Forces (People and Earth) Problem

[IntellectIsStrength]

There are about 6.3 billion people on the planet. Suppose that the world's population gather at one spot on the planet. Assuming each person takes up 1 m^2 of space on avg, the spot is 6.3 billion m^2. Assume that each person's mass is 70 kg on average. Suppose all those people jump at the same time. THe people, while pushing, are in contact with the Earth for a time of 0.2 s and leave the ground with a speed of 5 m/s. The distance traveled by the people while pushing the Earth is 0.5 m. Mass of the Earth is 5.98x19^24 kg.

Find the force with which the people push the earth.

 

[whozum]

Thats a pretty cool problem. Find the force of one person, then multiply it by 6.3 billion people. I'm assuming your going to simplify the Earth as flat.

 

[Doc Al]

Hint: What impulse does the Earth give to the people?

 

[PRodQuanta]

Doc Al is correct. You have to use the impulse-momentum theorem =

$$F \Delta t = \Delta p$$ where: $$\Delta p = mv_f - mv_i$$

So first, find your $$\Delta$$momentum, then solve for $$F$$, and there you have it, your Force vector.

Paden Roder

 

[IntellectIsStrength]

Thank for the replies.
I'm 100% sure this question is possible without momentum and impulse since we haven't studied those yet. My teacher did this question today in class and I understood it quite clearly but now I can't seem to figure out.
I know first I have to figure out the weight of the people which would be equal to the Force pulling the Earth up. I'm not sure where to go from here.

 

[whozum]

Why is F = mv/t giving me an insanely wrong answer?

 

[Doc Al]

I'm 100% sure this question is possible without momentum and impulse since we haven't studied those yet.

You can always caculate the average acceleration of the people, then apply Newton's 2nd law.

 

[IntellectIsStrength]

You can always caculate the average acceleration of the people, then apply Newton's 2nd law.

Thanks a lot, I got it

 

[Severian596]

Sorry for the slightly OT post (rather, a non-helpful reply), but that really IS a cool problem. I'm trying to picture a crowd of 6.3 billion people in "one place"...it would literally be an ocean as far as the eye can see.