# Levers and torque

## Homework Statement

given a lever and a place to stand, Archimedes claimed to be able to move the earth. amusing he could use the moon as a privet point, how long would the lever have to be? (the earth moon distance is 382000km

## Homework Equations

toque = (force)(lever arm)
toque =I cross alpha

## The Attempt at a Solution

i cant get my head round this at all, this is my "logic":
If Archimedes had somewhere to stand (outside the earth) then his acceleration/force he exerts could be anything depending on the mass of the body on which he is standing. In addition due to the earth and the sun being in essentially equilibrium would any small force from an external reference frame to the Earth move it albeit very slightly?

Any pointers as to the thought process i need to solve this would be of great help!

Many thanks
Ryan

toque =I cross alpha

Is this the equation of the torque ??

The equation is
t= F cross R = F × R sin(alpha);

So ,
How to solve it and get the required torque ??
I think that is not your intended question when you post this thread
(:

In addition due to the earth and the sun being in essentially equilibrium would any small force from an external reference frame to the Earth move it albeit very slightly?

I think that this force is very small that has no impact on the equilibrium of earth-sum system , [since m1 is very small according to the general low of gravity ] and , consequently , F is negligible .
However , I'm not very sure ,,!

If Archimedes had somewhere to stand (outside the earth) then his acceleration/force he exerts could be anything depending on the mass of the body on which he is standing

Sorry if I may not get your point ,, That maybe because my English ,,

I think that the force will be the force of gravitation between two bodies [Newton general law of gravitation] OR it could be the gravitational force due to the gravity of moon
[ if he will stand on the moon ] What other forces do you mean ?? ,,

I dont what the force is that's my point he cant stand on the moon since that is the pivot point, since we do not know where he is standing how can we know the force that he can exert on the lever to try and move the Earth..

Thanks :)

Doc Al
Mentor
I dont what the force is that's my point he cant stand on the moon since that is the pivot point, since we do not know where he is standing how can we know the force that he can exert on the lever to try and move the Earth..
You need not know the force. For the sake of this problem (admittedly not a very realistic one!), why not assume that everything (the Earth and Archimedes) is under the influence of the same gravitational field. (Field, not force.) Just to see what you'd get for a lever arm.

haruspex
Homework Helper
Gold Member
I'm not too sure what answer is expected, but I would argue that he doesn't even need a lever. If I jump in the air the Earth moves, though not very much. If he has to do it using a lever, and the moon as the pivot point, that does set a certain constraint on the lever length.

Also, merely having a pivot point is not enough - he also needs some way to generate a reaction. He listed "a place to stand", but strictly speaking that is only going to help if he is going to push upwards (whatever that means). I assume Doc Al is thinking in terms of setting Mr A, the moon and the Earth all on the surface of some giant planet, and the lever being used to raise the Earth in that gravitational field. The force then comes from A's weight, and he should have said "a highly attractive place to stand". But moving need not consist of lifting.

CWatters