What would happen if everyone jumped at once?
The current human population on Earth is estimated to be about 7.6 billion people. The global average body mass for a human is 62kg (it sounds small because in America our average is 80.7kg, about 180 pounds). The humans will be jumping, giving themselves potential energy mgh at their max height (about 0.5 meters for this analysis) and then that kinetic energy will be converted to kinetic energy that will be involved in the collision that hits the Earth. If a 62kg person accelerates toward the Earth at 9.8m/s^2 for 0.5 meters, mgh can be used to calculate the KE on impact.
m1 is the mass of all of the humans on Earth. This can be estimated to 7.6B*62= 471,200,000,000kg. If you assume that all of the humans on Earth jump 0.5 meters and use mgh to calculate the KE, then 235,600,000,000J=KE. 235.6GJ is an immense amount of energy, but this energy is facing a mass of 5.972 × 10^24 kg.
If you consider "everyone jumping at once" to be an inelastic collision in which all of the kinetic energy of the humans is transferred to the Earth, we can model the system as
m1*v1=(m1+m2)v2
m1 is 471,200,000,000.
0.5=1/2*9.8*t^2
0.5/4.9=t^2
t=0.1020408163 sec
vf=at, 9.8x0.10204= 0.999m/s
471,200,000,000*0.999=(471,200,000,000+5.972 × 10^24)v2
~(1/5.972 × 10^24)m/s.
For such a collision with numbers that are so unmatched a vf is meaningless, it is difficult to retain any information from this. 1 over the mass of the Earth in kg is an absurdly small number and proves that the Earth would move, but only a very small distance. In physics, we are accustomed to analyzing collisions that involve two masses of relatively comparable size. This results in a meaningful Vf that is logical. Because the mass of all of the people on Earth is only 0.000000000000789% (total human mass divided by earth mass equals 7.890154052x10^-14) it is difficult to retain useful information from this data.
I did find a video on this subject by one of my favorite YouTube channels on this topic that says if everyone jumped at once, the Earth would move, for an instant, about the distance of 1/100th of the width of a single hydrogen atom.
https://youtu.be/jHbyQ_AQP8c
The answer is at about 2min in.
The current human population on Earth is estimated to be about 7.6 billion people. The global average body mass for a human is 62kg (it sounds small because in America our average is 80.7kg, about 180 pounds). The humans will be jumping, giving themselves potential energy mgh at their max height (about 0.5 meters for this analysis) and then that kinetic energy will be converted to kinetic energy that will be involved in the collision that hits the Earth. If a 62kg person accelerates toward the Earth at 9.8m/s^2 for 0.5 meters, mgh can be used to calculate the KE on impact.
m1 is the mass of all of the humans on Earth. This can be estimated to 7.6B*62= 471,200,000,000kg. If you assume that all of the humans on Earth jump 0.5 meters and use mgh to calculate the KE, then 235,600,000,000J=KE. 235.6GJ is an immense amount of energy, but this energy is facing a mass of 5.972 × 10^24 kg.
If you consider "everyone jumping at once" to be an inelastic collision in which all of the kinetic energy of the humans is transferred to the Earth, we can model the system as
m1*v1=(m1+m2)v2
m1 is 471,200,000,000.
0.5=1/2*9.8*t^2
0.5/4.9=t^2
t=0.1020408163 sec
vf=at, 9.8x0.10204= 0.999m/s
471,200,000,000*0.999=(471,200,000,000+5.972 × 10^24)v2
~(1/5.972 × 10^24)m/s.
For such a collision with numbers that are so unmatched a vf is meaningless, it is difficult to retain any information from this. 1 over the mass of the Earth in kg is an absurdly small number and proves that the Earth would move, but only a very small distance. In physics, we are accustomed to analyzing collisions that involve two masses of relatively comparable size. This results in a meaningful Vf that is logical. Because the mass of all of the people on Earth is only 0.000000000000789% (total human mass divided by earth mass equals 7.890154052x10^-14) it is difficult to retain useful information from this data.
I did find a video on this subject by one of my favorite YouTube channels on this topic that says if everyone jumped at once, the Earth would move, for an instant, about the distance of 1/100th of the width of a single hydrogen atom.
https://youtu.be/jHbyQ_AQP8c
The answer is at about 2min in.
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