What would happen to the the 5.98e24 kg Earth?

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If 270 million people in the US jumped simultaneously, exerting an average force of 800 N each for 0.10 seconds, the total force exerted would be significant. The calculations show that the change in momentum for the Earth would equal the total momentum generated by the people. The formula p(e) = (270e6) * 800 * 0.1 is used to find the Earth's resulting velocity. The resulting velocity of Earth is extremely small, illustrating that despite the large number of people, the mass of Earth is so great that the impact is negligible. Overall, the exercise demonstrates the principles of momentum conservation in a closed system.
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Homework Statement



If 270 million people in the US jumped in the air at simultaneously, pushing off Earth with an average force of 800 N each for a time of 0.10 seconds, what would happen to the the 5.98e24 kg Earth? Show calculation that justifies your answer.

Homework Equations



F = mv/t
p = mv

The Attempt at a Solution



F = 800 N
t = 0.10 s
m = 5.98e24 kg

800 = (5.98e24 * v) / 0.10

v = 1.3378 e -23

p = 5.98e24 * 1.3378e-23
p = 80 kg*m/s
 
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Thats almost right. You forgot the 270 million bit.
 
chaoseverlasting said:
Thats almost right. You forgot the 270 million bit.

so do i just times 270 mil by 80?
 
Not quite. F=dp/dt, dp=Fdt. Total change in momentum is zero for the system, therefore,
p(e)=p(people).

This gives p(e)=(270e6)*800*0.1. From this you find the velocity of earth.
 
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