Answered

If you felt an earthquake with a magnitude of 6.0 on the Richter scale and your friend felt an earthquake in Japan with a magnitude of 5.0, how much more ground shaking would you feel compared to your friend in Japan?



$M=10^R$



Where:

$M$ = ground movement

$R$ = Richter scale magnitude


AWe need more information to answer
B4 times more
CThe shaking would be the same
D2 times more
E10 times more

Verified Answer :

  • Identify the ground movement model: \(M = 10^R\).
  • Calculate the movement for both magnitudes: \(M_1 = 10^{6} = 1,000,000\) and \(M_2 = 10^{5} = 100,000\).
  • Find the ratio between the movements: \(\frac{M_1}{M_2} = \frac{10^6}{10^5} = 10\).
  • Conclude that the ground shaking is \(\boxed{10 \text{ times more}}\).

Explanation

  1. Problem Analysis and Data Overview

The magnitude of an earthquake is measured on the Richter scale, which is a logarithmic scale. The ground movement \(M\) produced by an earthquake can be determined using the formula \(M = 10^R\), where \(R\) is the Richter scale magnitude. We are given two earthquakes with magnitudes of \(R_1 = 6.0\) and \(R_2 = 5.0\). Our goal is to compare the ground movement of these two events by calculating the ratio of their ground movements, \(M_1\) and \(M_2\), respectively.

  1. Calculating Ground Movement and Comparison Ratio

Using the given formula, we calculate the ground movement for each earthquake:
For the first earthquake (magnitude \(6.0\)):
\[M_1 = 10^{6.0} = 1,000,000\]
For the second earthquake (magnitude \(5.0\)):
\[M_2 = 10^{5.0} = 100,000\]
To determine how much more ground shaking is experienced in the first earthquake compared to the second, we compute the ratio:
\[\frac{M_1}{M_2} = \frac{10^6}{10^5}\]
By applying the laws of exponents, which state that \(\frac{a^x}{a^y} = a^{x-y}\), we find:
\[\frac{M_1}{M_2} = 10^{6-5} = 10^1 = 10\]
Therefore, the ground shaking caused by an earthquake of magnitude \(6.0\) is 10 times greater than that of an earthquake of magnitude \(5.0\).

Examples

Understanding logarithmic scales is essential for interpreting scientific data like earthquakes. If a magnitude 7 earthquake occurs, its ground movement would be 10 times greater than a magnitude 6 event and 100 times greater than a magnitude 5 event. This simple calculation helps in assessing the potential impact and necessary disaster preparedness for different seismic activities.

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