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Extra Credit Blog!!!

There are 7.6 billion people in the world. If everyoen gathered together at one place at one time and all jumped together, what woul happen to the Earth? 


Simply put, even if everyone on the planet jumped at the exact same time the eath would be virtually uneffected. This is becasue teh mass of the earth is approximately 5.972 * 10^624 kg and if you were to calculate the mass of all humans put together it would not come near that number. 

Conservation of momentum:
p1i + p2i = p1f + p2f
m1v1+m2v2=m1v1f+m2v2f

Numbers:
  • Human population as of December 2017= 7.6 billion
  • Mass of the Earth= 5.972 * 1-^24 kg
  • Average human mass=136 lb/62kg
  • Average vertical jump=0.5 m


In the equations, 1 represents the Earth and 2 represents the people.  In this situation the equation is elastic becuase the Eaerth is in the system and momentum is always conserved.

1/2m1v1^2+1/2m2v2^2=mgh  --> h initial = 0
1/2m1v1^2+1/2m2v2^2=0
1/2m1v1^2=-1/2m2v2^2
m1v1=-m2v2
v1=-m2v2/m1

Then I used this to calculate teh velocity of teh people, when h did not = 0. 

1/2m1v1^2+1/2m2v2^2=m2gh
m1v1^2+m2v2^2=2m2gh
m2v2^2=2m2gh-m1v1^2
v2^2=(2m2gh-m1v1^2)/m2
v2^2=2gh-m1v1^2/m2
v2=sq. rt 2gh-m1v1^2/m2

Then, I solved for the velocity of the earth using theses equations together:

v1^2=(2ghm2^2/m1^2)-(m2v1^2/m1)

Next, I solved for v1 to get the velocity of the Earth.

v1^2+(m2v1^2/m1)=(2ghm2^2/m1^2)
v1^2(1+m2/m1)=(2ghm2^2/m1^2)
v1^2=2ghm2^2/m1^2(1+m2/m1)
v1^2 = 2ghm2^2/ (m1^2+m2m1)
v1 = sq. rt. 2ghm2^2/ (m1^2+m2m1)

Finally, I then plugged in the values. First I found the mass of the total population of the people which was (7.6*10^9)*62=4.712*10^11kg.

v2 = sq. rt. 2*9.8* (4.712 x 10^11)^2 / (5.972 x 10^24)^2 + (5.972 x 10^24)*(4.712 x 10^11)
v2 = (2.17589 x 10^24)/ (3.56648 x 10^49)
v2 = 6.10095 x 10^-26 m/s

This means that the velocity of the jump would only be effected by 6.10095 * 10^-26 m/s. The total mass of the population is insignificant compared to the mass of the Earth. This makes it difficult for the jump to effect the Earth's momentum. Realistically people can only jump up to half a meter high. The increase of mass to the center of the Earth would increase the rate of rotation. Huge earthquakes only increase the earths rotation by 100,000ths of a second. However, the current population of the earth would have to increase by seven million times what it is now to eave make that much of a difference. The collective mass of the population is just too insignificant compared to the Earths so it will not have an effect. The T.F Green Airport in Warwick could handle thousands of passangers a day at a rate of 500% capacity for years without even making a dent in the crowd. 

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