Question

At 11:00 a.m. on September 7, 2001, more than one million British schoolchildren jumped up and down for one minute to simulate an earthquake.

(a) Find the energy stored in the children’s bodies that was converted into internal energy in the ground and their bodies and propagated into the ground by seismic waves during the experiment. Assume 1050000 children of average mass 36 kg jumped times each, raising their centers of mass 25 kg

by each time and briefly resting between one jump and the next.

(b) Of the energy that propagated into the ground, most pro-duced high-frequency “microtremor” vibrations that were rapidly damped and did not travel far. Assume 0.01 of the total energy was carried away by long range seismic waves. The magnitude of an earthquake on the Richter scale is given by

$M=\frac{logE-4.8}{1.5}$

Where is the seismic wave energy in joules. According to this model, what was the magnitude of the demonstration quake

Short answer

(a) The stored energy in the children’s bodies that convert edinto internal energy in the ground and their bodies and propagated into the ground by seismic waves was $1111320000\text{J}$

(b) The magnitude of the demonstration earthquake in Richter scale was 0.164

Step-by-step solution

Given data:

Average mass of each child m= 36 kg

Height to which the center of mass of each children got raised is,

$$\begin{gathered} h=25\text{cm} \\ =25·\left(1\text{cm}\times \frac{1\text{m}}{100\text{cm}}\right) \\ =0.25\text{m} \end{gathered}$$

Total number of children N= 105000

Number of times each child jumped n=12

Percentage of total energy transferred carried away by seismic waves is 0.001%

The magnitude of an earthquake on the Richter scale is,

$M=\frac{\log E-4.8}{1.5}$

Potential energy:

The potential energy of a mass at a height from the ground is,

P=mgh

Here, g is the acceleration due to the gravity of value 9.8

Step 3:(a) Determining the transferred energy:

From each jump, the energy transferred is the potential energy gathered at the maximum height. From equation (II), the value of this energy per child is

Therefore, the total energy transferred is

$$\begin{gathered} E=Nn{E}_1 \\ =1050000\times 12\times 88.2\text{J} \\ =1111320000\text{J} \end{gathered}$$

Thus, the total energy transferred is 1111320000J

Determining the magnitude of the demonstration wave:

The amount of energy carried away as seismic waves is

$$\begin{gathered} E\text{'}=\frac{0.01}{100}\times 1111320000\text{J} \\ =111132\text{J} \end{gathered}$$

From equation (I), the magnitude of the earthquake is

$$\begin{gathered} M=\frac{\log E\text{'}-4.8}{1.5} \\ =\frac{\log \left(111132\text{J}\right)-4.8}{1.5} \\ =0.164 \end{gathered}$$

Hence, the required magnitude of the earthquake is 0.164