Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

How long would that lever have to be?

That is to say, how long a lever would be needed on Earth, to lift a sphere with the mass of Earth if a human of average size were to sit on the other side of the lever?

  • 1
    I'm pretty sure Archimedes was speaking metaphorically. From the standpoint of actual physics, this is not a well defined question, so there's really no meaningful answer to give. (I can reopen this if other people feel that there is a meaningful answer, or if you can make it more specific.) – David Z Feb 8 '11 at 21:51
  • While I understand that the quote was metaphorical, a long lever would reduce the amount of energy needed to lift an object, Would it not? To raise a sphere with the mass of Earth how long a lever would be needed such that a human of average strength could lift it? – Adam Feb 8 '11 at 21:59
  • That's much better :) I've reopened the question. – David Z Feb 8 '11 at 22:04
  • ""a long lever would reduce the amount of energy needed to lift an object, Would it not? "" Of course not! A lever will neither creat nor destroy energy. What he does, is reducing the force by the levers ratio, but at the same time multiplying the way to move by the same factor. – Georg Feb 8 '11 at 22:44
  • @Georg: yes, the work you have to do is the same, but you can spread it over very long time. – gigacyan Feb 8 '11 at 22:48
up vote 8 down vote accepted

The mass of Earth is $6\times10^{24}kg$. If Archimedes can lift 60 kg, he would need a lever with an arm ratio of $10^{23}:1$. So if the short arm is one meter long, the lever length will be $10^{23}$ meters plus one. Also, note that he would have to push the lever for $10^{20}$ meters to shift the Earth just by one millimeter.

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    You are off by a factor of two for a cute reason. If the weight weighed as much as Earth, Earth would get pushed down as much as the weight would go up. – Mark Eichenlaub Feb 8 '11 at 22:19
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    I'd prefer a lever with 10⁻23 meters and 1 meter :=) Hopefully Adam has understood that the length is irrelevant, only ratio of the ends counts. – Georg Feb 8 '11 at 22:19
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    @Mark: at these orders of magnitude it is excusable to be wrong by a factor of 2 :) – gigacyan Feb 8 '11 at 22:26
  • @Giga I agree. I just thought it was a nice point to include in terms of physics. – Mark Eichenlaub Feb 8 '11 at 22:29
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    This calculation is straight forward, but it caries an implicit assumption that the whole Earth lies "near the Earth's surface" as that is the condition needed to use the usual value of $g$. – dmckee Feb 9 '11 at 0:27

In addition to @gigacyan answer: length of the lever, as he said, $10^{23}$ meters or 10 million light years. For comparison - Andromeda Galaxy is the nearest spiral galaxy to the Milky Way approximately 2.5 million light-years away. It takes 10 thousand years to push the lever for $10^{20}$ meters at the speed of light.

Technically any leaver that lifts an object away from the earth also lifts the earth away from said object.

The amount needed to lift the Earth is negligible. Move the lever a modest amount 3 or 4 feet and the Earth would be moved the equivalent of an electron; not much but still moved.

protected by Qmechanic Jan 3 '13 at 20:17

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