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#1
01-15-2011, 10:55 PM
 duffer Guest Join Date: Dec 2003
Newton's 3rd law of motion. Is this true?

No idea where I read this. Nor even if it was online or in print. The statement was that even with the astronomical difference in mass, when a person jumps the Earth moves a distance "downward". Of course, the amount of movement is immeasurable for practical purposes, but it happens nonetheless. Is this true? It makes sense but want some verification.
#2
01-15-2011, 10:58 PM
 friedo Charter Member Join Date: May 2000 Location: Brooklyn Posts: 19,254
Yes, it's true. Additionally, when the person falls back down, the Earth falls a little bit up. The force exerted by jumping, and subsequently by gravity, acts equally on the person and the planet. The difference in total distance traveled is due to the Earth's rather larger mass.
#3
01-15-2011, 11:06 PM
 Crazyhorse Guest Join Date: Sep 2008
Quote:
 Originally Posted by friedo The difference in total distance traveled is due to the Earth's rather larger mass.
According to Cecil the earth weighs "6 sextillion, 588 quintillion short tons." That's an awful lot - but with obesity on the rise we might need to rethink the wisdom of trampolines one day in the future.
#4
01-16-2011, 12:07 AM
 MikeS Charter Member Join Date: Oct 2001 Location: Williamstown, MA Posts: 3,043
Quote:
 Originally Posted by duffer The statement was that even with the astronomical difference in mass, when a person jumps the Earth moves a distance "downward". Of course, the amount of movement is immeasurable for practical purposes, but it happens nonetheless.
To put this in perspective, if you have a mass of 75 kg (a weight of about 165 lbs on Earth), and you jump 1 metre into the air, the Earth moves "downwards" by about 10-23 metres. This is several million times smaller than the size of an atom's nucleus.
#5
01-16-2011, 12:33 AM
 automagic Guest Join Date: Oct 2010
The entire earth does not actually move. A more accurate description is that the earth stretches and compresses when you jump. Imagine a punching bag. If you punch it hard it will move proportionality to how hard you hit it. It you only tap the punching bag it will only slightly lose its shape, but all the energy was transferred even though the entire punching bag did not actually move.

If the punching bag was a steel pipe instead then there is not much to compress and the pipe will probably move. If the earth was perfectly rigid, then the entire earth would move, by the calculated amount, proportional to how much you weigh and how high you jumped.
#6
01-16-2011, 12:39 AM
 The Second Stone Guest Join Date: May 2008
That is assuming ideal bodies. The people downstairs can feel me jump, and a seismograph next door can pick it up. But the most sensitive instruments ever invented can't distinguish me from the background noise the next county over, much less on the other side of the globe.

Last edited by The Second Stone; 01-16-2011 at 12:41 AM.
#7
01-16-2011, 01:08 AM
 fuzzypickles BANNED Join Date: Jul 2003 Location: The 11th Dimension Posts: 1,436
Quote:
 Originally Posted by The Second Stone But the most sensitive instruments ever invented can't distinguish me from the background noise the next county over, much less on the other side of the globe.
They can if you're a Seahawks fan.
#8
01-16-2011, 03:40 AM
 Peanuthead Guest Join Date: May 2002
Quote:
 Originally Posted by duffer No idea where I read this. Nor even if it was online or in print. The statement was that even with the astronomical difference in mass, when a person jumps the Earth moves a distance "downward". Of course, the amount of movement is immeasurable for practical purposes, but it happens nonetheless. Is this true? It makes sense but want some verification.
Uh-oh! I hope the Chinese aren't reading this.
#9
01-16-2011, 07:51 AM
 Napier Charter Member Join Date: Jan 2001 Location: Mid Atlantic, USA Posts: 7,175
Quote:
 Originally Posted by automagic The entire earth does not actually move. A more accurate description is that the earth stretches and compresses when you jump. Imagine a punching bag. If you punch it hard it will move proportionality to how hard you hit it. It you only tap the punching bag it will only slightly lose its shape, but all the energy was transferred even though the entire punching bag did not actually move. If the punching bag was a steel pipe instead then there is not much to compress and the pipe will probably move. If the earth was perfectly rigid, then the entire earth would move, by the calculated amount, proportional to how much you weigh and how high you jumped.
I think this is incorrect or at least misleading. The entire Earth DOES move, and it also stretches and compresses. How these effects combine at any particular location would be very difficult to figure out exactly, and I would guess there are locations that move the "wrong way", but still the center of mass of the Earth moves the right way and by the right amount as other posters are describing. For that matter, when you jump, you are doing quite a lot of stretching and compression yourself, and we can only speak to your center of gravity in directly answering the OP.
#10
01-16-2011, 08:11 AM
 Ronald C. Semone Member Join Date: Mar 2004 Posts: 1,404
Quote:
 Originally Posted by Peanuthead Uh-oh! I hope the Chinese aren't reading this.
Whatever happened to International Jump Day?
#11
01-16-2011, 08:11 AM
 runner pat Charter Member Join Date: Nov 2000 Location: Riding my handcycle Posts: 11,276
So when Chuck Norris does pushups, he really is pushing the Earth down.

