\begin{problem*}{7.4}
At 11:00AM on September 7, 2001, more than one million British school
children jumped up and down for one minute.  The curriculum focus of
the ``Giant Jump'' was on earthquakes, but it was integrated with many
other topics, such as exercise, geography, cooperation, testing
hypothesis, ans setting world records.  Children built their own
seismographs that registered local effects.
\Part{a} Find the mechanical energy released in the experiment.
Assume that $N_c=1,050,000$ children of an average mass $m=36.0\U{kg}$
jump $N_j=12$ times each, raising their centers of mass by
$h=25.0\U{cm}$ each time and briefly resting between one jump and the
next.  The free gall acceleration in Britain is $g=9.81\U{m/s}^2$.
\Part{b} Most of the energy is converted very rapidly into internal
energy within the bodies of the children and the floors of the school
buildings.  Of the energy that propagates into the ground, most
produces high frequency ``microtremor'' vibrations that are rapidly
damped and cannot travel far.  Assume that $p=0.01\U{\%}$ of the
energy is carried away by a long-range seismic wave.  The magnitude of
an earthquake on the Richter scale is given by
\begin{equation}
 M=\frac{\log E - 4.8}{1.5}
\end{equation}
Where E is the seismic wave energy in joules.
According to this model, what is the magnitude of the demonstration quake?
It did not register above background noise overseas or on the seismograph of the Wolverton Seismic Vault, Hampshire.
\end{problem*} % problem 7.4

\begin{solution}
\Part{a}
From ``briefly resting between each jump'' we are to conclude that
each collision is perfectly inelastic (that all the mechanical energy
the student had during the jump was lost into internal energies).  The
energy lost by one student preforming a single jump is just $U_g=mgh$,
so the energy lost during the entire experiment is
\begin{equation}
 E_T=N_c N_j mgh
  =1.05\E{6} \cdot 12 \cdot 36.0\U{kg} \cdot 9.81\U{m/s}^2 \cdot 0.250\U{m}
  =\ans{1.11\E{9}\U{J}}
\end{equation}

\Part{b}
The energy in long-range seismic waves is given by $E=pE_t/100$ so the
magnitude of the ``quake'' is
\begin{equation}
 M=\frac{\log( 0.01 \cdot 1.11\E{9} ) - 4.8}{1.5}
  =\ans{0.164}
\end{equation}
\end{solution}
