Math Investigation

Topics: Richter magnitude scale, Earthquake, Logarithm Pages: 10 (3398 words) Published: February 14, 2013


Table of Contents
I. Introduction………………………….….……3 II. Body………………………………….……....4 III. Conclusion………………………….…..…...13 IV. Bibliography………………...………………15

I. Introduction
Logarithms are important arithmetic concept in mathematics, sciences and engineering. To understand many scientific ideas, logarithms needed to be learnt. Logarithms are the opposite of exponentials. In logarithms, the exponentials are inversed. The usual exponentials would be written , however using logarithms, the exponentials will be inversed and written into. Logarithms can be used in many different functions in real life. It can be used in many calculations or scales. Logarithms are especially for big or large numbers. Large timelines, large distances, decibel scales, pH scales, cryptography, measuring brightness of the stars, study of population, chemical reactions, pitch in music and also even study of population. Nevertheless, the most famous or well-known usage of logarithms that is most studied is for the Richter scale.

The Richter scale was developed in 1935 by Charles F. R to compare the sizes of earthquakes. On the Richter scale, when the result measures 5.0, it means that it has shaking amplitude that is ten times greater than the 4.0. The Richter scale is not used to express damage. In the Richter scale, the scale is a base-10 logarithmic scale = log10.

The analysis in the investigation will allow readers to understand the usage of logarithms in real life, focusing on earthquake, proving that logarithms do have important usage in life. The earth is where humans live in, and broadening their knowledge about the basics of how to calculate its movement will be very useful. It will contain results, patterns and information about logarithms through numbers of calculations and also suggestions about handling the earthquake or movement of earth itself.

II. Body
Explosives| Mass| Mass (kg)| Energy (kJ)| Log of Energy| Magnitude| Richter Scale| Large blast at a construction site| 30 pounds| 13.60776| 6.28E+04| 4.79767594| 0.865117293| 0.9| Large quarry or mine blast| 1 ton| 1000| 4.61E+06| 6.663889299| 2.109259532| 2| Small nuclear weapon| 1000 tons| 1000000| 4.61E+09| 9.663889299| 4.109259532| 4| Average tornado (total energy)| 5100 tons| 5100000| 2.35E+10| 10.37145947| 4.580972983| 5| Little Skull Mtn., NV Quake, 1992| 80 000 tons| 80000000| 3.69E+11| 11.56697929| 5.37798619| 5| Double Spring Flat, NV Quake, 1994| 1000000 tons| 1000000000| 4.61E+12| 12.6638893| 6.109259532| 6| Northridge, CA Quake, 1994| 5000000 tons| 5000000000| 2.31E+13| 13.3628593| 6.575239535| 7| Largest Thermonuclear weapon| 32000000 tons| 32000000000| 1.48E+14| 14.16903928| 7.112692851| 7| Landers, CA Quake, 1992| 160000000 tons| 1.6E+11| 7.38E+14| 14.86800928| 7.578672854| 8| San Francisco, CA Quake, 1906| 1000000000 tons| 1E+12| 4.61E+15| 15.6638893| 8.109259532| 8| Anchorage, AK Quake, 1964| 5000000000 tons| 5E+12| 2.31E+16| 16.3628593| 8.575239535| 9| Chilean Quake, 1960| 32000000000 tons| 3.2E+13| 1.48E+17| 17.16903928| 9.112692851| 9| Earth's daily solar energy| 160000000000000 tons| 1.6E+17| 7.38E+20| 20.86800928| 11.57867285| 10| Table 1: Conversion From Energy to Richter Scale.

The table above shows various quantities of explosives are compared with different events and some famous earthquakes. In order to know the magnitude, some calculations needed to be done. First of all, the mass should be converted into kilograms. One pound=0.453592, while 1 ton=1000kg. After converting it into kilograms, it needs to be converted into kilojoules to represent energy (E). In order to do that, it has to be multiplied by 4612 and the result should be in scientific notations. The “E” in the table is a...
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