*flees*
#12
01-16-2011, 11:24 AM
 CookingWithGas Charter Member Join Date: Mar 1999 Location: Tysons Corner VA Posts: 8,983
The question has been answered but I thought I would add something. The earth and a person form a system with a center of mass. Barring external forces the center of mass doesn't move. So if you jump, the force you exert on the earth to jump causes the earth to move exactly enough to keep the center of mass in the same place.

On a grander scale the moon and the earth form such a system and the orbit of the moon around the earth causes the earth to wobble a little such that the center of gravity of the system stays in the same place.

(A discussion of what "same place" means is likely to ensue since there is no absolute reference point, but try not to think about that too hard in this context.)
#13
01-16-2011, 12:12 PM
 JWT Kottekoe Guest Join Date: Apr 2003
Quote:
 Originally Posted by automagic The entire earth does not actually move.
I'm glad auotmagic pointed this out. Yes, the center of gravity does move exactly as described, but most of this is due to the local compression of the earth (or whatever structure you are jumping from). This local mass is moved toward the center of the earth, shifting the center of gravity of the earth in the opposite direction to the the motion of the jumper.

Another anology would be a trampoline. When you jump, the trampoline mat moves in the other direction. Some, but not all of the momentum gets tranfered to the floor of the gymnasium. Some, but not all of that gets transfered to the gymansium's foundation, etc. Analyzing exactly what moves and by how much is a complex mechanical problem. Only if the earth were completely rigid, would the center of the earth move anywhere near as much as the center of gravity of the earth.
#14
01-16-2011, 01:35 PM
 TriPolar Member Join Date: Oct 2007 Location: rhode island Posts: 19,740
Could someone clear up the CG matter? Does the CG of the system, you and the earth remain the same or change?

Another question, forces can be vectored, so does the earth actually have to move at all? Can't the forces be directed into opposite directions that eliminate any global movement?
#15
01-16-2011, 02:07 PM
 Chronos Charter Member Join Date: Jan 2000 Location: The Land of Cleves Posts: 47,932
Quote:
 Could someone clear up the CG matter? Does the CG of the system, you and the earth remain the same or change?
The center of gravity of a closed system can never change. In fact, this is one way of describing Newton's Third Law.

Quote:
 Another question, forces can be vectored, so does the earth actually have to move at all? Can't the forces be directed into opposite directions that eliminate any global movement?
The fact that force is a vector is precisely why this is impossible. Energy is a scalar, not a vector, and so energy can be redirected in a different direction, but the direction of a force is inherent to it.
#16
01-16-2011, 03:03 PM
 TriPolar Member Join Date: Oct 2007 Location: rhode island Posts: 19,740
Thanks. I need to do some studying to understand the second part about forces and vectors though.

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