At 11:00 AM on September 7, 2001, more than one million British school children

Question

At 11:00 AM on September 7, 2001, more than one million British school children 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 that 1 200 000 children of average mass 35.0 kg jump 15 times each, raising their centers of mass by 27.0 cm each time and briefly resting between one jump and the next. ___ J b) Of the energy that propagated into the ground, most produced 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 = (log E ? 4.8) / (1.5) where E is the seismic wave energy in joules. According to this model, what is the magnitude of the demonstration quake? _____on the Richter scale

Explanation / Answer

A] m = 41.5 h = 28.5 cm = 0.285 m g = 9.81 m/s^2 # of children = 1,050,000 # Jumps = 12 Energy of one child J = m*g*h J = 41.5*9.81*0.285 J = 116.03 J Energy for all children participating. J = 116.03*1,050,000 J = 1.22 *10^8 J Each child jumps 12 times J = 1.22*10^8*12 J = 1.46*10^9 J B] Only 1% of the energy is used. So ... 1% 1.46*10^9 = 1.46*10^7 M = (log(E) - 4.8)/1.5 M = (log(1.46*10^7) - 4.8)/1.5 M = (7.16 - 4.8)/1.5 M = 1.57 which is not much.

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