/2.

Fig.3

To visualize the data got from the experiment and find the relationship between the height and the amplitude, Logger Pro 3 was used to draw the graph, which is shown in Fig.4.

 Fig.4

The result of the amplitude is not very precise, causing the relatively large error bars, but it does show a proportional relationship between the height of the ball and the amplitude.

2. Density of the ball

Theory

The theory of this part is the similar to the one of the previous part. The potential energy mgh of the ball will be transferred into kinetic energy once starting falling and then the potential energy of the water, causing a little tsunami. With the volume remaining constant, the denser the ball is the greater mass it has, thus the greater the potential energy it contains. Therefore the energy tranfered to the water will be greater, causing a larger amplitude.

Algodoo simulation

In the lab it is rather time-consuming to find materials of different densities and the same shape as the plasticine-made sphere used in the previous part, so in this part of investigation Algodoo was used to make simulations. Algodoo is a simulation program in which the different properties of objects can be varied.

To make a tank three rectangles were perpendicularly connected to each other. Several solid objects were put in the tank at first and then got liquefied, and in such way a certain amount of liquid was created in the tank. The density of the liquid was set to 1 kg/m3 as the one of water. As is shown in Fig.5, a pair of holders was set to make sure that the ball was dropped from the same place all the time.

Fig.5

As is shown in Fig.5, a pair of holders was set to make sure that the ball was dropped from the same place all the time.

Fig.6

The amplitude of the wave in the simulation is not very easy to measure directly. This problem was solved by a tiny floating object in the water shown in Fig.6. The density of the object was set as 0.9 kg/m3, which was slightly smaller than the density of water. Therefore the ball would be floating on the surface without being thrown up to the sky when a little “tsunami” came to it. The Y position of the ball was recorded to get the amplitude of the waves created.

Fig.7

In addition to the table, the five graphs of the Y position of the floating object from 5 sets of data were put together in Fig.8.

Fig.8

The data of the amplitude in each set does not change much with the change of density, and the five graphs generally coincided, which confirms the previous result. This shows that the relation between the density of the ball and the amplitude is rather weak or does not exist at all, which is against my theory above.

To make sure that the result was not caused by too small change in density, another experiment with greater changes was done in Algodoo, and the data table with the coincided graphs were attached below in Fig. 9.

Fig. 9

The second simulation still doesn't show a strong link between density and amplitude. After doing all the experiment again, a phenomenon grabbed my attention: the speed of the ball was barely reduced in the water in for all the values of density expect for 5. This indicates that the values of density used in the experiment were too big compared to the density of water, instead of being too small as I thought after the first simulation.

This suggests a third simulation with smaller variables(density), which means the mass will be smaller since the volume is fixed. According to Newton's Second Law, with a smaller mass the acceleration equivalent to F/m will be greater. In this case the speed of the ball will be significantly reduced so that the kinetic energy of the ball will be better absorbed and then transferred into the potential energy of the water in a relatively greater ratio.

Fig.10

The result of the third simulation was shown in Fig.10. In this simulation the ball stopped completely in the water for every value of density, so that the KE was completely absorbed. In Fig.10 the relationship between density and amplitude was much more clear. Within the domain The amplitude of the wave is proportional to the density of the ball.

KE-Transferring Capacity

After the three simulations above two pieces of information sparked my interest:

1. The amplitude of the wave is proportional to the density of the ball within a domain of density with relatively small values.

2. With density got greater until it was too big compared to density of water, the acceleration was rather small, causing a lower-ratio KE transferring to the PE of the wave.

From the information given above I wonder whether there is a limit for the tank on the amount of KE energy it can absorb from the ball. Assuming there is a limit, I named it as "KE-Transferring Capacity" (KETC), the density of the ball at which the water stopping transferring more PE from the KE of the ball, to make the further investigation a bit easier.

Fig.11

To find the value of KETC, simulations with wider range of the density were made in Algodoo, and the data table is shown in Fig.11. As we can see in the blue frame, when the density went beyond 2.0 kg/m³ the amplitude stopped getting bigger and was going around 0.512 m, indicating that the PE of the water has reached the limit KETC.

Fig.12

The data was put into Logger Pro 3 and the graph shown in Fig.12 was drawn by the software. From Fig.12 it can be clearly observed that when the density is relatively small, the amplitude is proportional to the density; when the density reaches somewhere near 2.0 kg/m³ the ampliutde will not increase any more with the increase of density because the tank has reached its KETC in the blue frame therefore no more PE will be tranferred to the water  from the KE of the sphere.

Conclusion and Evaluation

The aim of this investigation is to investigate the relationship between the height and density of a sphere and the amplitude of the wave created. By experiment in the physics lab and simulations in Algodoo it was found that the amplitude is proportional to the height of the sphere, and it is proportional to the density of the sphere until it reaches KETC. Essentially the amplitude depend on the amount of final PE the water gets from the KE of the sphere.

When doing the labs the water tank used was not very big so that the force between the water and the sides of the tank had a relatively big effects on the waves: the force made it harder for waves to vibrate because it tends to be more “sticky” in a small tank.

The holder used in the labs was not very tight and it was hard to make sure the ball was falling into the water in the same position and in the midpoint of the width of water.

The KETC of the tank is probably caused mostly by the limited depth of the tank. With limited depth there was not enough time for the KE of spheres to be transferred into the PE of the water when the density was getting above 2.0 kg/m³.

However, if the tank were deep enough for sphere to completely stop and the KE was completely transferred, even though the amount of PE the water gets increase, it would have a bigger effect to the lower part of the water than the surface, which may not have a big influence on the amplitude. There seems to be a “trade-off” here. Apparently there is something interesting to be investigate, and further investigations will be made to explore the topic of the KETC and even more in the future.

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