[neilep (OP)]

I once heard that if everybody in China, or everybody in the world jumped up and down at the same time that the consequence would be catastrophic. It all sounds like a load of bull to me, but is there any scientific evidence to suggest that there would be a noticeable effect on the planet or is it as i said just poppycock ?...I mean only a third of the world is covered by land and a huge amount of that is baron is it not ?

Ta

'Men are the same as women...just inside out !'

[qpan]

Well, doing a quick calculation;
1.4 billion peeps in China
Average mass = 60kg
Jump height = 0.5m
kinetic energy when landing from jump
          = m x g x h = 60 x 9.81 x 0.5
          = 294.3 J per person
= 4.1202 x 10^11 J for everyone in China added together

mass of Earth = 5.9742 × 10^24 kilograms

=> KE gained by earth = 2.47 x 10^11 J = 1/2 x M x V^2
Velocity gained = sqrt( 2.47 x 10^11 x 2 / (5.9742 × 10^24) )
                = 3.714 x 10^-7 m/s

Which unfortuneately isn't a lot! This means that not much would happen even if evenone managed to land at exactly the same time!

I have also heard of this before, but unfortuneately its not true!




"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe

[neilep (OP)]

Phew !!...thanks QI....I've been jumping on the spot the last few hours and I can confirm that apart from a butterfly induced tummy there was no ill effect to the surrounding environment....thanks for doing the maths...cheers.

'Men are the same as women...just inside out !'

[DrN]

but what about force = mass x acceleration?
so force = 60 x 9.81 N = 588.6 N
multiplied by 1.4 billion = 824 billion newtons. if thats right, then that sounds like a lot to me! but would it have any effect on the trajectory of the earths orbit? wouldn't it have the same effect as a meteor hit? long time since i did physics.

[qpan]

Yep- thats right, its a big force, but the earth is massive. 824 billion newtons would cause an instantaneous acceleration of (824 x 10^9)/(5.9742 × 10^24) = 1.379x10^-13 m/s^2. Which is not zero but pretty close! Your equation doesn't actually apply for people jumping and landing - the equation is actually the force exerted by all the people in China standing still on the Earth. When you take jumping into account, you need to account for how high everyone jumps (work against gravity) and to do that you need to take into account energy!

"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe

[neilep (OP)]

Phew !!..well that's a relief...I was about to gather all my friends (well..people who I know !) and start jumping again....you clever people are just soooo great.[]

'Men are the same as women...just inside out !'

[Quantumcat]

Wow, I should get a copy of this and give it to my physics teahcer, she loves to make us do problems like this, lol!
Yesterday we timed outselves running up stairs and calculated the power exerted. It was fun.

Am I dead? Am I alive? I'm both!

[DrN]

I'm beginning to learn something i think!
'for every action there is an equal and opposite reaction'
so when someone jumps up they exert an equal 'force' downwards as they do going upwards, and the same for when they land again, so there would be no net gain of force in any direction. therefore the law F=ma means that the person accelerates a lot, because of their small mass, while the earth barely moves, due to its enormous mass. the two forces exerted on both the earth and the person must be the same (equal and opposite).
it would only work if something hit the earth that hadn't actually propelled itself from the surface beforehand, or maybe if something jumped but never landed?

[jai]

equal and opposite reaction. however the mass that you are pushing against and landing against is heavier than the mass of the air, hence the reason that you move upwards. so surely if every one stood on one small area of the earth, say england, and jumped then we might have some small effect on the earths trajectory?

yes, but.........

[qpan]

quote:Originally posted by fishytails

I'm beginning to learn something i think!
'for every action there is an equal and opposite reaction'
so when someone jumps up they exert an equal 'force' downwards as they do going upwards, and the same for when they land again, so there would be no net gain of force in any direction. therefore the law F=ma means that the person accelerates a lot, because of their small mass, while the earth barely moves, due to its enormous mass. the two forces exerted on both the earth and the person must be the same (equal and opposite).
it would only work if something hit the earth that hadn't actually propelled itself from the surface beforehand, or maybe if something jumped but never landed?

Yep- fishytails, your right. When we jump, we are exerting a force downwards on the Earth. As we are in the air, the Earth pulls us down and therefore, we exert a force on it pulling it up! When we finally land, we exert another force downwards on the Earth. The centre of gravity of the system containing the Earth and the people does not change while jumping, as when the people jump up the Earth moves slightly in the opposite direction. As the person moves back towards the Earth after jumping, the Earth also moves slightly closer to them.

Therefore, while the system would oscillate for a little while (in miniscule proportions) after jumping, the net effect of jumping would actually be zero (think of conservation of momentum - initial momentum = 0, then final momentum of system must be zero as there are no external forces).

So really, only external objects can affect the Earth's orbit in the long term.

"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe

[neilep (OP)]

What happens if we all climb a ladder and just fall a couple of feet without launching ourselves off in the first place ?

'Men are the same as women...just inside out !'

[tweener]

Climbing the ladder would still be exerting the same force as jumping, just much more slowly.

----
John - The Eternal Pessimist.